Daily Papers

Model-based human pose estimation is currently approached through two different paradigms. Optimization-based methods fit a parametric body model to 2D observations in an iterative manner, leading to accurate image-model alignments, but are often slow and sensitive to the initialization. In contrast, regression-based methods, that use a deep network to directly estimate the model parameters from pixels, tend to provide reasonable, but not pixel accurate, results while requiring huge amounts of supervision. In this work, instead of investigating which approach is better, our key insight is that the two paradigms can form a strong collaboration. A reasonable, directly regressed estimate from the network can initialize the iterative optimization making the fitting faster and more accurate. Similarly, a pixel accurate fit from iterative optimization can act as strong supervision for the network. This is the core of our proposed approach SPIN (SMPL oPtimization IN the loop). The deep network initializes an iterative optimization routine that fits the body model to 2D joints within the training loop, and the fitted estimate is subsequently used to supervise the network. Our approach is self-improving by nature, since better network estimates can lead the optimization to better solutions, while more accurate optimization fits provide better supervision for the network. We demonstrate the effectiveness of our approach in different settings, where 3D ground truth is scarce, or not available, and we consistently outperform the state-of-the-art model-based pose estimation approaches by significant margins. The project website with videos, results, and code can be found at https://seas.upenn.edu/~nkolot/projects/spin.

Interactive digital agents (IDAs) leverage APIs of stateful digital environments to perform tasks in response to user requests. While IDAs powered by instruction-tuned large language models (LLMs) can react to feedback from interface invocations in multi-step exchanges, they have not been trained in their respective digital environments. Prior methods accomplish less than half of tasks in sophisticated benchmarks such as AppWorld. We present a reinforcement learning (RL) approach that trains IDAs directly in their target environments. We formalize this training as a partially observable Markov decision process and derive LOOP, a data- and memory-efficient variant of proximal policy optimization. LOOP uses no value network and maintains exactly one copy of the underlying LLM in memory, making its implementation straightforward and as memory-efficient as fine-tuning a single LLM. A 32-billion-parameter agent trained with LOOP in the AppWorld environment outperforms the much larger OpenAI o1 agent by 9 percentage points (15% relative). To our knowledge, this is the first reported application of RL to IDAs that interact with a stateful, multi-domain, multi-app environment via direct API calls. Our analysis sheds light on the effectiveness of RL in this area, showing that the agent learns to consult the API documentation, avoid unwarranted assumptions, minimize confabulation, and recover from setbacks.

With the advent of large language models (LLMs) like GPT-3, a natural question is the extent to which these models can be utilized for source code optimization. This paper presents methodologically stringent case studies applied to well-known open source python libraries pillow and numpy. We find that contemporary LLM ChatGPT-4 (state September and October 2023) is surprisingly adept at optimizing energy and compute efficiency. However, this is only the case in interactive use, with a human expert in the loop. Aware of experimenter bias, we document our qualitative approach in detail, and provide transcript and source code. We start by providing a detailed description of our approach in conversing with the LLM to optimize the _getextrema function in the pillow library, and a quantitative evaluation of the performance improvement. To demonstrate qualitative replicability, we report further attempts on another locus in the pillow library, and one code locus in the numpy library, to demonstrate generalization within and beyond a library. In all attempts, the performance improvement is significant (factor up to 38). We have also not omitted reporting of failed attempts (there were none). We conclude that LLMs are a promising tool for code optimization in open source libraries, but that the human expert in the loop is essential for success. Nonetheless, we were surprised by how few iterations were required to achieve substantial performance improvements that were not obvious to the expert in the loop. We would like bring attention to the qualitative nature of this study, more robust quantitative studies would need to introduce a layer of selecting experts in a representative sample -- we invite the community to collaborate.

This paper explores the effects of various forms of regularization in the context of language model alignment via self-play. While both reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) require to collect costly human-annotated pairwise preferences, the self-play fine-tuning (SPIN) approach replaces the rejected answers by data generated from the previous iterate. However, the SPIN method presents a performance instability issue in the learning phase, which can be mitigated by playing against a mixture of the two previous iterates. In the same vein, we propose in this work to address this issue from two perspectives: first, by incorporating an additional Kullback-Leibler (KL) regularization to stay at the proximity of the reference policy; second, by using the idea of fictitious play which smoothens the opponent policy across all previous iterations. In particular, we show that the KL-based regularizer boils down to replacing the previous policy by its geometric mixture with the base policy inside of the SPIN loss function. We finally discuss empirical results on MT-Bench as well as on the Hugging Face Open LLM Leaderboard.

Post-training quantization (PTQ) techniques applied to weights, activations, and the KV cache greatly reduce memory usage, latency, and power consumption of Large Language Models (LLMs), but may lead to large quantization errors when outliers are present. Recent findings suggest that rotating activation or weight matrices helps remove outliers and benefits quantization. In this work, we identify a collection of applicable rotation parameterizations that lead to identical outputs in full-precision Transformer architectures, and find that some random rotations lead to much better quantization than others, with an up to 13 points difference in downstream zero-shot reasoning performance. As a result, we propose SpinQuant that optimizes (or learns) the rotation matrices with Cayley optimization on a small validation set. With 4-bit quantization of weight, activation, and KV-cache, SpinQuant narrows the accuracy gap on zero-shot reasoning tasks with full precision to merely 2.9 points on the LLaMA-2 7B model, surpassing LLM-QAT by 19.1 points and SmoothQuant by 25.0 points. SpinQuant also outperforms concurrent work QuaRot, which applies random rotations to remove outliers. In particular, for LLaMA-2 7B/LLaMA-3 8B models that are hard to quantize, SpinQuant reduces the gap to full precision by 30.2%/34.1% relative to QuaRot.

Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.

Advanced compiler technology is crucial for enabling machine learning applications to run on novel hardware, but traditional compilers fail to deliver performance, popular auto-tuners have long search times and expert-optimized libraries introduce unsustainable costs. To address this, we developed LoopTune, a deep reinforcement learning compiler that optimizes tensor computations in deep learning models for the CPU. LoopTune optimizes tensor traversal order while using the ultra-fast lightweight code generator LoopNest to perform hardware-specific optimizations. With a novel graph-based representation and action space, LoopTune speeds up LoopNest by 3.2x, generating an order of magnitude faster code than TVM, 2.8x faster than MetaSchedule, and 1.08x faster than AutoTVM, consistently performing at the level of the hand-tuned library Numpy. Moreover, LoopTune tunes code in order of seconds.

Even after fine-tuning and reinforcement learning, large language models (LLMs) can be difficult, if not impossible, to control reliably with prompts alone. We propose a new inference-time approach to enforcing syntactic and semantic constraints on the outputs of LLMs, called sequential Monte Carlo (SMC) steering. The key idea is to specify language generation tasks as posterior inference problems in a class of discrete probabilistic sequence models, and replace standard decoding with sequential Monte Carlo inference. For a computational cost similar to that of beam search, SMC can steer LLMs to solve diverse tasks, including infilling, generation under syntactic constraints, and prompt intersection. To facilitate experimentation with SMC steering, we present a probabilistic programming library, LLaMPPL (https://github.com/probcomp/hfppl), for concisely specifying new generation tasks as language model probabilistic programs, and automating steering of LLaMA-family Transformers.

Resource scheduling and allocation is a critical component of many high impact systems ranging from congestion control to cloud computing. Finding more optimal solutions to these problems often has significant impact on resource and time savings, reducing device wear-and-tear, and even potentially improving carbon emissions. In this paper, we focus on a specific instance of a scheduling problem, namely the memory mapping problem that occurs during compilation of machine learning programs: That is, mapping tensors to different memory layers to optimize execution time. We introduce an approach for solving the memory mapping problem using Reinforcement Learning. RL is a solution paradigm well-suited for sequential decision making problems that are amenable to planning, and combinatorial search spaces with high-dimensional data inputs. We formulate the problem as a single-player game, which we call the mallocGame, such that high-reward trajectories of the game correspond to efficient memory mappings on the target hardware. We also introduce a Reinforcement Learning agent, mallocMuZero, and show that it is capable of playing this game to discover new and improved memory mapping solutions that lead to faster execution times on real ML workloads on ML accelerators. We compare the performance of mallocMuZero to the default solver used by the Accelerated Linear Algebra (XLA) compiler on a benchmark of realistic ML workloads. In addition, we show that mallocMuZero is capable of improving the execution time of the recently published AlphaTensor matrix multiplication model.

Optimizer states are a major source of memory consumption for training neural networks, limiting the maximum trainable model within given memory budget. Compressing the optimizer states from 32-bit floating points to lower bitwidth is promising to reduce the training memory footprint, while the current lowest achievable bitwidth is 8-bit. In this work, we push optimizer states bitwidth down to 4-bit through a detailed empirical analysis of first and second moments. Specifically, we find that moments have complicated outlier patterns, that current block-wise quantization cannot accurately approximate. We use a smaller block size and propose to utilize both row-wise and column-wise information for better quantization. We further identify a zero point problem of quantizing the second moment, and solve this problem with a linear quantizer that excludes the zero point. Our 4-bit optimizers are evaluated on a wide variety of benchmarks including natural language understanding, machine translation, image classification, and instruction tuning. On all the tasks our optimizers can achieve comparable accuracy with their full-precision counterparts, while enjoying better memory efficiency.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

High-performance sparse matrix-matrix (SpMM) multiplication is paramount for science and industry, as the ever-increasing sizes of data prohibit using dense data structures. Yet, existing hardware, such as Tensor Cores (TC), is ill-suited for SpMM, as it imposes strict constraints on data structures that cannot be met by unstructured sparsity found in many applications. To address this, we introduce (S)parse (Ma)trix Matrix (T)ensor Core-accelerated (SMaT): a novel SpMM library that utilizes TCs for unstructured sparse matrices. Our block-sparse library leverages the low-level CUDA MMA (matrix-matrix-accumulate) API, maximizing the performance offered by modern GPUs. Algorithmic optimizations such as sparse matrix permutation further improve performance by minimizing the number of non-zero blocks. The evaluation on NVIDIA A100 shows that SMaT outperforms SotA libraries (DASP, cuSPARSE, and Magicube) by up to 125x (on average 2.6x). SMaT can be used to accelerate many workloads in scientific computing, large-model training, inference, and others.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

Despite recent advancements, most computational methods for molecule optimization are constrained to single- or double-property optimization tasks and suffer from poor scalability and generalizability to novel optimization tasks. Meanwhile, Large Language Models (LLMs) demonstrate remarkable out-of-domain generalizability to novel tasks. To demonstrate LLMs' potential for molecule optimization, we introduce MoMUInstruct, the first high-quality instruction-tuning dataset specifically focused on complex multi-property molecule optimization tasks. Leveraging MoMUInstruct, we develop GeLLM^3Os, a series of instruction-tuned LLMs for molecule optimization. Extensive evaluations across 5 in-domain and 5 out-of-domain tasks demonstrate that GeLLM^3Os consistently outperform state-of-the-art baselines. GeLLM^3Os also exhibit outstanding zero-shot generalization to unseen tasks, significantly outperforming powerful closed-source LLMs. Such strong generalizability demonstrates the tremendous potential of GeLLM^3Os as foundational models for molecule optimization, thereby tackling novel optimization tasks without resource-intensive retraining. MoMUInstruct, models, and code are accessible through https://github.com/ninglab/GeLLMO.

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.

Creating high-quality data for training robust language-instructed agents is a long-lasting challenge in embodied AI. In this paper, we introduce a Self-Refining Data Flywheel (SRDF) that generates high-quality and large-scale navigational instruction-trajectory pairs by iteratively refining the data pool through the collaboration between two models, the instruction generator and the navigator, without any human-in-the-loop annotation. Specifically, SRDF starts with using a base generator to create an initial data pool for training a base navigator, followed by applying the trained navigator to filter the data pool. This leads to higher-fidelity data to train a better generator, which can, in turn, produce higher-quality data for training the next-round navigator. Such a flywheel establishes a data self-refining process, yielding a continuously improved and highly effective dataset for large-scale language-guided navigation learning. Our experiments demonstrate that after several flywheel rounds, the navigator elevates the performance boundary from 70% to 78% SPL on the classic R2R test set, surpassing human performance (76%) for the first time. Meanwhile, this process results in a superior generator, evidenced by a SPICE increase from 23.5 to 26.2, better than all previous VLN instruction generation methods. Finally, we demonstrate the scalability of our method through increasing environment and instruction diversity, and the generalization ability of our pre-trained navigator across various downstream navigation tasks, surpassing state-of-the-art methods by a large margin in all cases.

We introduce a novel paradigm in compiler optimization powered by Large Language Models with compiler feedback to optimize the code size of LLVM assembly. The model takes unoptimized LLVM IR as input and produces optimized IR, the best optimization passes, and instruction counts of both unoptimized and optimized IRs. Then we compile the input with generated optimization passes and evaluate if the predicted instruction count is correct, generated IR is compilable, and corresponds to compiled code. We provide this feedback back to LLM and give it another chance to optimize code. This approach adds an extra 0.53% improvement over -Oz to the original model. Even though, adding more information with feedback seems intuitive, simple sampling techniques achieve much higher performance given 10 or more samples.

We explore the novel application of Large Language Models to code optimization. We present a 7B-parameter transformer model trained from scratch to optimize LLVM assembly for code size. The model takes as input unoptimized assembly and outputs a list of compiler options to best optimize the program. Crucially, during training, we ask the model to predict the instruction counts before and after optimization, and the optimized code itself. These auxiliary learning tasks significantly improve the optimization performance of the model and improve the model's depth of understanding. We evaluate on a large suite of test programs. Our approach achieves a 3.0% improvement in reducing instruction counts over the compiler, outperforming two state-of-the-art baselines that require thousands of compilations. Furthermore, the model shows surprisingly strong code reasoning abilities, generating compilable code 91% of the time and perfectly emulating the output of the compiler 70% of the time.

Model-based reinforcement learning (MBRL) is a sample efficient technique to obtain control policies, yet unavoidable modeling errors often lead performance deterioration. The model in MBRL is often solely fitted to reconstruct dynamics, state observations in particular, while the impact of model error on the policy is not captured by the training objective. This leads to a mismatch between the intended goal of MBRL, enabling good policy and value learning, and the target of the loss function employed in practice, future state prediction. Naive intuition would suggest that value-aware model learning would fix this problem and, indeed, several solutions to this objective mismatch problem have been proposed based on theoretical analysis. However, they tend to be inferior in practice to commonly used maximum likelihood (MLE) based approaches. In this paper we propose the Value-gradient weighted Model Learning (VaGraM), a novel method for value-aware model learning which improves the performance of MBRL in challenging settings, such as small model capacity and the presence of distracting state dimensions. We analyze both MLE and value-aware approaches and demonstrate how they fail to account for exploration and the behavior of function approximation when learning value-aware models and highlight the additional goals that must be met to stabilize optimization in the deep learning setting. We verify our analysis by showing that our loss function is able to achieve high returns on the Mujoco benchmark suite while being more robust than maximum likelihood based approaches.

Code optimization is a daunting task that requires a significant level of expertise from experienced programmers. This level of expertise is not sufficient when compared to the rapid development of new hardware architectures. Towards advancing the whole code optimization process, recent approaches rely on machine learning and artificial intelligence techniques. This paper introduces a new framework to decrease the complexity of code optimization. The proposed framework builds on large language models (LLMs) and reinforcement learning (RL) and enables LLMs to receive feedback from their environment (i.e., unit tests) during the fine-tuning process. We compare our framework with existing state-of-the-art models and show that it is more efficient with respect to speed and computational usage, as a result of the decrement in training steps and its applicability to models with fewer parameters. Additionally, our framework reduces the possibility of logical and syntactical errors. Toward evaluating our approach, we run several experiments on the PIE dataset using a CodeT5 language model and RRHF, a new reinforcement learning algorithm. We adopt a variety of evaluation metrics with regards to optimization quality, and speedup. The evaluation results demonstrate that the proposed framework has similar results in comparison with existing models using shorter training times and smaller pre-trained models. In particular, we accomplish an increase of 5.6% and 2.2 over the baseline models concerning the %OP T and SP metrics.

As large language model (LLM) inference demands ever-greater resources, there is a rapid growing trend of using low-bit weights to shrink memory usage and boost inference efficiency. However, these low-bit LLMs introduce the need for mixed-precision matrix multiplication (mpGEMM), which is a crucial yet under-explored operation that involves multiplying lower-precision weights with higher-precision activations. Unfortunately, current hardware does not natively support mpGEMM, resulting in indirect and inefficient dequantization-based implementations. To address the mpGEMM requirements in low-bit LLMs, we explored the lookup table (LUT)-based approach for mpGEMM. However, a conventional LUT implementation falls short of its potential. To fully harness the power of LUT-based mpGEMM, we introduce LUT Tensor Core, a software-hardware co-design optimized for low-bit LLM inference. Specifically, we introduce software-based operator fusion and table symmetrization techniques to optimize table precompute and table storage, respectively. Then, LUT Tensor Core proposes the hardware design featuring an elongated tiling shape design to enhance table reuse and a bit-serial design to support various precision combinations in mpGEMM. Moreover, we design an end-to-end compilation stack with new instructions for LUT-based mpGEMM, enabling efficient LLM compilation and optimizations. The evaluation on low-bit LLMs (e.g., BitNet, LLAMA) shows that LUT Tensor Core achieves more than a magnitude of improvements on both compute density and energy efficiency.

Recent research explores optimization using large language models (LLMs) by either iteratively seeking next-step solutions from LLMs or directly prompting LLMs for an optimizer. However, these approaches exhibit inherent limitations, including low operational efficiency, high sensitivity to prompt design, and a lack of domain-specific knowledge. We introduce LLaMoCo, the first instruction-tuning framework designed to adapt LLMs for solving optimization problems in a code-to-code manner. Specifically, we establish a comprehensive instruction set containing well-described problem prompts and effective optimization codes. We then develop a novel two-phase learning strategy that incorporates a contrastive learning-based warm-up procedure before the instruction-tuning phase to enhance the convergence behavior during model fine-tuning. The experiment results demonstrate that a CodeGen (350M) model fine-tuned by our LLaMoCo achieves superior optimization performance compared to GPT-4 Turbo and the other competitors across both synthetic and realistic problem sets. The fine-tuned model and the usage instructions are available at https://anonymous.4open.science/r/LLaMoCo-722A.

Optimizing scientific software is a difficult task because codebases are often large and complex, and performance can depend upon several factors including the algorithm, its implementation, and hardware among others. Causes of poor performance can originate from disparate sources and be difficult to diagnose. Recent years have seen a multitude of work that use large language models (LLMs) to assist in software development tasks. However, these tools are trained to model the distribution of code as text, and are not specifically designed to understand performance aspects of code. In this work, we introduce a reinforcement learning based methodology to align the outputs of code LLMs with performance. This allows us to build upon the current code modeling capabilities of LLMs and extend them to generate better performing code. We demonstrate that our fine-tuned model improves the expected speedup of generated code over base models for a set of benchmark tasks from 0.9 to 1.6 for serial code and 1.9 to 4.5 for OpenMP code.

Recently, large language models (LLMs) have demonstrated excellent performance in understanding human instructions and generating code, which has inspired researchers to explore the feasibility of generating RTL code with LLMs. However, the existing approaches to fine-tune LLMs on RTL codes typically are conducted on fixed datasets, which do not fully stimulate the capability of LLMs and require large amounts of reference data. To mitigate these issues , we introduce a simple yet effective iterative training paradigm named ITERTL. During each iteration, samples are drawn from the model trained in the previous cycle. Then these new samples are employed for training in this loop. Through this iterative approach, the distribution mismatch between the model and the training samples is reduced. Additionally, the model is thus enabled to explore a broader generative space and receive more comprehensive feedback. Theoretical analyses are conducted to investigate the mechanism of the effectiveness. Experimental results show the model trained through our proposed approach can compete with and even outperform the state-of-the-art (SOTA) open-source model with nearly 37\% reference samples, achieving remarkable 42.9\% and 62.2\% pass@1 rate on two VerilogEval evaluation datasets respectively. While using the same amount of reference samples, our method can achieved a relative improvement of 16.9\% and 12.5\% in pass@1 compared to the non-iterative method. This study facilitates the application of LLMs for generating RTL code in practical scenarios with limited data.

We introduce an optical tweezer platform for assembling and individually manipulating a two-dimensional register of nuclear spin qubits. Each nuclear spin qubit is encoded in the ground ^{1}S_{0} manifold of ^{87}Sr and is individually manipulated by site-selective addressing beams. We observe that spin relaxation is negligible after 5 seconds, indicating that T_1gg5 s. Furthermore, utilizing simultaneous manipulation of subsets of qubits, we demonstrate significant phase coherence over the entire register, estimating T_2^star = left(21pm7right) s and measuring T_2^echo=left(42pm6right) s.

Language Model Programs, i.e. sophisticated pipelines of modular language model (LM) calls, are increasingly advancing NLP tasks, but they require crafting prompts that are jointly effective for all modules. We study prompt optimization for LM programs, i.e. how to update these prompts to maximize a downstream metric without access to module-level labels or gradients. To make this tractable, we factorize our problem into optimizing the free-form instructions and few-shot demonstrations of every module and introduce several strategies to craft task-grounded instructions and navigate credit assignment across modules. Our strategies include (i) program- and data-aware techniques for proposing effective instructions, (ii) a stochastic mini-batch evaluation function for learning a surrogate model of our objective, and (iii) a meta-optimization procedure in which we refine how LMs construct proposals over time. Using these insights we develop MIPRO, a novel algorithm for optimizing LM programs. MIPRO outperforms baseline optimizers on five of seven diverse multi-stage LM programs using a best-in-class open-source model (Llama-3-8B), by as high as 13% accuracy. We have released our new optimizers and benchmark in DSPy at http://dspy.ai

Stateful optimizers maintain gradient statistics over time, e.g., the exponentially smoothed sum (SGD with momentum) or squared sum (Adam) of past gradient values. This state can be used to accelerate optimization compared to plain stochastic gradient descent but uses memory that might otherwise be allocated to model parameters, thereby limiting the maximum size of models trained in practice. In this paper, we develop the first optimizers that use 8-bit statistics while maintaining the performance levels of using 32-bit optimizer states. To overcome the resulting computational, quantization, and stability challenges, we develop block-wise dynamic quantization. Block-wise quantization divides input tensors into smaller blocks that are independently quantized. Each block is processed in parallel across cores, yielding faster optimization and high precision quantization. To maintain stability and performance, we combine block-wise quantization with two additional changes: (1) dynamic quantization, a form of non-linear optimization that is precise for both large and small magnitude values, and (2) a stable embedding layer to reduce gradient variance that comes from the highly non-uniform distribution of input tokens in language models. As a result, our 8-bit optimizers maintain 32-bit performance with a small fraction of the memory footprint on a range of tasks, including 1.5B parameter language modeling, GLUE finetuning, ImageNet classification, WMT'14 machine translation, MoCo v2 contrastive ImageNet pretraining+finetuning, and RoBERTa pretraining, without changes to the original optimizer hyperparameters. We open-source our 8-bit optimizers as a drop-in replacement that only requires a two-line code change.

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible solutions, and therefore valid Lagrangian dual bounds, for linear and nonlinear conic optimization problems. The paper introduces a systematic dual completion procedure, differentiable conic projection layers, and a self-supervised learning framework based on Lagrangian duality. It also provides closed-form dual completion formulae for broad classes of conic problems, which eliminate the need for costly implicit layers. The effectiveness of DLL is demonstrated on linear and nonlinear conic optimization problems. The proposed methodology significantly outperforms a state-of-the-art learning-based method, and achieves 1000x speedups over commercial interior-point solvers with optimality gaps under 0.5\% on average.

Logic synthesis, a pivotal stage in chip design, entails optimizing chip specifications encoded in hardware description languages like Verilog into highly efficient implementations using Boolean logic gates. The process involves a sequential application of logic minimization heuristics (``synthesis recipe"), with their arrangement significantly impacting crucial metrics such as area and delay. Addressing the challenge posed by the broad spectrum of design complexities - from variations of past designs (e.g., adders and multipliers) to entirely novel configurations (e.g., innovative processor instructions) - requires a nuanced `synthesis recipe` guided by human expertise and intuition. This study conducts a thorough examination of learning and search techniques for logic synthesis, unearthing a surprising revelation: pre-trained agents, when confronted with entirely novel designs, may veer off course, detrimentally affecting the search trajectory. We present ABC-RL, a meticulously tuned alpha parameter that adeptly adjusts recommendations from pre-trained agents during the search process. Computed based on similarity scores through nearest neighbor retrieval from the training dataset, ABC-RL yields superior synthesis recipes tailored for a wide array of hardware designs. Our findings showcase substantial enhancements in the Quality-of-result (QoR) of synthesized circuits, boasting improvements of up to 24.8% compared to state-of-the-art techniques. Furthermore, ABC-RL achieves an impressive up to 9x reduction in runtime (iso-QoR) when compared to current state-of-the-art methodologies.

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To automate problem formulation and solving, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of approach suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, the model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming, and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.

Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM kernels has been the pressure placed on DRAM memory. One approach to tackle this problem is to use an inner product method for the SpGEMM kernel implementation. While the inner product produces fewer intermediate results, it can end up saturating the memory bandwidth, given the high number of redundant fetches of the input matrix elements. Using an outer product-based SpGEMM kernel can reduce redundant fetches, but at the cost of increased overhead due to extra computation and memory accesses for producing/managing partial products. In this thesis, we introduce a novel SpGEMM kernel implementation based on the row-wise product approach. We leverage atomic instructions to merge intermediate partial products as they are generated. The use of atomic instructions eliminates the need to create partial product matrices. To evaluate our row-wise product approach, we map an optimized SpGEMM kernel to a custom accelerator designed to accelerate graph-based applications. The targeted accelerator is an experimental system named PIUMA, being developed by Intel. PIUMA provides several attractive features, including fast context switching, user-configurable caches, globally addressable memory, non-coherent caches, and asynchronous pipelines. We tailor our SpGEMM kernel to exploit many of the features of the PIUMA fabric. This thesis compares our SpGEMM implementation against prior solutions, all mapped to the PIUMA framework. We briefly describe some of the PIUMA architecture features and then delve into the details of our optimized SpGEMM kernel. Our SpGEMM kernel can achieve 9.4x speedup as compared to competing approaches.

RAG systems consist of multiple modules to work together. However, these modules are usually separately trained. We argue that a system like RAG that incorporates multiple modules should be jointly optimized to achieve optimal performance. To demonstrate this, we design a specific pipeline called SmartRAG that includes a policy network and a retriever. The policy network can serve as 1) a decision maker that decides when to retrieve, 2) a query rewriter to generate a query most suited to the retriever, and 3) an answer generator that produces the final response with/without the observations. We then propose to jointly optimize the whole system using a reinforcement learning algorithm, with the reward designed to encourage the system to achieve the best performance with minimal retrieval cost. When jointly optimized, all the modules can be aware of how other modules are working and thus find the best way to work together as a complete system. Empirical results demonstrate that the jointly optimized SmartRAG can achieve better performance than separately optimized counterparts.

We introduce CAMRL, the first curriculum-based asymmetric multi-task learning (AMTL) algorithm for dealing with multiple reinforcement learning (RL) tasks altogether. To mitigate the negative influence of customizing the one-off training order in curriculum-based AMTL, CAMRL switches its training mode between parallel single-task RL and asymmetric multi-task RL (MTRL), according to an indicator regarding the training time, the overall performance, and the performance gap among tasks. To leverage the multi-sourced prior knowledge flexibly and to reduce negative transfer in AMTL, we customize a composite loss with multiple differentiable ranking functions and optimize the loss through alternating optimization and the Frank-Wolfe algorithm. The uncertainty-based automatic adjustment of hyper-parameters is also applied to eliminate the need of laborious hyper-parameter analysis during optimization. By optimizing the composite loss, CAMRL predicts the next training task and continuously revisits the transfer matrix and network weights. We have conducted experiments on a wide range of benchmarks in multi-task RL, covering Gym-minigrid, Meta-world, Atari video games, vision-based PyBullet tasks, and RLBench, to show the improvements of CAMRL over the corresponding single-task RL algorithm and state-of-the-art MTRL algorithms. The code is available at: https://github.com/huanghanchi/CAMRL

Chemistry plays a crucial role in many domains, such as drug discovery and material science. While large language models (LLMs) such as GPT-4 exhibit remarkable capabilities on natural language processing tasks, existing work shows their performance on chemistry tasks is discouragingly low. In this paper, however, we demonstrate that our developed LLMs can achieve very strong results on a comprehensive set of chemistry tasks, outperforming the most advanced GPT-4 across all the tasks by a substantial margin and approaching the SoTA task-specific models. The key to our success is a large-scale, comprehensive, high-quality dataset for instruction tuning named SMolInstruct. It contains 14 meticulously selected chemistry tasks and over three million high-quality samples, laying a solid foundation for training and evaluating LLMs for chemistry. Based on SMolInstruct, we fine-tune a set of open-source LLMs, among which, we find that Mistral serves as the best base model for chemistry tasks. We further conduct analysis on the impact of trainable parameters, providing insights for future research.

We present the design, implementation and engineering experience in building and deploying MegaScale, a production system for training large language models (LLMs) at the scale of more than 10,000 GPUs. Training LLMs at this scale brings unprecedented challenges to training efficiency and stability. We take a full-stack approach that co-designs the algorithmic and system components across model block and optimizer design, computation and communication overlapping, operator optimization, data pipeline, and network performance tuning. Maintaining high efficiency throughout the training process (i.e., stability) is an important consideration in production given the long extent of LLM training jobs. Many hard stability issues only emerge at large scale, and in-depth observability is the key to address them. We develop a set of diagnosis tools to monitor system components and events deep in the stack, identify root causes, and derive effective techniques to achieve fault tolerance and mitigate stragglers. MegaScale achieves 55.2% Model FLOPs Utilization (MFU) when training a 175B LLM model on 12,288 GPUs, improving the MFU by 1.34x compared to Megatron-LM. We share our operational experience in identifying and fixing failures and stragglers. We hope by articulating the problems and sharing our experience from a systems perspective, this work can inspire future LLM systems research.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.

Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs' deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains unclear how to improve the thinking abilities of less powerful base models. In this work, we introduce S^2R, an efficient framework that enhances LLM reasoning by teaching models to self-verify and self-correct during inference. Specifically, we first initialize LLMs with iterative self-verification and self-correction behaviors through supervised fine-tuning on carefully curated data. The self-verification and self-correction skills are then further strengthened by both outcome-level and process-level reinforcement learning, with minimized resource requirements, enabling the model to adaptively refine its reasoning process during inference. Our results demonstrate that, with only 3.1k self-verifying and self-correcting behavior initialization samples, Qwen2.5-math-7B achieves an accuracy improvement from 51.0\% to 81.6\%, outperforming models trained on an equivalent amount of long-CoT distilled data. Extensive experiments and analysis based on three base models across both in-domain and out-of-domain benchmarks validate the effectiveness of S^2R. Our code and data are available at https://github.com/NineAbyss/S2R.

As synthetic data becomes higher quality and proliferates on the internet, machine learning models are increasingly trained on a mix of human- and machine-generated data. Despite the successful stories of using synthetic data for representation learning, using synthetic data for generative model training creates "self-consuming loops" which may lead to training instability or even collapse, unless certain conditions are met. Our paper aims to stabilize self-consuming generative model training. Our theoretical results demonstrate that by introducing an idealized correction function, which maps a data point to be more likely under the true data distribution, self-consuming loops can be made exponentially more stable. We then propose self-correction functions, which rely on expert knowledge (e.g. the laws of physics programmed in a simulator), and aim to approximate the idealized corrector automatically and at scale. We empirically validate the effectiveness of self-correcting self-consuming loops on the challenging human motion synthesis task, and observe that it successfully avoids model collapse, even when the ratio of synthetic data to real data is as high as 100%.

Finding the optimal pass sequence of compilation can lead to a significant reduction in program size and/or improvement in program efficiency. Prior works on compilation pass ordering have two major drawbacks. They either require an excessive budget (in terms of compilation steps) at compile time or fail to generalize to unseen programs. In this paper, for code-size reduction tasks, we propose a novel pipeline to find program-dependent pass sequences within 45 compilation calls. It first identifies a coreset of 50 pass sequences via greedy optimization of a submodular function, and then learns a policy with Graph Neural Network (GNN) to pick the optimal sequence by predicting the normalized values of the pass sequences in the coreset. Despite its simplicity, our pipeline outperforms the default -Oz flag by an average of 4.7% over a large collection (4683) of unseen code repositories from diverse domains across 14 datasets. In comparison, previous approaches like reinforcement learning on the raw pass sequence space may take days to train due to sparse reward, and may not generalize well in held-out ones from different domains. Our results demonstrate that existing human-designed compiler flags can be improved with a simple yet effective technique that transforms the raw action space into a small one with denser rewards.

Pipeline parallelism is one of the key components for large-scale distributed training, yet its efficiency suffers from pipeline bubbles which were deemed inevitable. In this work, we introduce a scheduling strategy that, to our knowledge, is the first to successfully achieve zero pipeline bubbles under synchronous training semantics. The key idea behind this improvement is to split the backward computation into two parts, one that computes gradient for the input and another that computes for the parameters. Based on this idea, we handcraft novel pipeline schedules that significantly outperform the baseline methods. We further develop an algorithm that automatically finds an optimal schedule based on specific model configuration and memory limit. Additionally, to truly achieve zero bubble, we introduce a novel technique to bypass synchronizations during the optimizer step. Experimental evaluations show that our method outperforms the 1F1B schedule up to 23% in throughput under a similar memory limit. This number can be further pushed to 31% when the memory constraint is relaxed. We believe our results mark a major step forward in harnessing the true potential of pipeline parallelism. We open sourced our implementation based on the popular Megatron-LM repository on https://github.com/sail-sg/zero-bubble-pipeline-parallelism.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

The emergence of quantum reinforcement learning (QRL) is propelled by advancements in quantum computing (QC) and machine learning (ML), particularly through quantum neural networks (QNN) built on variational quantum circuits (VQC). These advancements have proven successful in addressing sequential decision-making tasks. However, constructing effective QRL models demands significant expertise due to challenges in designing quantum circuit architectures, including data encoding and parameterized circuits, which profoundly influence model performance. In this paper, we propose addressing this challenge with differentiable quantum architecture search (DiffQAS), enabling trainable circuit parameters and structure weights using gradient-based optimization. Furthermore, we enhance training efficiency through asynchronous reinforcement learning (RL) methods facilitating parallel training. Through numerical simulations, we demonstrate that our proposed DiffQAS-QRL approach achieves performance comparable to manually-crafted circuit architectures across considered environments, showcasing stability across diverse scenarios. This methodology offers a pathway for designing QRL models without extensive quantum knowledge, ensuring robust performance and fostering broader application of QRL.

The ML community is rapidly exploring techniques for prompting language models (LMs) and for stacking them into pipelines that solve complex tasks. Unfortunately, existing LM pipelines are typically implemented using hard-coded "prompt templates", i.e. lengthy strings discovered via trial and error. Toward a more systematic approach for developing and optimizing LM pipelines, we introduce DSPy, a programming model that abstracts LM pipelines as text transformation graphs, i.e. imperative computational graphs where LMs are invoked through declarative modules. DSPy modules are parameterized, meaning they can learn (by creating and collecting demonstrations) how to apply compositions of prompting, finetuning, augmentation, and reasoning techniques. We design a compiler that will optimize any DSPy pipeline to maximize a given metric. We conduct two case studies, showing that succinct DSPy programs can express and optimize sophisticated LM pipelines that reason about math word problems, tackle multi-hop retrieval, answer complex questions, and control agent loops. Within minutes of compiling, a few lines of DSPy allow GPT-3.5 and llama2-13b-chat to self-bootstrap pipelines that outperform standard few-shot prompting (generally by over 25% and 65%, respectively) and pipelines with expert-created demonstrations (by up to 5-46% and 16-40%, respectively). On top of that, DSPy programs compiled to open and relatively small LMs like 770M-parameter T5 and llama2-13b-chat are competitive with approaches that rely on expert-written prompt chains for proprietary GPT-3.5. DSPy is available at https://github.com/stanfordnlp/dspy

In this study, we propose a simple method for fault-tolerant Strassen-like matrix multiplications. The proposed method is based on using two distinct Strassen-like algorithms instead of replicating a given one. We have realized that using two different algorithms, new check relations arise resulting in more local computations. These local computations are found using computer aided search. To improve performance, special parity (extra) sub-matrix multiplications (PSMMs) are generated (two of them) at the expense of increasing communication/computation cost of the system. Our preliminary results demonstrate that the proposed method outperforms a Strassen-like algorithm with two copies and secures a very close performance to three copy version using only 2 PSMMs, reducing the total number of compute nodes by around 24\% i.e., from 21 to 16.

The correctness of computations remains a significant challenge in computer science, with traditional approaches relying on automated testing or formal verification. Self-testing/correcting programs introduce an alternative paradigm, allowing a program to verify and correct its own outputs via randomized reductions, a concept that previously required manual derivation. In this paper, we present Bitween, a method and tool for automated learning of randomized (self)-reductions and program properties in numerical programs. Bitween combines symbolic analysis and machine learning, with a surprising finding: polynomial-time linear regression, a basic optimization method, is not only sufficient but also highly effective for deriving complex randomized self-reductions and program invariants, often outperforming sophisticated mixed-integer linear programming solvers. We establish a theoretical framework for learning these reductions and introduce RSR-Bench, a benchmark suite for evaluating Bitween's capabilities on scientific and machine learning functions. Our empirical results show that Bitween surpasses state-of-the-art tools in scalability, stability, and sample efficiency when evaluated on nonlinear invariant benchmarks like NLA-DigBench. Bitween is open-source as a Python package and accessible via a web interface that supports C language programs.

We present QuantumLLMInstruct (QLMMI), an innovative dataset featuring over 500,000 meticulously curated instruction-following problem-solution pairs designed specifically for quantum computing - the largest and most comprehensive dataset of its kind. Originating from over 90 primary seed domains and encompassing hundreds of subdomains autonomously generated by LLMs, QLMMI marks a transformative step in the diversity and richness of quantum computing datasets. Designed for instruction fine-tuning, QLMMI seeks to significantly improve LLM performance in addressing complex quantum computing challenges across a wide range of quantum physics topics. While Large Language Models (LLMs) have propelled advancements in computational science with datasets like Omni-MATH and OpenMathInstruct, these primarily target Olympiad-level mathematics, leaving quantum computing largely unexplored. The creation of QLMMI follows a rigorous four-stage methodology. Initially, foundational problems are developed using predefined templates, focusing on critical areas such as synthetic Hamiltonians, QASM code generation, Jordan-Wigner transformations, and Trotter-Suzuki quantum circuit decompositions. Next, detailed and domain-specific solutions are crafted to ensure accuracy and relevance. In the third stage, the dataset is enriched through advanced reasoning techniques, including Chain-of-Thought (CoT) and Task-Oriented Reasoning and Action (ToRA), which enhance problem-solution diversity while adhering to strict mathematical standards. Lastly, a zero-shot Judge LLM performs self-assessments to validate the dataset's quality and reliability, minimizing human oversight requirements.

LLM-based Automatic Prompt Optimization, which typically utilizes LLMs as Prompt Optimizers to self-reflect and refine prompts, has shown promising performance in recent studies. Despite the success, the underlying mechanism of this approach remains unexplored, and the true effectiveness of LLMs as Prompt Optimizers requires further validation. In this work, we conducted a comprehensive study to uncover the actual mechanism of LLM-based Prompt Optimization. Our findings reveal that the LLM optimizers struggle to identify the true causes of errors during reflection, tending to be biased by their own prior knowledge rather than genuinely reflecting on the errors. Furthermore, even when the reflection is semantically valid, the LLM optimizers often fail to generate appropriate prompts for the target models with a single prompt refinement step, partly due to the unpredictable behaviors of the target models. Based on the observations, we introduce a new "Automatic Behavior Optimization" paradigm, which directly optimizes the target model's behavior in a more controllable manner. We hope our study can inspire new directions for automatic prompt optimization development.

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning fields. The validity of existing works heavily rely on either a restrictive Lower- Level Strong Convexity (LLSC) condition or on solving a series of approximation subproblems with high accuracy or both. In this work, by averaging the upper and lower level objectives, we propose a single loop Bi-level Averaged Method of Multipliers (sl-BAMM) for BLO that is simple yet efficient for large-scale BLO and gets rid of the limited LLSC restriction. We further provide non-asymptotic convergence analysis of sl-BAMM towards KKT stationary points, and the comparative advantage of our analysis lies in the absence of strong gradient boundedness assumption, which is always required by others. Thus our theory safely captures a wider variety of applications in deep learning, especially where the upper-level objective is quadratic w.r.t. the lower-level variable. Experimental results demonstrate the superiority of our method.

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability.

Large Language Models (LLMs) have emerged as powerful tools for complex Operations Research (OR) in automating optimization modeling. However, current methodologies heavily rely on prompt engineering (e.g., multi-agent cooperation) with proprietary LLMs, raising data privacy concerns that could be prohibitive in industry applications. To tackle this issue, we propose training open-source LLMs for optimization modeling. We identify four critical requirements for the training dataset of OR LLMs, design and implement OR-Instruct, a semi-automated process for creating synthetic data tailored to specific requirements. We also introduce the IndustryOR benchmark, the first industrial benchmark for testing LLMs on solving real-world OR problems. We apply the data from OR-Instruct to various open-source LLMs of 7b size (termed as ORLMs), resulting in a significantly improved capability for optimization modeling. Our best-performing ORLM achieves state-of-the-art performance on the NL4OPT, MAMO, and IndustryOR benchmarks. Our code and data will be available at https://github.com/Cardinal-Operations/ORLM.

We present an approach to model-based RL that achieves a new state of the art performance on the challenging Craftax-classic benchmark, an open-world 2D survival game that requires agents to exhibit a wide range of general abilities -- such as strong generalization, deep exploration, and long-term reasoning. With a series of careful design choices aimed at improving sample efficiency, our MBRL algorithm achieves a reward of 67.4% after only 1M environment steps, significantly outperforming DreamerV3, which achieves 53.2%, and, for the first time, exceeds human performance of 65.0%. Our method starts by constructing a SOTA model-free baseline, using a novel policy architecture that combines CNNs and RNNs. We then add three improvements to the standard MBRL setup: (a) "Dyna with warmup", which trains the policy on real and imaginary data, (b) "nearest neighbor tokenizer" on image patches, which improves the scheme to create the transformer world model (TWM) inputs, and (c) "block teacher forcing", which allows the TWM to reason jointly about the future tokens of the next timestep.

In the realm of Large Language Models, the balance between instruction data quality and quantity has become a focal point. Recognizing this, we introduce a self-guided methodology for LLMs to autonomously discern and select cherry samples from vast open-source datasets, effectively minimizing manual curation and potential cost for instruction tuning an LLM. Our key innovation, the Instruction-Following Difficulty (IFD) metric, emerges as a pivotal tool to identify discrepancies between a model's expected responses and its autonomous generation prowess. Through the adept application of IFD, cherry samples are pinpointed, leading to a marked uptick in model training efficiency. Empirical validations on renowned datasets like Alpaca and WizardLM underpin our findings; with a mere 10% of conventional data input, our strategy showcases improved results. This synthesis of self-guided cherry-picking and the IFD metric signifies a transformative leap in the optimization of LLMs, promising both efficiency and resource-conscious advancements. Codes, data, and models are available: https://github.com/MingLiiii/Cherry_LLM

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice. The states forming the preconditioner and its inverse root restrict the maximum size of models trained by second-order optimizers. To address this, compressing 32-bit optimizer states to lower bitwidths has shown promise in reducing memory usage. However, current approaches only pertain to first-order optimizers. In this paper, we propose the first 4-bit second-order optimizers, exemplified by 4-bit Shampoo, maintaining performance similar to that of 32-bit ones. We show that quantizing the eigenvector matrix of the preconditioner in 4-bit Shampoo is remarkably better than quantizing the preconditioner itself both theoretically and experimentally. By rectifying the orthogonality of the quantized eigenvector matrix, we enhance the approximation of the preconditioner's eigenvector matrix, which also benefits the computation of its inverse 4-th root. Besides, we find that linear square quantization slightly outperforms dynamic tree quantization when quantizing second-order optimizer states. Evaluation on various networks for image classification demonstrates that our 4-bit Shampoo achieves comparable test accuracy to its 32-bit counterpart while being more memory-efficient. The source code will be made available.

Recent years have seen considerable advancements in multi-step reasoning with Large Language Models (LLMs). The previous studies have elucidated the merits of integrating feedback or search mechanisms during model inference to improve the reasoning accuracy. The Process-Supervised Reward Model (PRM), typically furnishes LLMs with step-by-step feedback during the training phase, akin to Proximal Policy Optimization (PPO) or reject sampling. Our objective is to examine the efficacy of PRM in the inference phase to help discern the optimal solution paths for multi-step tasks such as mathematical reasoning and code generation. To this end, we propose a heuristic greedy search algorithm that employs the step-level feedback from PRM to optimize the reasoning pathways explored by LLMs. This tailored PRM demonstrated enhanced results compared to the Chain of Thought (CoT) on mathematical benchmarks like GSM8K and MATH. Additionally, to explore the versatility of our approach, we develop a novel method to automatically generate step-level reward dataset for coding tasks and observed similar improved performance in the code generation tasks. Thus highlighting the robust nature of our reward-model-based approach to inference for reasoning tasks.

Vector similarity search presents significant challenges in terms of scalability for large and high-dimensional datasets, as well as in providing native support for hybrid queries. Serverless computing and cloud functions offer attractive benefits such as elasticity and cost-effectiveness, but are difficult to apply to data-intensive workloads. Jointly addressing these two main challenges, we present SQUASH, the first fully serverless vector search solution with rich support for hybrid queries. It features OSQ, an optimized and highly parallelizable quantization-based approach for vectors and attributes. Its segment-based storage mechanism enables significant compression in resource-constrained settings and offers efficient dimensional extraction operations. SQUASH performs a single distributed pass to guarantee the return of sufficiently many vectors satisfying the filter predicate, achieving high accuracy and avoiding redundant computation for vectors which fail the predicate. A multi-level search workflow is introduced to prune most vectors early to minimize the load on Function-as-a-Service (FaaS) instances. SQUASH is designed to identify and utilize retention of relevant data in re-used runtime containers, which eliminates redundant I/O and reduces costs. Finally, we demonstrate a new tree-based method for rapid FaaS invocation, enabling the bi-directional flow of data via request/response payloads. Experiments comparing SQUASH with state-of-the-art serverless vector search solutions and server-based baselines on vector search benchmarks confirm significant performance improvements at a lower cost.

This study examines the performance of finite spin quantum batteries (QBs) using Heisenberg spin models with Dzyaloshinsky-Moriya (DM) and Kaplan--Shekhtman--Entin-Wohlman--Aharony (KSEA) interactions. The QBs are modeled as interacting quantum spins in local inhomogeneous magnetic fields, inducing variable Zeeman splitting. We derive analytical expressions for the maximal extractable work, ergotropy and the capacity of QBs, as recently examined by Yang et al. [Phys. Rev. Lett. 131, 030402 (2023)]. These quantities are analytically linked through certain quantum correlations, as posited in the aforementioned study. Different Heisenberg spin chain models exhibit distinct behaviors under varying conditions, emphasizing the importance of model selection for optimizing QB performance. In antiferromagnetic (AFM) systems, maximum ergotropy occurs with a Zeeman splitting field applied to either spin, while ferromagnetic (FM) systems benefit from a uniform Zeeman field. Temperature significantly impacts QB performance, with ergotropy in the AFM case being generally more robust against temperature increases compared to the FM case. Incorporating DM and KSEA couplings can significantly enhance the capacity and ergotropy extraction of QBs. However, there exists a threshold beyond which additional increases in these interactions cause a sharp decline in capacity and ergotropy. This behavior is influenced by temperature and quantum coherence, which signal the occurrence of a sudden phase transition. The resource theory of quantum coherence proposed by Baumgratz et al. [Phys. Rev. Lett. 113, 140401 (2014)] plays a crucial role in enhancing ergotropy and capacity. However, ergotropy is limited by both the system's capacity and the amount of coherence. These findings support the theoretical framework of spin-based QBs and may benefit future research on quantum energy storage devices.

Complex multi-step reasoning tasks, such as solving mathematical problems or generating code, remain a significant hurdle for even the most advanced large language models (LLMs). Verifying LLM outputs with an Outcome Reward Model (ORM) is a standard inference-time technique aimed at enhancing the reasoning performance of LLMs. However, this still proves insufficient for reasoning tasks with a lengthy or multi-hop reasoning chain, where the intermediate outcomes are neither properly rewarded nor penalized. Process supervision addresses this limitation by assigning intermediate rewards during the reasoning process. To date, the methods used to collect process supervision data have relied on either human annotation or per-step Monte Carlo estimation, both prohibitively expensive to scale, thus hindering the broad application of this technique. In response to this challenge, we propose a novel divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named OmegaPRM for the efficient collection of high-quality process supervision data. This algorithm swiftly identifies the first error in the Chain of Thought (CoT) with binary search and balances the positive and negative examples, thereby ensuring both efficiency and quality. As a result, we are able to collect over 1.5 million process supervision annotations to train a Process Reward Model (PRM). Utilizing this fully automated process supervision alongside the weighted self-consistency algorithm, we have enhanced the instruction tuned Gemini Pro model's math reasoning performance, achieving a 69.4\% success rate on the MATH benchmark, a 36\% relative improvement from the 51\% base model performance. Additionally, the entire process operates without any human intervention, making our method both financially and computationally cost-effective compared to existing methods.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called Moccasin with only O(n) integer variables, where n is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with O(n^2) Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today's PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented in JAX), and evaluate on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 19.8 billion tokens generated during the training in Lean, STP proves 26.3% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (61.7%, pass@3200), Proofnet-test (23.1%, pass@3200) and PutnamBench (8/644, pass@3200).

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global so(2,2) part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.

Recently, a wide range of memory-efficient LLM training algorithms have gained substantial popularity. These methods leverage the low-rank structure of gradients to project optimizer states into a subspace using projection matrix found by singular value decomposition (SVD). However, convergence of these algorithms is highly dependent on the update rules of their projection matrix. In this work, we provide the first convergence guarantee for arbitrary update rules of projection matrix. This guarantee is generally applicable to optimizers that can be analyzed with Hamiltonian Descent, including most common ones, such as LION, Adam. Inspired by our theoretical understanding, we propose Online Subspace Descent, a new family of subspace descent optimizer without SVD. Instead of updating the projection matrix with eigenvectors, Online Subspace Descent updates the projection matrix with online PCA. Online Subspace Descent is flexible and introduces only minimum overhead to training. We show that for the task of pretraining LLaMA models ranging from 60M to 7B parameters on the C4 dataset, Online Subspace Descent achieves lower perplexity and better downstream tasks performance than state-of-the-art low-rank training methods across different settings and narrows the gap with full-rank baselines.

A modified LAB algorithm is introduced in this paper. It builds upon the original LAB algorithm (Reddy et al. 2023), which is a socio-inspired algorithm that models competitive and learning behaviours within a group, establishing hierarchical roles. The proposed algorithm incorporates the roulette wheel approach and a reduction factor introducing inter-group competition and iteratively narrowing down the sample space. The algorithm is validated by solving the benchmark test problems from CEC 2005 and CEC 2017. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The algorithm exhibited improved and superior robustness as well as search space exploration capabilities. Furthermore, a Clustering-Based Search Space Reduction (C-SSR) method is proposed, making the algorithm capable to solve constrained problems. The C-SSR method enables the algorithm to identify clusters of feasible regions, satisfying the constraints and contributing to achieve the optimal solution. This method demonstrates its effectiveness as a potential alternative to traditional constraint handling techniques. The results obtained using the Modified LAB algorithm are then compared with those achieved by other recent metaheuristic algorithms.

During early optimization passes, compilers must make predictions for machine-dependent characteristics such as execution unit utilization, number of register spills, latency, throughput etc. to generate better code. Often a hand-written static/analytical hardware cost model is built into the compiler. However, the need for more sophisticated and varied predictions has become more pronounced with the development of deep learning compilers which need to optimize dataflow graphs. Such compilers usually employ a much higher level MLIR form as an IR representation before lowering to traditional LLVM-IR. A static/analytical cost model in such a scenario is cumbersome and error prone as the opcodes represent very high level algebraic/arithmetic operations. Hence, we develop a machine learning-based cost model for high-level MLIR which can predict different target variables of interest such as CPU/GPU/xPU utilization, instructions executed, register usage etc. By considering the incoming MLIR as a text input a la NLP models we can apply well-known techniques from modern NLP research to help predict hardware characteristics more accurately. We expect such precise ML-driven hardware cost models to guide our deep learning compiler in graph level optimizations around operator fusion, local memory allocation, kernel scheduling etc. as well as in many kernel-level optimizations such as loop interchange, LICM and unroll. We report early work-in -progress results of developing such models on high-level MLIR representing dataflow graphs emitted by Pytorch/Tensorflow-like frameworks as well as lower-level dialects like affine. We show that these models can provide reasonably good estimates with low error bounds for various hardware characteristics of interest and can be a go-to mechanism for hardware cost modelling in the future.

Large language models (LLMs) are notoriously memory-intensive during training, particularly with the popular AdamW optimizer. This memory burden necessitates using more or higher-end GPUs or reducing batch sizes, limiting training scalability and throughput. To address this, various memory-efficient optimizers have been proposed to reduce optimizer memory usage. However, they face critical challenges: (i) reliance on costly SVD operations; (ii) significant performance trade-offs compared to AdamW; and (iii) still substantial optimizer memory overhead to maintain competitive performance. In this work, we identify that AdamW's learning rate adaptation rule can be effectively coarsened as a structured learning rate update. Based on this insight, we propose Approximated Gradient Scaling for Memory-Efficient LLM Optimization (APOLLO), which approximates learning rate scaling using an auxiliary low-rank optimizer state based on pure random projection. This structured learning rate update rule makes APOLLO highly tolerant to further memory reductions while delivering comparable pre-training performance. Even its rank-1 variant, APOLLO-Mini, achieves superior pre-training performance compared to AdamW with SGD-level memory costs. Extensive experiments demonstrate that the APOLLO series performs on-par with or better than AdamW, while achieving greater memory savings by nearly eliminating the optimization states of AdamW. These savings provide significant system-level benefits: (1) Enhanced Throughput: 3x throughput on an 8xA100-80GB setup compared to AdamW by supporting 4x larger batch sizes. (2) Improved Model Scalability: Pre-training LLaMA-13B with naive DDP on A100-80GB GPUs without system-level optimizations. (3) Low-End GPU Friendly Pre-training: Pre-training LLaMA-7B on a single GPU using less than 12 GB of memory with weight quantization.

Large language models demonstrate remarkable capabilities across various domains, especially mathematics and logic reasoning. However, current evaluations overlook physics-based reasoning - a complex task requiring physics theorems and constraints. We present PhysReason, a 1,200-problem benchmark comprising knowledge-based (25%) and reasoning-based (75%) problems, where the latter are divided into three difficulty levels (easy, medium, hard). Notably, problems require an average of 8.1 solution steps, with hard requiring 15.6, reflecting the complexity of physics-based reasoning. We propose the Physics Solution Auto Scoring Framework, incorporating efficient answer-level and comprehensive step-level evaluations. Top-performing models like Deepseek-R1, Gemini-2.0-Flash-Thinking, and o3-mini-high achieve less than 60% on answer-level evaluation, with performance dropping from knowledge questions (75.11%) to hard problems (31.95%). Through step-level evaluation, we identified four key bottlenecks: Physics Theorem Application, Physics Process Understanding, Calculation, and Physics Condition Analysis. These findings position PhysReason as a novel and comprehensive benchmark for evaluating physics-based reasoning capabilities in large language models. Our code and data will be published at https:/dxzxy12138.github.io/PhysReason.

Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. The major learning paradigm is expert iteration, which necessitates a pre-defined dataset comprising numerous mathematical problems. In this process, LLMs attempt to prove problems within the dataset and iteratively refine their capabilities through self-training on the proofs they discover. We propose to use large scale LEAN problem datasets Lean-workbook for expert iteration with more than 20,000 CPU days. During expert iteration, we found log-linear trends between solved problem amount with proof length and CPU usage. We train a critic model to select relatively easy problems for policy models to make trials and guide the model to search for deeper proofs. InternLM2.5-StepProver achieves open-source state-of-the-art on MiniF2F, Lean-Workbook-Plus, ProofNet, and Putnam benchmarks. Specifically, it achieves a pass of 65.9% on the MiniF2F-test and proves (or disproves) 17.0% of problems in Lean-Workbook-Plus which shows a significant improvement compared to only 9.5% of problems proved when Lean-Workbook-Plus was released. We open-source our models and searched proofs at https://github.com/InternLM/InternLM-Math and https://huggingface.co/datasets/internlm/Lean-Workbook.

We demonstrate a coherent spin shuttle through a GaAs/AlGaAs quadruple-quantum-dot array. Starting with two electrons in a spin-singlet state in the first dot, we shuttle one electron over to either the second, third or fourth dot. We observe that the separated spin-singlet evolves periodically into the m=0 spin-triplet and back before it dephases due to nuclear spin noise. We attribute the time evolution to differences in the local Zeeman splitting between the respective dots. With the help of numerical simulations, we analyse and discuss the visibility of the singlet-triplet oscillations and connect it to the requirements for coherent spin shuttling in terms of the inter-dot tunnel coupling strength and rise time of the pulses. The distribution of entangled spin pairs through tunnel coupled structures may be of great utility for connecting distant qubit registers on a chip.

In this paper, we have studied the performance and role of local optimizers in quantum variational circuits. We studied the performance of the two most popular optimizers and compared their results with some popular classical machine learning algorithms. The classical algorithms we used in our study are support vector machine (SVM), gradient boosting (GB), and random forest (RF). These were compared with a variational quantum classifier (VQC) using two sets of local optimizers viz AQGD and COBYLA. For experimenting with VQC, IBM Quantum Experience and IBM Qiskit was used while for classical machine learning models, sci-kit learn was used. The results show that machine learning on noisy immediate scale quantum machines can produce comparable results as on classical machines. For our experiments, we have used a popular restaurant sentiment analysis dataset. The extracted features from this dataset and then after applying PCA reduced the feature set into 5 features. Quantum ML models were trained using 100 epochs and 150 epochs on using EfficientSU2 variational circuit. Overall, four Quantum ML models were trained and three Classical ML models were trained. The performance of the trained models was evaluated using standard evaluation measures viz, Accuracy, Precision, Recall, F-Score. In all the cases AQGD optimizer-based model with 100 Epochs performed better than all other models. It produced an accuracy of 77% and an F-Score of 0.785 which were highest across all the trained models.

Model quantification uses low bit-width values to represent the weight matrices of models, which is a promising approach to reduce both storage and computational overheads of deploying highly anticipated LLMs. However, existing quantization methods suffer severe performance degradation when the bit-width is extremely reduced, and thus focus on utilizing 4-bit or 8-bit values to quantize models. This paper boldly quantizes the weight matrices of LLMs to 1-bit, paving the way for the extremely low bit-width deployment of LLMs. For this target, we introduce a 1-bit quantization-aware training (QAT) framework named OneBit, including a novel 1-bit parameter representation method to better quantize LLMs as well as an effective parameter initialization method based on matrix decomposition to improve the convergence speed of the QAT framework. Sufficient experimental results indicate that OneBit achieves good performance (at least 83% of the non-quantized performance) with robust training processes when only using 1-bit weight matrices.

The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (ibm\_fez) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of approx0.37% and approx0.31%, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states |H_Lrangle and |T_Lrangle achieve fidelities of 0.8806pm0.0002 and 0.8665pm0.0003, respectively, which are both above the magic state distillation threshold. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as 0.8356pm0.0003. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.

Large Language Models (LLMs) are consistently improving at increasingly realistic software engineering (SE) tasks. In real-world software stacks, significant SE effort is spent developing foundational system software like the Linux kernel. Unlike application-level software, a systems codebase like Linux is multilingual (low-level C/Assembly/Bash/Rust); gigantic (>20 million lines); critical (impacting billions of devices worldwide), and highly concurrent (involving complex multi-threading). To evaluate if ML models are useful while developing such large-scale systems-level software, we introduce kGym (a platform) and kBench (a dataset). The kGym platform provides a SE environment for large-scale experiments on the Linux kernel, including compiling and running kernels in parallel across several virtual machines, detecting operations and crashes, inspecting logs, and querying and patching the code base. We use kGym to facilitate evaluation on kBench, a crash resolution benchmark drawn from real-world Linux kernel bugs. An example bug in kBench contains crashing stack traces, a bug-reproducer file, a developer-written fix, and other associated data. To understand current performance, we conduct baseline experiments by prompting LLMs to resolve Linux kernel crashes. Our initial evaluations reveal that the best performing LLM achieves 0.72% and 5.38% in the unassisted and assisted (i.e., buggy files disclosed to the model) settings, respectively. These results highlight the need for further research to enhance model performance in SE tasks. Improving performance on kBench requires models to master new learning skills, including understanding the cause of crashes and repairing faults, writing memory-safe and hardware-aware code, and understanding concurrency. As a result, this work opens up multiple avenues of research at the intersection of machine learning and systems software.

One of the challenges of quantizing a large language model (LLM) is the presence of outliers. Outliers often make uniform quantization schemes less effective, particularly in extreme cases such as 4-bit quantization. We introduce KurTail, a new post-training quantization (PTQ) scheme that leverages Kurtosis-based rotation to mitigate outliers in the activations of LLMs. Our method optimizes Kurtosis as a measure of tailedness. This approach enables the quantization of weights, activations, and the KV cache in 4 bits. We utilize layer-wise optimization, ensuring memory efficiency. KurTail outperforms existing quantization methods, offering a 13.3\% boost in MMLU accuracy and a 15.5\% drop in Wiki perplexity compared to QuaRot. It also outperforms SpinQuant with a 2.6\% MMLU gain and reduces perplexity by 2.9\%, all while reducing the training cost. For comparison, learning the rotation using SpinQuant for Llama3-70B requires at least four NVIDIA H100 80GB GPUs, whereas our method requires only a single GPU, making it a more accessible solution for consumer GPU.

Large language models~(LLMs) are instruction followers, but it can be challenging to find the best instruction for different situations, especially for black-box LLMs on which backpropagation is forbidden. Instead of directly optimizing the discrete instruction, we optimize a low-dimensional soft prompt applied to an open-source LLM to generate the instruction for the black-box LLM. On each iteration of the proposed method, which we call InstructZero, a soft prompt is converted into an instruction using the open-source LLM, which is then submitted to the black-box LLM for zero-shot evaluation, and the performance is sent to Bayesian optimization to produce new soft prompts improving the zero-shot performance. We evaluate InstructZero on different combinations of open-source LLMs and APIs including Vicuna and ChatGPT. Our results show that InstructZero outperforms SOTA auto-instruction methods across a variety of downstream tasks. Our code and data are publicly available at https://github.com/Lichang-Chen/InstructZero.

Well-designed prompts are crucial for enhancing Large language models' (LLMs) reasoning capabilities while aligning their outputs with task requirements across diverse domains. However, manually designed prompts require expertise and iterative experimentation. While existing prompt optimization methods aim to automate this process, they rely heavily on external references such as ground truth or by humans, limiting their applicability in real-world scenarios where such data is unavailable or costly to obtain. To address this, we propose Self-Supervised Prompt Optimization (SPO), a cost-efficient framework that discovers effective prompts for both closed and open-ended tasks without requiring external reference. Motivated by the observations that prompt quality manifests directly in LLM outputs and LLMs can effectively assess adherence to task requirements, we derive evaluation and optimization signals purely from output comparisons. Specifically, SPO selects superior prompts through pairwise output comparisons evaluated by an LLM evaluator, followed by an LLM optimizer that aligns outputs with task requirements. Extensive experiments demonstrate that SPO outperforms state-of-the-art prompt optimization methods, achieving comparable or superior results with significantly lower costs (e.g., 1.1% to 5.6% of existing methods) and fewer samples (e.g., three samples). The code is available at https://github.com/geekan/MetaGPT.

The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the underlying phases of complex systems such as spin-glasses. Regardless of the method used for detection, the intrinsic phase of a system exists whether or not replicas are considered. We introduce a single replica method of spin-glass phase detection using the field's variation experienced by each spin in a system configuration. This method focuses on a single replica with quenched random couplings. Each spin inevitably observes a different field from the others. Our results show that the mean and variance of fields named "Spontaneous Configurational Field" experienced by spins are suitable indicators to explore different ferromagnetic, paramagnetic, and mixed phases. To classify different phases of the system with defined indicators we have developed an algorithm based on machine learning to analyze the desired samples.

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.

Training models to effectively use test-time compute is crucial for improving the reasoning performance of LLMs. Current methods mostly do so via fine-tuning on search traces or running RL with 0/1 outcome reward, but do these approaches efficiently utilize test-time compute? Would these approaches continue to scale as the budget improves? In this paper, we try to answer these questions. We formalize the problem of optimizing test-time compute as a meta-reinforcement learning (RL) problem, which provides a principled perspective on spending test-time compute. This perspective enables us to view the long output stream from the LLM as consisting of several episodes run at test time and leads us to use a notion of cumulative regret over output tokens as a way to measure the efficacy of test-time compute. Akin to how RL algorithms can best tradeoff exploration and exploitation over training, minimizing cumulative regret would also provide the best balance between exploration and exploitation in the token stream. While we show that state-of-the-art models do not minimize regret, one can do so by maximizing a dense reward bonus in conjunction with the outcome 0/1 reward RL. This bonus is the ''progress'' made by each subsequent block in the output stream, quantified by the change in the likelihood of eventual success. Using these insights, we develop Meta Reinforcement Fine-Tuning, or MRT, a new class of fine-tuning methods for optimizing test-time compute. MRT leads to a 2-3x relative gain in performance and roughly a 1.5x gain in token efficiency for math reasoning compared to outcome-reward RL.

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that extract information about errors to enable error correction: as higher measurement weights require higher implementation costs and introduce more errors, it is important in code design to optimize measurement weight. This underlies the surging interest in quantum low-density parity-check (qLDPC) codes, the study of which has primarily focused on the asymptotic (large-code-limit) properties. In this work, we introduce a versatile and computationally efficient approach to stabilizer code weight reduction based on reinforcement learning (RL), which produces new low-weight codes that substantially outperform the state of the art in practically relevant parameter regimes, extending significantly beyond previously accessible small distances. For example, our approach demonstrates savings in physical qubit overhead compared to existing results by 1 to 2 orders of magnitude for weight 6 codes and brings the overhead into a feasible range for near-future experiments. We also investigate the interplay between code parameters using our RL framework, offering new insights into the potential efficiency and power of practically viable coding strategies. Overall, our results demonstrate how RL can effectively advance the crucial yet challenging problem of quantum code discovery and thereby facilitate a faster path to the practical implementation of fault-tolerant quantum technologies.

Matrix multiplication (MatMul) typically dominates the overall computational cost of large language models (LLMs). This cost only grows as LLMs scale to larger embedding dimensions and context lengths. In this work, we show that MatMul operations can be completely eliminated from LLMs while maintaining strong performance at billion-parameter scales. Our experiments show that our proposed MatMul-free models achieve performance on-par with state-of-the-art Transformers that require far more memory during inference at a scale up to at least 2.7B parameters. We investigate the scaling laws and find that the performance gap between our MatMul-free models and full precision Transformers narrows as the model size increases. We also provide a GPU-efficient implementation of this model which reduces memory usage by up to 61% over an unoptimized baseline during training. By utilizing an optimized kernel during inference, our model's memory consumption can be reduced by more than 10x compared to unoptimized models. To properly quantify the efficiency of our architecture, we build a custom hardware solution on an FPGA which exploits lightweight operations beyond what GPUs are capable of. We processed billion-parameter scale models at 13W beyond human readable throughput, moving LLMs closer to brain-like efficiency. This work not only shows how far LLMs can be stripped back while still performing effectively, but also points at the types of operations future accelerators should be optimized for in processing the next generation of lightweight LLMs. Our code implementation is available at https://github.com/ridgerchu/matmulfreellm.

Recent advances in 1-bit Large Language Models (LLMs), such as BitNet and BitNet b1.58, present a promising approach to enhancing the efficiency of LLMs in terms of speed and energy consumption. These developments also enable local LLM deployment across a broad range of devices. In this work, we introduce bitnet.cpp, a tailored software stack designed to unlock the full potential of 1-bit LLMs. Specifically, we develop a set of kernels to support fast and lossless inference of ternary BitNet b1.58 LLMs on CPUs. Extensive experiments demonstrate that bitnet.cpp achieves significant speedups, ranging from 2.37x to 6.17x on x86 CPUs and from 1.37x to 5.07x on ARM CPUs, across various model sizes. The code is available at https://github.com/microsoft/BitNet.

As the use of large language models (LLMs) for code generation becomes more prevalent in software development, it is critical to enhance both the efficiency and correctness of the generated code. Existing methods and models primarily focus on the correctness of LLM-generated code, ignoring efficiency. In this work, we present Effi-Code, an approach to enhancing code generation in LLMs that can improve both efficiency and correctness. We introduce a Self-Optimization process based on Overhead Profiling that leverages open-source LLMs to generate a high-quality dataset of correct and efficient code samples. This dataset is then used to fine-tune various LLMs. Our method involves the iterative refinement of generated code, guided by runtime performance metrics and correctness checks. Extensive experiments demonstrate that models fine-tuned on the Effi-Code show significant improvements in both code correctness and efficiency across task types. For example, the pass@1 of DeepSeek-Coder-6.7B-Instruct generated code increases from 43.3\% to 76.8\%, and the average execution time for the same correct tasks decreases by 30.5\%. Effi-Code offers a scalable and generalizable approach to improving code generation in AI systems, with potential applications in software development, algorithm design, and computational problem-solving. The source code of Effi-Code was released in https://github.com/huangd1999/Effi-Code.

Optimization is ubiquitous. While derivative-based algorithms have been powerful tools for various problems, the absence of gradient imposes challenges on many real-world applications. In this work, we propose Optimization by PROmpting (OPRO), a simple and effective approach to leverage large language models (LLMs) as optimizers, where the optimization task is described in natural language. In each optimization step, the LLM generates new solutions from the prompt that contains previously generated solutions with their values, then the new solutions are evaluated and added to the prompt for the next optimization step. We first showcase OPRO on linear regression and traveling salesman problems, then move on to prompt optimization where the goal is to find instructions that maximize the task accuracy. With a variety of LLMs, we demonstrate that the best prompts optimized by OPRO outperform human-designed prompts by up to 8% on GSM8K, and by up to 50% on Big-Bench Hard tasks.

In Large Language Model (LLM) development, Reinforcement Learning from Human Feedback (RLHF) is crucial for aligning models with human values and preferences. RLHF traditionally relies on the Kullback-Leibler (KL) divergence between the current policy and a frozen initial policy as a reference, which is added as a penalty in policy optimization algorithms like Proximal Policy Optimization (PPO). While this constraint prevents models from deviating too far from the initial checkpoint, it limits exploration of the reward landscape, reducing the model's ability to discover higher-quality solutions. As a result, policy optimization is often trapped in a narrow region of the parameter space, leading to suboptimal alignment and performance. This paper presents SALSA (Soup-based Alignment Learning for Stronger Adaptation), a novel approach designed to overcome these limitations by creating a more flexible and better located reference model through weight-space averaging of two independent supervised fine-tuned (SFT) models. This model soup allows for larger deviation in KL divergence and exploring a promising region of the solution space without sacrificing stability. By leveraging this more robust reference model, SALSA fosters better exploration, achieving higher rewards and improving model robustness, out-of-distribution generalization, and performance. We validate the effectiveness of SALSA through extensive experiments on popular open models (Llama2-7B, Mistral-7B, and Gemma-2B) across various benchmarks (MT-Bench, Arena-Hard, UltraFeedback), where it consistently surpasses PPO by fostering deeper exploration and achieving superior alignment in LLMs.

Code Large Language Models (Code LLMs) have demonstrated outstanding performance in code-related tasks. Several instruction tuning approaches have been proposed to boost the code generation performance of pre-trained Code LLMs. In this paper, we introduce a diverse instruction model (DolphCoder) with self-evaluating for code generation. It learns diverse instruction targets and combines a code evaluation objective to enhance its code generation ability. Our model achieves superior performance on the HumanEval and MBPP benchmarks, demonstrating new insights for future code instruction tuning work. Our key findings are: (1) Augmenting more diverse responses with distinct reasoning paths increases the code capability of LLMs. (2) Improving one's ability to evaluate the correctness of code solutions also enhances their ability to create it.

Code Language Models have been trained to generate accurate solutions, typically with no regard for runtime. On the other hand, previous works that explored execution optimisation have observed corresponding drops in functional correctness. To that end, we introduce Code-Optimise, a framework that incorporates both correctness (passed, failed) and runtime (quick, slow) as learning signals via self-generated preference data. Our framework is both lightweight and robust as it dynamically selects solutions to reduce overfitting while avoiding a reliance on larger models for learning signals. Code-Optimise achieves significant improvements in pass@k while decreasing the competitive baseline runtimes by an additional 6% for in-domain data and up to 3% for out-of-domain data. As a byproduct, the average length of the generated solutions is reduced by up to 48% on MBPP and 23% on HumanEval, resulting in faster and cheaper inference. The generated data and codebase will be open-sourced at www.open-source.link.

With the rapid evolution of large language models (LLM), reinforcement learning (RL) has emerged as a pivotal technique for code generation and optimization in various domains. This paper presents a systematic survey of the application of RL in code optimization and generation, highlighting its role in enhancing compiler optimization, resource allocation, and the development of frameworks and tools. Subsequent sections first delve into the intricate processes of compiler optimization, where RL algorithms are leveraged to improve efficiency and resource utilization. The discussion then progresses to the function of RL in resource allocation, emphasizing register allocation and system optimization. We also explore the burgeoning role of frameworks and tools in code generation, examining how RL can be integrated to bolster their capabilities. This survey aims to serve as a comprehensive resource for researchers and practitioners interested in harnessing the power of RL to advance code generation and optimization techniques.

Dynamic shape computations have become critical in modern machine learning workloads, especially in emerging large language models. The success of these models has driven demand for deploying them to a diverse set of backend environments. In this paper, we present Relax, a compiler abstraction for optimizing end-to-end dynamic machine learning workloads. Relax introduces first-class symbolic shape annotations to track dynamic shape computations globally across the program. It also introduces a cross-level abstraction that encapsulates computational graphs, loop-level tensor programs, and library calls in a single representation to enable cross-level optimizations. We build an end-to-end compilation framework using the proposed approach to optimize dynamic shape models. Experimental results on large language models show that Relax delivers performance competitive with state-of-the-art hand-optimized systems across platforms and enables deployment of emerging dynamic models to a broader set of environments, including mobile phones, embedded devices, and web browsers.

Model-based reinforcement learning (MBRL) has been shown to be a powerful framework for data-efficiently learning control of continuous tasks. Recent work in MBRL has mostly focused on using more advanced function approximators and planning schemes, with little development of the general framework. In this paper, we identify a fundamental issue of the standard MBRL framework -- what we call the objective mismatch issue. Objective mismatch arises when one objective is optimized in the hope that a second, often uncorrelated, metric will also be optimized. In the context of MBRL, we characterize the objective mismatch between training the forward dynamics model w.r.t.~the likelihood of the one-step ahead prediction, and the overall goal of improving performance on a downstream control task. For example, this issue can emerge with the realization that dynamics models effective for a specific task do not necessarily need to be globally accurate, and vice versa globally accurate models might not be sufficiently accurate locally to obtain good control performance on a specific task. In our experiments, we study this objective mismatch issue and demonstrate that the likelihood of one-step ahead predictions is not always correlated with control performance. This observation highlights a critical limitation in the MBRL framework which will require further research to be fully understood and addressed. We propose an initial method to mitigate the mismatch issue by re-weighting dynamics model training. Building on it, we conclude with a discussion about other potential directions of research for addressing this issue.

A domain wall (DW) which moves parallel to a magnetically compensated interface between an antiferromagnetic insulator (AFMI) and a two-dimensional (2D) metal can pump spin polarization into the metal. It is assumed that localized spins of a collinear AFMI interact with itinerant electrons through their exchange interaction on the interface. We employed the formalism of Keldysh Green's functions for electrons which experience potential and spin-orbit scattering on random impurities. This formalism allows a unified analysis of spin pumping, spin diffusion and spin relaxation effects on a 2D electron gas. It is shown that the pumping of a nonstaggered magnetization into the metal film takes place in the second order with respect to the interface exchange interaction. At sufficiently weak spin relaxation this pumping effect can be much stronger than the first-order effect of the Pauli magnetism which is produced by the small nonstaggered exchange field of the DW. It is shown that the pumped polarization is sensitive to the geometry of the electron's Fermi surface and increases when the wave vector of the staggered magnetization approaches the nesting vector of the Fermi surface. In a disordered diffusive electron gas the induced spin polarization follows the motion of the domain wall. It is distributed asymmetrically around the DW over a distance which can be much larger than the DW width.

Neural networks are sensitive to hyper-parameter and architecture choices. Automated Machine Learning (AutoML) is a promising paradigm for automating these choices. Current ML software libraries, however, are quite limited in handling the dynamic interactions among the components of AutoML. For example, efficientNAS algorithms, such as ENAS and DARTS, typically require an implementation coupling between the search space and search algorithm, the two key components in AutoML. Furthermore, implementing a complex search flow, such as searching architectures within a loop of searching hardware configurations, is difficult. To summarize, changing the search space, search algorithm, or search flow in current ML libraries usually requires a significant change in the program logic. In this paper, we introduce a new way of programming AutoML based on symbolic programming. Under this paradigm, ML programs are mutable, thus can be manipulated easily by another program. As a result, AutoML can be reformulated as an automated process of symbolic manipulation. With this formulation, we decouple the triangle of the search algorithm, the search space and the child program. This decoupling makes it easy to change the search space and search algorithm (without and with weight sharing), as well as to add search capabilities to existing code and implement complex search flows. We then introduce PyGlove, a new Python library that implements this paradigm. Through case studies on ImageNet and NAS-Bench-101, we show that with PyGlove users can easily convert a static program into a search space, quickly iterate on the search spaces and search algorithms, and craft complex search flows to achieve better results.

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized parameter-sharing (RPS) methods have gained traction for model compression at start of training. In this paper, we comprehensively assess the trade-off between memory and accuracy across RPS, pruning techniques, and building smaller models. Our findings demonstrate that RPS, which is both data and model-agnostic, consistently outperforms/matches smaller models and all moderately informed pruning strategies, such as MAG, SNIP, SYNFLOW, and GRASP, across the entire compression range. This advantage becomes particularly pronounced in higher compression scenarios. Notably, even when compared to highly informed pruning techniques like Lottery Ticket Rewinding (LTR), RPS exhibits superior performance in high compression settings. This points out inherent capacity advantage that RPS enjoys over sparse models. Theoretically, we establish RPS as a superior technique in terms of memory-efficient representation when compared to pruning for linear models. This paper argues in favor of paradigm shift towards RPS based models. During our rigorous evaluation of RPS, we identified issues in the state-of-the-art RPS technique ROAST, specifically regarding stability (ROAST's sensitivity to initialization hyperparameters, often leading to divergence) and Pareto-continuity (ROAST's inability to recover the accuracy of the original model at zero compression). We provably address both of these issues. We refer to the modified RPS, which incorporates our improvements, as STABLE-RPS.

Code Large Language Models (Code LLMs) have emerged as powerful tools, revolutionizing the software development landscape by automating the coding process and reducing time and effort required to build applications. This paper focuses on training Code LLMs to specialize in the field of quantum computing. We begin by discussing the unique needs of quantum computing programming, which differ significantly from classical programming approaches or languages. A Code LLM specializing in quantum computing requires a foundational understanding of quantum computing and quantum information theory. However, the scarcity of available quantum code examples and the rapidly evolving field, which necessitates continuous dataset updates, present significant challenges. Moreover, we discuss our work on training Code LLMs to produce high-quality quantum code using the Qiskit library. This work includes an examination of the various aspects of the LLMs used for training and the specific training conditions, as well as the results obtained with our current models. To evaluate our models, we have developed a custom benchmark, similar to HumanEval, which includes a set of tests specifically designed for the field of quantum computing programming using Qiskit. Our findings indicate that our model outperforms existing state-of-the-art models in quantum computing tasks. We also provide examples of code suggestions, comparing our model to other relevant code LLMs. Finally, we introduce a discussion on the potential benefits of Code LLMs for quantum computing computational scientists, researchers, and practitioners. We also explore various features and future work that could be relevant in this context.

Off-policy dynamic programming (DP) techniques such as Q-learning have proven to be important in sequential decision-making problems. In the presence of function approximation, however, these techniques often diverge due to the absence of Bellman completeness in the function classes considered, a crucial condition for the success of DP-based methods. In this paper, we show how off-policy learning techniques based on return-conditioned supervised learning (RCSL) are able to circumvent these challenges of Bellman completeness, converging under significantly more relaxed assumptions inherited from supervised learning. We prove there exists a natural environment in which if one uses two-layer multilayer perceptron as the function approximator, the layer width needs to grow linearly with the state space size to satisfy Bellman completeness while a constant layer width is enough for RCSL. These findings take a step towards explaining the superior empirical performance of RCSL methods compared to DP-based methods in environments with near-optimal datasets. Furthermore, in order to learn from sub-optimal datasets, we propose a simple framework called MBRCSL, granting RCSL methods the ability of dynamic programming to stitch together segments from distinct trajectories. MBRCSL leverages learned dynamics models and forward sampling to accomplish trajectory stitching while avoiding the need for Bellman completeness that plagues all dynamic programming algorithms. We propose both theoretical analysis and experimental evaluation to back these claims, outperforming state-of-the-art model-free and model-based offline RL algorithms across several simulated robotics problems.

Following natural instructions is crucial for the effective application of Retrieval-Augmented Generation (RAG) systems. Despite recent advancements in Large Language Models (LLMs), research on assessing and improving instruction-following (IF) alignment within the RAG domain remains limited. To address this issue, we propose VIF-RAG, the first automated, scalable, and verifiable synthetic pipeline for instruction-following alignment in RAG systems. We start by manually crafting a minimal set of atomic instructions (<100) and developing combination rules to synthesize and verify complex instructions for a seed set. We then use supervised models for instruction rewriting while simultaneously generating code to automate the verification of instruction quality via a Python executor. Finally, we integrate these instructions with extensive RAG and general data samples, scaling up to a high-quality VIF-RAG-QA dataset (>100k) through automated processes. To further bridge the gap in instruction-following auto-evaluation for RAG systems, we introduce FollowRAG Benchmark, which includes approximately 3K test samples, covering 22 categories of general instruction constraints and four knowledge-intensive QA datasets. Due to its robust pipeline design, FollowRAG can seamlessly integrate with different RAG benchmarks. Using FollowRAG and eight widely-used IF and foundational abilities benchmarks for LLMs, we demonstrate that VIF-RAG markedly enhances LLM performance across a broad range of general instruction constraints while effectively leveraging its capabilities in RAG scenarios. Further analysis offers practical insights for achieving IF alignment in RAG systems. Our code and datasets are released at https://FollowRAG.github.io.

Large language models (LLMs) with long sequences begin to power more and more fundamentally new applications we use every day. Existing methods for long-sequence LLM training are neither efficient nor compatible with commonly-used training algorithms such as FlashAttention. We design Buff to address these issues. Buff decouples all of the sharding dimensions into a new hierarchical space, and systematically analyzes the memory and communication cost of LLM training. Then, it generates an effective hybrid parallelism strategy. We design a new selective overlap mechanism to mitigate the communication overhead introduced by the hybrid parallelism. We also implement memory management techniques to reduce GPU memory fragmentation. Evaluation results show that Buff generates parallelization strategies that match or outperform existing methods in model FLOPs utilization.

We introduce RL4CO, an extensive reinforcement learning (RL) for combinatorial optimization (CO) benchmark. RL4CO employs state-of-the-art software libraries as well as best practices in implementation, such as modularity and configuration management, to be efficient and easily modifiable by researchers for adaptations of neural network architecture, environments, and algorithms. Contrary to the existing focus on specific tasks like the traveling salesman problem (TSP) for performance assessment, we underline the importance of scalability and generalization capabilities for diverse optimization tasks. We also systematically benchmark sample efficiency, zero-shot generalization, and adaptability to changes in data distributions of various models. Our experiments show that some recent state-of-the-art methods fall behind their predecessors when evaluated using these new metrics, suggesting the necessity for a more balanced view of the performance of neural CO solvers. We hope RL4CO will encourage the exploration of novel solutions to complex real-world tasks, allowing to compare with existing methods through a standardized interface that decouples the science from the software engineering. We make our library publicly available at https://github.com/kaist-silab/rl4co.

Many approaches such as Quine-McCluskey algorithm, Karnaugh map solving, Petrick's method and McBoole's method have been devised to simplify Boolean expressions in order to optimize hardware implementation of digital circuits. However, the algorithmic implementations of these methods are hard-coded and also their computation time is proportional to the number of minterms involved in the expression. In this paper, we propose KarNet, where the ability of Convolutional Neural Networks to model relationships between various cell locations and values by capturing spatial dependencies is exploited to solve Karnaugh maps. In order to do so, a Karnaugh map is represented as an image signal, where each cell is considered as a pixel. Experimental results show that the computation time of KarNet is independent of the number of minterms and is of the order of one-hundredth to one-tenth that of the rule-based methods. KarNet being a learned system is found to achieve nearly a hundred percent accuracy, precision, and recall. We train KarNet to solve four variable Karnaugh maps and also show that a similar method can be applied on Karnaugh maps with more variables. Finally, we show a way to build a fully accurate and computationally fast system using KarNet.

Building generalist models has recently demonstrated remarkable capabilities in diverse scientific domains. Within the realm of molecular learning, several studies have explored unifying diverse tasks across diverse domains. However, negative conflicts and interference between molecules and knowledge from different domain may have a worse impact in threefold. First, conflicting molecular representations can lead to optimization difficulties for the models. Second, mixing and scaling up training data across diverse tasks is inherently challenging. Third, the computational cost of refined pretraining is prohibitively high. To address these limitations, this paper presents Omni-Mol, a scalable and unified LLM-based framework for direct instruction tuning. Omni-Mol builds on three key components to tackles conflicts: (1) a unified encoding mechanism for any task input; (2) an active-learning-driven data selection strategy that significantly reduces dataset size; (3) a novel design of the adaptive gradient stabilization module and anchor-and-reconcile MoE framework that ensures stable convergence. Experimentally, Omni-Mol achieves state-of-the-art performance across 15 molecular tasks, demonstrates the presence of scaling laws in the molecular domain, and is supported by extensive ablation studies and analyses validating the effectiveness of its design. The code and weights of the powerful AI-driven chemistry generalist are open-sourced at: https://anonymous.4open.science/r/Omni-Mol-8EDB.

Large language models (LLMs) have revolutionized natural language processing tasks. However, their practical deployment is hindered by their immense memory and computation requirements. Although recent post-training quantization (PTQ) methods are effective in reducing memory footprint and improving the computational efficiency of LLM, they hand-craft quantization parameters, which leads to low performance and fails to deal with extremely low-bit quantization. To tackle this issue, we introduce an Omnidirectionally calibrated Quantization (OmniQuant) technique for LLMs, which achieves good performance in diverse quantization settings while maintaining the computational efficiency of PTQ by efficiently optimizing various quantization parameters. OmniQuant comprises two innovative components including Learnable Weight Clipping (LWC) and Learnable Equivalent Transformation (LET). LWC modulates the extreme values of weights by optimizing the clipping threshold. Meanwhile, LET tackles activation outliers by shifting the challenge of quantization from activations to weights through a learnable equivalent transformation. Operating within a differentiable framework using block-wise error minimization, OmniQuant can optimize the quantization process efficiently for both weight-only and weight-activation quantization. For instance, the LLaMA-2 model family with the size of 7-70B can be processed with OmniQuant on a single A100-40G GPU within 1-16 hours using 128 samples. Extensive experiments validate OmniQuant's superior performance across diverse quantization configurations such as W4A4, W6A6, W4A16, W3A16, and W2A16. Additionally, OmniQuant demonstrates effectiveness in instruction-tuned models and delivers notable improvements in inference speed and memory reduction on real devices. Codes and models are available at https://github.com/OpenGVLab/OmniQuant.

Key-Value (KV) cache has become a bottleneck of LLMs for long-context generation. Despite the numerous efforts in this area, the optimization for the decoding phase is generally ignored. However, we believe such optimization is crucial, especially for long-output generation tasks based on the following two observations: (i) Excessive compression during the prefill phase, which requires specific full context impairs the comprehension of the reasoning task; (ii) Deviation of heavy hitters occurs in the reasoning tasks with long outputs. Therefore, SCOPE, a simple yet efficient framework that separately performs KV cache optimization during the prefill and decoding phases, is introduced. Specifically, the KV cache during the prefill phase is preserved to maintain the essential information, while a novel strategy based on sliding is proposed to select essential heavy hitters for the decoding phase. Memory usage and memory transfer are further optimized using adaptive and discontinuous strategies. Extensive experiments on LongGenBench show the effectiveness and generalization of SCOPE and its compatibility as a plug-in to other prefill-only KV compression methods.

Large Language Models (LLMs) have demonstrated great potential in various language processing tasks, and recent studies have explored their application in compiler optimizations. However, all these studies focus on the conventional open-source LLMs, such as Llama2, which lack enhanced reasoning mechanisms. In this study, we investigate the errors produced by the fine-tuned 7B-parameter Llama2 model as it attempts to learn and apply a simple peephole optimization for the AArch64 assembly code. We provide an analysis of the errors produced by the LLM and compare it with state-of-the-art OpenAI models which implement advanced reasoning logic, including GPT-4o and GPT-o1 (preview). We demonstrate that OpenAI GPT-o1, despite not being fine-tuned, outperforms the fine-tuned Llama2 and GPT-4o. Our findings indicate that this advantage is largely due to the chain-of-thought reasoning implemented in GPT-o1. We hope our work will inspire further research on using LLMs with enhanced reasoning mechanisms and chain-of-thought for code generation and optimization.

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely functional language with array operations. It is the first one to deliver a provably efficient, purely functional, and denotationally correct reverse-mode differentiation. We show that our transformation is semantically correct and verifies the cheap gradient principle. Inspired by PROPs and compilation to categories, we introduce a novel intermediate representation that we call 'unary form'. Our reverse-mode transformation is factored as a compilation scheme through this intermediate representation. We obtain provably efficient gradients by performing general partial evaluation optimizations after our reverse-mode transformation, as opposed to manually derived ones. For simple first-order programs, the obtained output programs resemble static-single-assignment (SSA) code. We emphasize the modularity of our approach and show how our language can easily be enriched with more optimized primitives, as required for some speed-ups in practice.

Recent advancements have introduced machine learning frameworks to enhance the Branch and Bound (B\&B) branching policies for solving Mixed Integer Linear Programming (MILP). These methods, primarily relying on imitation learning of Strong Branching, have shown superior performance. However, collecting expert samples for imitation learning, particularly for Strong Branching, is a time-consuming endeavor. To address this challenge, we propose Contrastive Learning with Augmented MILPs for Branching (CAMBranch), a framework that generates Augmented MILPs (AMILPs) by applying variable shifting to limited expert data from their original MILPs. This approach enables the acquisition of a considerable number of labeled expert samples. CAMBranch leverages both MILPs and AMILPs for imitation learning and employs contrastive learning to enhance the model's ability to capture MILP features, thereby improving the quality of branching decisions. Experimental results demonstrate that CAMBranch, trained with only 10\% of the complete dataset, exhibits superior performance. Ablation studies further validate the effectiveness of our method.

Recent studies in using deep reinforcement learning (DRL) to solve Job-shop scheduling problems (JSSP) focus on construction heuristics. However, their performance is still far from optimality, mainly because the underlying graph representation scheme is unsuitable for modelling partial solutions at each construction step. This paper proposes a novel DRL-guided improvement heuristic for solving JSSP, where graph representation is employed to encode complete solutions. We design a Graph Neural-Network-based representation scheme, consisting of two modules to effectively capture the information of dynamic topology and different types of nodes in graphs encountered during the improvement process. To speed up solution evaluation during improvement, we present a novel message-passing mechanism that can evaluate multiple solutions simultaneously. We prove that the computational complexity of our method scales linearly with problem size. Experiments on classic benchmarks show that the improvement policy learned by our method outperforms state-of-the-art DRL-based methods by a large margin.

Recently, the Muon optimizer based on matrix orthogonalization has demonstrated strong results in training small-scale language models, but the scalability to larger models has not been proven. We identify two crucial techniques for scaling up Muon: (1) adding weight decay and (2) carefully adjusting the per-parameter update scale. These techniques allow Muon to work out-of-the-box on large-scale training without the need of hyper-parameter tuning. Scaling law experiments indicate that Muon achieves sim!2times computational efficiency compared to AdamW with compute optimal training. Based on these improvements, we introduce Moonlight, a 3B/16B-parameter Mixture-of-Expert (MoE) model trained with 5.7T tokens using Muon. Our model improves the current Pareto frontier, achieving better performance with much fewer training FLOPs compared to prior models. We open-source our distributed Muon implementation that is memory optimal and communication efficient. We also release the pretrained, instruction-tuned, and intermediate checkpoints to support future research.

General-purpose LLM judges capable of human-level evaluation provide not only a scalable and accurate way of evaluating instruction-following LLMs but also new avenues for supervising and improving their performance. One promising way of leveraging LLM judges for supervision is through Minimum Bayes Risk (MBR) decoding, which uses a reference-based evaluator to select a high-quality output from amongst a set of candidate outputs. In the first part of this work, we explore using MBR decoding as a method for improving the test-time performance of instruction-following LLMs. We find that MBR decoding with reference-based LLM judges substantially improves over greedy decoding, best-of-N decoding with reference-free judges and MBR decoding with lexical and embedding-based metrics on AlpacaEval and MT-Bench. These gains are consistent across LLMs with up to 70B parameters, demonstrating that smaller LLM judges can be used to supervise much larger LLMs. Then, seeking to retain the improvements from MBR decoding while mitigating additional test-time costs, we explore iterative self-training on MBR-decoded outputs. We find that self-training using Direct Preference Optimisation leads to significant performance gains, such that the self-trained models with greedy decoding generally match and sometimes exceed the performance of their base models with MBR decoding.

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a score of 71.31 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously. Empirical results also validate the exploration efficiency of CDPO.

In order to improve reproducibility, deep reinforcement learning (RL) has been adopting better scientific practices such as standardized evaluation metrics and reporting. However, the process of hyperparameter optimization still varies widely across papers, which makes it challenging to compare RL algorithms fairly. In this paper, we show that hyperparameter choices in RL can significantly affect the agent's final performance and sample efficiency, and that the hyperparameter landscape can strongly depend on the tuning seed which may lead to overfitting. We therefore propose adopting established best practices from AutoML, such as the separation of tuning and testing seeds, as well as principled hyperparameter optimization (HPO) across a broad search space. We support this by comparing multiple state-of-the-art HPO tools on a range of RL algorithms and environments to their hand-tuned counterparts, demonstrating that HPO approaches often have higher performance and lower compute overhead. As a result of our findings, we recommend a set of best practices for the RL community, which should result in stronger empirical results with fewer computational costs, better reproducibility, and thus faster progress. In order to encourage the adoption of these practices, we provide plug-and-play implementations of the tuning algorithms used in this paper at https://github.com/facebookresearch/how-to-autorl.

Recently, Mixture-of-Experts (short as MoE) architecture has achieved remarkable success in increasing the model capacity of large-scale language models. However, MoE requires incorporating significantly more parameters than the base model being extended. In this paper, we propose building a parameter-efficient MoE architecture by sharing information among experts. We adopt the matrix product operator (MPO, a tensor decomposition from quantum many-body physics) to reconstruct the parameter matrix in the expert layer and increase model capacity for pre-trained language models by sharing parameters of the central tensor (containing the core information) among different experts while enabling the specificity through the auxiliary tensors (complementing the central tensor) of different experts. To address the unbalanced optimization issue, we further design the gradient mask strategy for the MPO-based MoE architecture. Extensive experiments based on T5 and GPT-2 show improved performance and efficiency of the pre-trained language model (27.2x reduction in total parameters for the superior model performance, compared with the Switch Transformers). Our code is publicly available at https://github.com/RUCAIBox/MPOE.

The ever-growing ecosystem of LLMs has posed a challenge in selecting the most appropriate pre-trained model to fine-tune amidst a sea of options. Given constrained resources, fine-tuning all models and making selections afterward is unrealistic. In this work, we formulate this resource-constrained selection task into predicting fine-tuning performance and illustrate its natural connection with scaling laws. Unlike pre-training, We find that the fine-tuning scaling curve includes not just the well-known "power phase" but also the previously unobserved "pre-power phase". We also explain why existing scaling laws fail to capture this phase transition phenomenon both theoretically and empirically. To address this, we introduce the concept of "pre-learned data size" into our rectified scaling law, which overcomes theoretical limitations and fits experimental results much better. By leveraging our law, we propose a novel LLM selection algorithm that selects the near-optimal model with hundreds of times less resource consumption, while other methods may provide negatively correlated selection.

Large language models (LLMs) are increasingly used for complex tasks requiring multiple chained generation calls, advanced prompting techniques, control flow, and interaction with external environments. However, efficient systems for programming and executing these applications are lacking. To bridge this gap, we introduce SGLang, a Structured Generation Language for LLMs. SGLang is designed for the efficient programming of LLMs and incorporates primitives for common LLM programming patterns. We have implemented SGLang as a domain-specific language embedded in Python, and we developed an interpreter, a compiler, and a high-performance runtime for SGLang. These components work together to enable optimizations such as parallelism, batching, caching, sharing, and other compilation techniques. Additionally, we propose RadixAttention, a novel technique that maintains a Least Recently Used (LRU) cache of the Key-Value (KV) cache for all requests in a radix tree, enabling automatic KV cache reuse across multiple generation calls at runtime. SGLang simplifies the writing of LLM programs and boosts execution efficiency. Our experiments demonstrate that SGLang can speed up common LLM tasks by up to 5x, while reducing code complexity and enhancing control.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches on 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.

The most popular framework for distributed training of machine learning models is the (synchronous) parameter server (PS). This paradigm consists of n workers, which iteratively compute updates of the model parameters, and a stateful PS, which waits and aggregates all updates to generate a new estimate of model parameters and sends it back to the workers for a new iteration. Transient computation slowdowns or transmission delays can intolerably lengthen the time of each iteration. An efficient way to mitigate this problem is to let the PS wait only for the fastest n-b updates, before generating the new parameters. The slowest b workers are called backup workers. The optimal number b of backup workers depends on the cluster configuration and workload, but also (as we show in this paper) on the hyper-parameters of the learning algorithm and the current stage of the training. We propose DBW, an algorithm that dynamically decides the number of backup workers during the training process to maximize the convergence speed at each iteration. Our experiments show that DBW 1) removes the necessity to tune b by preliminary time-consuming experiments, and 2) makes the training up to a factor 3 faster than the optimal static configuration.

We address the problem of code generation from multi-turn execution feedback. Existing methods either generate code without feedback or use complex, hierarchical reinforcement learning to optimize multi-turn rewards. We propose a simple yet scalable approach, muCode, that solves multi-turn code generation using only single-step rewards. Our key insight is that code generation is a one-step recoverable MDP, where the correct code can be recovered from any intermediate code state in a single turn. muCode iteratively trains both a generator to provide code solutions conditioned on multi-turn execution feedback and a verifier to score the newly generated code. Experimental evaluations show that our approach achieves significant improvements over the state-of-the-art baselines. We provide analysis of the design choices of the reward models and policy, and show the efficacy of muCode at utilizing the execution feedback. Our code is available at https://github.com/portal-cornell/muCode.

With the rapid growth in the number of Large Language Models (LLMs), there has been a recent interest in LLM routing, or directing queries to the cheapest LLM that can deliver a suitable response. Following this line of work, we introduce CARROT, a Cost AwaRe Rate Optimal rouTer that can select models based on any desired trade-off between performance and cost. Given a query, CARROT selects a model based on estimates of models' cost and performance. Its simplicity lends CARROT computational efficiency, while our theoretical analysis demonstrates minimax rate-optimality in its routing performance. Alongside CARROT, we also introduce the Smart Price-aware Routing (SPROUT) dataset to facilitate routing on a wide spectrum of queries with the latest state-of-the-art LLMs. Using SPROUT and prior benchmarks such as Routerbench and open-LLM-leaderboard-v2 we empirically validate CARROT's performance against several alternative routers.

Run-time steering strategies like Medprompt are valuable for guiding large language models (LLMs) to top performance on challenging tasks. Medprompt demonstrates that a general LLM can be focused to deliver state-of-the-art performance on specialized domains like medicine by using a prompt to elicit a run-time strategy involving chain of thought reasoning and ensembling. OpenAI's o1-preview model represents a new paradigm, where a model is designed to do run-time reasoning before generating final responses. We seek to understand the behavior of o1-preview on a diverse set of medical challenge problem benchmarks. Following on the Medprompt study with GPT-4, we systematically evaluate the o1-preview model across various medical benchmarks. Notably, even without prompting techniques, o1-preview largely outperforms the GPT-4 series with Medprompt. We further systematically study the efficacy of classic prompt engineering strategies, as represented by Medprompt, within the new paradigm of reasoning models. We found that few-shot prompting hinders o1's performance, suggesting that in-context learning may no longer be an effective steering approach for reasoning-native models. While ensembling remains viable, it is resource-intensive and requires careful cost-performance optimization. Our cost and accuracy analysis across run-time strategies reveals a Pareto frontier, with GPT-4o representing a more affordable option and o1-preview achieving state-of-the-art performance at higher cost. Although o1-preview offers top performance, GPT-4o with steering strategies like Medprompt retains value in specific contexts. Moreover, we note that the o1-preview model has reached near-saturation on many existing medical benchmarks, underscoring the need for new, challenging benchmarks. We close with reflections on general directions for inference-time computation with LLMs.

Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we develop an iterative approach that optimizes the preference between competing generated Chain-of-Thought (CoT) candidates by optimizing for winning vs. losing reasoning steps that lead to the correct answer. We train using a modified DPO loss (Rafailov et al., 2023) with an additional negative log-likelihood term, which we find to be crucial. We show reasoning improves across repeated iterations of this scheme. While only relying on examples in the training set, our approach results in increasing accuracy for Llama-2-70B-Chat from 55.6% to 81.6% on GSM8K (and 88.7% with majority voting out of 32 samples), from 12.5% to 20.8% on MATH, and from 77.8% to 86.7% on ARC-Challenge, which outperforms other Llama-2-based models not relying on additionally sourced datasets.

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present Symbol, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within Symbol, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by Symbol not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our Symbol framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.

Nowadays transformer-based Large Language Models (LLM) for code generation tasks usually apply sampling and filtering pipelines. Due to the sparse reward problem in code generation tasks caused by one-token incorrectness, transformer-based models will sample redundant programs till they find a correct one, leading to low efficiency. To overcome the challenge, we incorporate Experience Replay (ER) in the fine-tuning phase, where codes and programs produced are stored and will be replayed to give the LLM agent a chance to learn from past experiences. Based on the spirit of ER, we introduce a novel approach called BTP pipeline which consists of three phases: beam search sampling, testing phase, and prioritized experience replay phase. The approach makes use of failed programs collected by code models and replays programs with high Possibility and Pass-rate Prioritized value (P2Value) from the replay buffer to improve efficiency. P2Value comprehensively considers the possibility of transformers' output and pass rate and can make use of the redundant resources caused by the problem that most programs collected by LLMs fail to pass any tests. We empirically apply our approach in several LLMs, demonstrating that it enhances their performance in code generation tasks and surpasses existing baselines.

Compiler architects increasingly look to machine learning when building heuristics for compiler optimization. The promise of automatic heuristic design, freeing the compiler engineer from the complex interactions of program, architecture, and other optimizations, is alluring. However, most machine learning methods cannot replicate even the simplest of the abstract interpretations of data flow analysis that are critical to making good optimization decisions. This must change for machine learning to become the dominant technology in compiler heuristics. To this end, we propose ProGraML - Program Graphs for Machine Learning - a language-independent, portable representation of whole-program semantics for deep learning. To benchmark current and future learning techniques for compiler analyses we introduce an open dataset of 461k Intermediate Representation (IR) files for LLVM, covering five source programming languages, and 15.4M corresponding data flow results. We formulate data flow analysis as an MPNN and show that, using ProGraML, standard analyses can be learned, yielding improved performance on downstream compiler optimization tasks.

This paper explores the problem of collision-free motion generation for manipulators by formulating it as a global motion optimization problem. We develop a parallel optimization technique to solve this problem and demonstrate its effectiveness on massively parallel GPUs. We show that combining simple optimization techniques with many parallel seeds leads to solving difficult motion generation problems within 50ms on average, 60x faster than state-of-the-art (SOTA) trajectory optimization methods. We achieve SOTA performance by combining L-BFGS step direction estimation with a novel parallel noisy line search scheme and a particle-based optimization solver. To further aid trajectory optimization, we develop a parallel geometric planner that plans within 20ms and also introduce a collision-free IK solver that can solve over 7000 queries/s. We package our contributions into a state of the art GPU accelerated motion generation library, cuRobo and release it to enrich the robotics community. Additional details are available at https://curobo.org

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

Scaling test-time compute is a promising axis for improving LLM capabilities. However, test-time compute can be scaled in a variety of ways, and effectively combining different approaches remains an active area of research. Here, we explore this problem in the context of solving real-world GitHub issues from the SWE-bench dataset. Our system, named CodeMonkeys, allows models to iteratively edit a codebase by jointly generating and running a testing script alongside their draft edit. We sample many of these multi-turn trajectories for every issue to generate a collection of candidate edits. This approach lets us scale "serial" test-time compute by increasing the number of iterations per trajectory and "parallel" test-time compute by increasing the number of trajectories per problem. With parallel scaling, we can amortize up-front costs across multiple downstream samples, allowing us to identify relevant codebase context using the simple method of letting an LLM read every file. In order to select between candidate edits, we combine voting using model-generated tests with a final multi-turn trajectory dedicated to selection. Overall, CodeMonkeys resolves 57.4% of issues from SWE-bench Verified using a budget of approximately 2300 USD. Our selection method can also be used to combine candidates from different sources. Selecting over an ensemble of edits from existing top SWE-bench Verified submissions obtains a score of 66.2% and outperforms the best member of the ensemble on its own. We fully release our code and data at https://scalingintelligence.stanford.edu/pubs/codemonkeys.

In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial differential equations (PDEs). Our key result is that the difficulty in training these models is closely related to the conditioning of a specific differential operator. This operator, in turn, is associated to the Hermitian square of the differential operator of the underlying PDE. If this operator is ill-conditioned, it results in slow or infeasible training. Therefore, preconditioning this operator is crucial. We employ both rigorous mathematical analysis and empirical evaluations to investigate various strategies, explaining how they better condition this critical operator, and consequently improve training.

LangProp is a framework for iteratively optimizing code generated by large language models (LLMs) in a supervised/reinforcement learning setting. While LLMs can generate sensible solutions zero-shot, the solutions are often sub-optimal. Especially for code generation tasks, it is likely that the initial code will fail on certain edge cases. LangProp automatically evaluates the code performance on a dataset of input-output pairs, as well as catches any exceptions, and feeds the results back to the LLM in the training loop, so that the LLM can iteratively improve the code it generates. By adopting a metric- and data-driven training paradigm for this code optimization procedure, one could easily adapt findings from traditional machine learning techniques such as imitation learning, DAgger, and reinforcement learning. We demonstrate the first proof of concept of automated code optimization for autonomous driving in CARLA, showing that LangProp can generate interpretable and transparent driving policies that can be verified and improved in a metric- and data-driven way. Our code will be open-sourced and is available at https://github.com/shuishida/LangProp.

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

Existing learning rate schedules that do not require specification of the optimization stopping step T are greatly out-performed by learning rate schedules that depend on T. We propose an approach that avoids the need for this stopping time by eschewing the use of schedules entirely, while exhibiting state-of-the-art performance compared to schedules across a wide family of problems ranging from convex problems to large-scale deep learning problems. Our Schedule-Free approach introduces no additional hyper-parameters over standard optimizers with momentum. Our method is a direct consequence of a new theory we develop that unifies scheduling and iterate averaging. An open source implementation of our method is available (https://github.com/facebookresearch/schedule_free).

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

The emergence of large language models (LLMs) has significantly pushed the frontiers of program synthesis. Advancement of LLM-based program synthesis calls for a thorough evaluation of LLM-generated code. Most evaluation frameworks focus on the (functional) correctness of generated code; efficiency, as an important measure of code quality, has been overlooked in existing evaluations. In this work, we develop ENAMEL (EfficeNcy AutoMatic EvaLuator), a rigorous and high-standard benchmark for evaluating the capability of LLMs in generating efficient code. Firstly, we propose a new efficiency metric called eff@k, which generalizes the pass@k metric from correctness to efficiency and appropriately handles right-censored execution time. Furthermore, we derive an unbiased and variance-reduced estimator of eff@k via Rao--Blackwellization; we also provide a numerically stable implementation for the new estimator. Secondly, to set a high-standard for efficiency evaluation, we employ a human expert to design best algorithms and implementations as our reference solutions of efficiency, many of which are much more efficient than existing canonical solutions in HumanEval and HumanEval+. Moreover, to ensure a rigorous evaluation, we employ a human expert to curate strong test case generators to filter out wrong code and differentiate suboptimal algorithms. An extensive study across 30 popular LLMs using our benchmark ENAMEL shows that LLMs still fall short of generating expert-level efficient code. Using two subsets of our problem set, we demonstrate that such deficiency is because current LLMs struggle in designing advanced algorithms and are barely aware of implementation optimization. Our benchmark is publicly available at https://github.com/q-rz/enamel .

Reinforcement Learning from Human Feedback (RLHF) stands as a pivotal technique in empowering large language model (LLM) applications. Since RLHF involves diverse computational workloads and intricate dependencies among multiple LLMs, directly adopting parallelization techniques from supervised training can result in sub-optimal performance. To overcome this limitation, we propose a novel approach named parameter ReaLlocation, which dynamically redistributes LLM parameters in the cluster and adapts parallelization strategies during training. Building upon this idea, we introduce ReaLHF, a pioneering system capable of automatically discovering and running efficient execution plans for RLHF training given the desired algorithmic and hardware configurations. ReaLHF formulates the execution plan for RLHF as an augmented dataflow graph. Based on this formulation, ReaLHF employs a tailored search algorithm with a lightweight cost estimator to discover an efficient execution plan. Subsequently, the runtime engine deploys the selected plan by effectively parallelizing computations and redistributing parameters. We evaluate ReaLHF on the LLaMA-2 models with up to 4times70 billion parameters and 128 GPUs. The experiment results showcase ReaLHF's substantial speedups of 2.0-10.6times compared to baselines. Furthermore, the execution plans generated by ReaLHF exhibit an average of 26% performance improvement over heuristic approaches based on Megatron-LM. The source code of ReaLHF is publicly available at https://github.com/openpsi-project/ReaLHF .

We introduce QuaRot, a new Quantization scheme based on Rotations, which is able to quantize LLMs end-to-end, including all weights, activations, and KV cache in 4 bits. QuaRot rotates LLMs in a way that removes outliers from the hidden state without changing the output, making quantization easier. This computational invariance is applied to the hidden state (residual) of the LLM, as well as to the activations of the feed-forward components, aspects of the attention mechanism and to the KV cache. The result is a quantized model where all matrix multiplications are performed in 4-bits, without any channels identified for retention in higher precision. Our quantized LLaMa2-70B model has losses of at most 0.29 WikiText-2 perplexity and retains 99% of the zero-shot performance. Code is available at: https://github.com/spcl/QuaRot.

The advancement of large language models (LLMs) has significantly propelled the field of code generation. Previous work integrated reinforcement learning (RL) with compiler feedback for exploring the output space of LLMs to enhance code generation quality. However, the lengthy code generated by LLMs in response to complex human requirements makes RL exploration a challenge. Also, since the unit tests may not cover the complicated code, optimizing LLMs by using these unexecuted code snippets is ineffective. To tackle these challenges, we introduce StepCoder, a novel RL framework for code generation, consisting of two main components: CCCS addresses the exploration challenge by breaking the long sequences code generation task into a Curriculum of Code Completion Subtasks, while FGO only optimizes the model by masking the unexecuted code segments to provide Fine-Grained Optimization. In addition, we furthermore construct the APPS+ dataset for RL training, which is manually verified to ensure the correctness of unit tests. Experimental results show that our method improves the ability to explore the output space and outperforms state-of-the-art approaches in corresponding benchmarks.

Despite significant progress in challenging problems across various domains, applying state-of-the-art deep reinforcement learning (RL) algorithms remains challenging due to their sensitivity to the choice of hyperparameters. This sensitivity can partly be attributed to the non-stationarity of the RL problem, potentially requiring different hyperparameter settings at various stages of the learning process. Additionally, in the RL setting, hyperparameter optimization (HPO) requires a large number of environment interactions, hindering the transfer of the successes in RL to real-world applications. In this work, we tackle the issues of sample-efficient and dynamic HPO in RL. We propose a population-based automated RL (AutoRL) framework to meta-optimize arbitrary off-policy RL algorithms. In this framework, we optimize the hyperparameters and also the neural architecture while simultaneously training the agent. By sharing the collected experience across the population, we substantially increase the sample efficiency of the meta-optimization. We demonstrate the capabilities of our sample-efficient AutoRL approach in a case study with the popular TD3 algorithm in the MuJoCo benchmark suite, where we reduce the number of environment interactions needed for meta-optimization by up to an order of magnitude compared to population-based training.

Large Language Models have demonstrated remarkable capabilities in code generation, yet they often struggle with complex programming tasks that require deep algorithmic reasoning. While process supervision through learned reward models shows promise in guiding reasoning steps, it requires expensive training data and suffers from unreliable evaluation. We propose Outcome-Refining Process Supervision, a novel paradigm that treats outcome refinement itself as the process to be supervised. Our framework leverages concrete execution signals to ground the supervision of reasoning steps, while using tree-structured exploration to maintain multiple solution trajectories simultaneously. Experiments demonstrate that our approach enables even smaller models to achieve high success accuracy and performance metrics on competitive programming tasks, creates more reliable verification than traditional reward models without requiring training PRMs. Our approach achieves significant improvements across 5 models and 3 datasets: an average of 26.9% increase in correctness and 42.2% in efficiency. The results suggest that providing structured reasoning space with concrete verification signals is crucial for solving complex programming tasks. We open-source all our code and data at: https://github.com/zhuohaoyu/ORPS

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

First-order optimization (FOO) algorithms are pivotal in numerous computational domains such as machine learning and signal denoising. However, their application to complex tasks like neural network training often entails significant inefficiencies due to the need for many sequential iterations for convergence. In response, we introduce first-order optimization expedited with approximately parallelized iterations (OptEx), the first framework that enhances the efficiency of FOO by leveraging parallel computing to mitigate its iterative bottleneck. OptEx employs kernelized gradient estimation to make use of gradient history for future gradient prediction, enabling parallelization of iterations -- a strategy once considered impractical because of the inherent iterative dependency in FOO. We provide theoretical guarantees for the reliability of our kernelized gradient estimation and the iteration complexity of SGD-based OptEx, confirming that estimation errors diminish to zero as historical gradients accumulate and that SGD-based OptEx enjoys an effective acceleration rate of Omega(N) over standard SGD given parallelism of N. We also use extensive empirical studies, including synthetic functions, reinforcement learning tasks, and neural network training across various datasets, to underscore the substantial efficiency improvements achieved by OptEx.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

We present EE-LLM, a framework for large-scale training and inference of early-exit large language models (LLMs). While recent works have shown preliminary evidence for the efficacy of early exiting in accelerating LLM inference, EE-LLM makes a foundational step towards scaling up early-exit LLMs by supporting their training and inference with massive 3D parallelism. Built upon Megatron-LM, EE-LLM implements a variety of algorithmic innovations and performance optimizations tailored to early exiting, including a lightweight method that facilitates backpropagation for the early-exit training objective with pipeline parallelism, techniques of leveraging idle resources in the original pipeline schedule for computation related to early-exit layers, and two approaches of early-exit inference that are compatible with KV caching for autoregressive generation. Our analytical and empirical study shows that EE-LLM achieves great training efficiency with negligible computational overhead compared to standard LLM training, as well as outstanding inference speedup without compromising output quality. To facilitate further research and adoption, we release EE-LLM at https://github.com/pan-x-c/EE-LLM.

Large Language Models (LLMs) have demonstrated strong capabilities in text-based tasks but struggle with the complex reasoning required for physics problems, particularly in advanced arithmetic and conceptual understanding. While some research has explored ways to enhance LLMs in physics education using techniques such as prompt engineering and Retrieval Augmentation Generation (RAG), not enough effort has been made in addressing their limitations in physics reasoning. This paper presents a novel approach to improving LLM performance on physics questions using Reinforcement Learning with Human and Artificial Intelligence Feedback (RLHAIF). We evaluate several reinforcement learning methods, including Proximal Policy Optimization (PPO), Direct Preference Optimization (DPO), and Remax optimization. These methods are chosen to investigate RL policy performance with different settings on the PhyQA dataset, which includes challenging physics problems from high school textbooks. Our RLHAIF model, tested on leading LLMs like LLaMA2 and Mistral, achieved superior results, notably with the MISTRAL-PPO model, demonstrating marked improvements in reasoning and accuracy. It achieved high scores, with a 58.67 METEOR score and a 0.74 Reasoning score, making it a strong example for future physics reasoning research in this area.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm -- using only the number of iterations as feedback -- can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

We reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau singularities, using tools from polyhedral geometry and symbolic/numerical elimination. Inspired by the work of Gelfand, Kapranov, and Zelevinsky (GKZ) on generalized Euler integrals, we define the principal Landau determinant of a Feynman diagram. We illustrate with a number of examples that this algebraic formalism allows to compute many components of the Landau singular locus. We adapt the GKZ framework by carefully specializing Euler integrals to Feynman integrals. For instance, ultraviolet and infrared singularities are detected as irreducible components of an incidence variety, which project dominantly to the kinematic space. We compute principal Landau determinants for the infinite families of one-loop and banana diagrams with different mass configurations, and for a range of cutting-edge Standard Model processes. Our algorithms build on the Julia package Landau.jl and are implemented in the new open-source package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.

The dominant paradigm for RLHF is online and on-policy RL: synchronously generating from the large language model (LLM) policy, labelling with a reward model, and learning using feedback on the LLM's own outputs. While performant, this paradigm is computationally inefficient. Inspired by classical deep RL literature, we propose separating generation and learning in RLHF. This enables asynchronous generation of new samples while simultaneously training on old samples, leading to faster training and more compute-optimal scaling. However, asynchronous training relies on an underexplored regime, online but off-policy RLHF: learning on samples from previous iterations of our model. To understand the challenges in this regime, we investigate a fundamental question: how much off-policyness can we tolerate for asynchronous training to speed up learning but maintain performance? Among several RLHF algorithms we tested, we find that online DPO is most robust to off-policy data, and robustness increases with the scale of the policy model. We study further compute optimizations for asynchronous RLHF but find that they come at a performance cost, giving rise to a trade-off. Finally, we verify the scalability of asynchronous RLHF by training LLaMA 3.1 8B on an instruction-following task 40% faster than a synchronous run while matching final performance.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of introducing gradient delay, which impedes optimization and can lead to lower final model performance. We introduce Adaptive Braking (AB), a modification for momentum-based optimizers that mitigates the effects of gradient delay. AB dynamically scales the gradient based on the alignment of the gradient and the velocity. This can dampen oscillations along high curvature directions of the loss surface, stabilizing and accelerating asynchronous training. We show that applying AB on top of SGD with momentum enables training ResNets on CIFAR-10 and ImageNet-1k with delays D geq 32 update steps with minimal drop in final test accuracy.

In this work, we aim to teach robots to manipulate various thin-shell materials. Prior works studying thin-shell object manipulation mostly rely on heuristic policies or learn policies from real-world video demonstrations, and only focus on limited material types and tasks (e.g., cloth unfolding). However, these approaches face significant challenges when extended to a wider variety of thin-shell materials and a diverse range of tasks. While virtual simulations are shown to be effective in diverse robot skill learning and evaluation, prior thin-shell simulation environments only support a subset of thin-shell materials, which also limits their supported range of tasks. We introduce ThinShellLab - a fully differentiable simulation platform tailored for robotic interactions with diverse thin-shell materials possessing varying material properties, enabling flexible thin-shell manipulation skill learning and evaluation. Our experiments suggest that manipulating thin-shell objects presents several unique challenges: 1) thin-shell manipulation relies heavily on frictional forces due to the objects' co-dimensional nature, 2) the materials being manipulated are highly sensitive to minimal variations in interaction actions, and 3) the constant and frequent alteration in contact pairs makes trajectory optimization methods susceptible to local optima, and neither standard reinforcement learning algorithms nor trajectory optimization methods (either gradient-based or gradient-free) are able to solve the tasks alone. To overcome these challenges, we present an optimization scheme that couples sampling-based trajectory optimization and gradient-based optimization, boosting both learning efficiency and converged performance across various proposed tasks. In addition, the differentiable nature of our platform facilitates a smooth sim-to-real transition.

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an varepsilon-optimal policy with probability 1-delta under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

Large language models (LLMs) have shown remarkable performance in reasoning tasks but face limitations in mathematical and complex logical reasoning. Existing methods to improve LLMs' logical capabilities either involve traceable or verifiable logical sequences that generate more reliable responses by constructing logical structures yet increase computational costs, or introduces rigid logic template rules, reducing flexibility. In this paper, we propose Reversal of Thought (RoT), a novel framework aimed at enhancing the logical reasoning abilities of LLMs. RoT utilizes a Preference-Guided Reverse Reasoning warm-up strategy, which integrates logical symbols for pseudocode planning through meta-cognitive mechanisms and pairwise preference self-evaluation to generate task-specific prompts solely through demonstrations, aligning with LLMs' cognitive preferences shaped by Reinforcement Learning with Human Feedback (RLHF). Through reverse reasoning, we ultilize a Cognitive Preference Manager to assess knowledge boundaries and further expand LLMs' reasoning capabilities by aggregating solution logic for known tasks and stylistic templates for unknown tasks. Experiments across various tasks demonstrate that RoT surpasses existing baselines in both reasoning accuracy and efficiency.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

Training large neural networks typically requires sharing gradients between accelerators through specialized high-speed interconnects. Drawing from the signal processing principles of frequency decomposition and energy compaction, we demonstrate that synchronizing full optimizer states and model parameters during training is unnecessary. By decoupling momentum updates and allowing controlled divergence in optimizer states across accelerators, we achieve improved convergence compared to state-of-the-art optimizers. We introduce {De}coupled {Mo}mentum (DeMo), a fused optimizer and data parallel algorithm that reduces inter-accelerator communication requirements by several orders of magnitude. This enables training of large neural networks even with limited network bandwidth and heterogeneous hardware. Our method is topology-agnostic and architecture-independent and supports scalable clock-synchronous distributed training with negligible compute and memory overhead. Empirical results show that models trained with DeMo match or exceed the performance of equivalent models trained with AdamW, while eliminating the need for high-speed interconnects when pre-training large scale foundation models. An open source reference PyTorch implementation is published on GitHub at https://github.com/bloc97/DeMo

Prompting techniques such as chain-of-thought have established themselves as a popular vehicle for improving the outputs of large language models (LLMs). For code generation, however, their exact mechanics and efficacy are under-explored. We thus investigate the effects of a wide range of prompting strategies with a focus on automatic re-prompting over multiple turns and computational requirements. After systematically decomposing reasoning, instruction, and execution feedback prompts, we conduct an extensive grid search on the competitive programming benchmarks CodeContests and TACO for multiple LLM families and sizes (Llama 3.0 and 3.1, 8B, 70B, 405B, and GPT-4o). Our study reveals strategies that consistently improve performance across all models with small and large sampling budgets. We then show how finetuning with such an optimal configuration allows models to internalize the induced reasoning process and obtain improvements in performance and scalability for multi-turn code generation.

We present rStar-Math to demonstrate that small language models (SLMs) can rival or even surpass the math reasoning capability of OpenAI o1, without distillation from superior models. rStar-Math achieves this by exercising "deep thinking" through Monte Carlo Tree Search (MCTS), where a math policy SLM performs test-time search guided by an SLM-based process reward model. rStar-Math introduces three innovations to tackle the challenges in training the two SLMs: (1) a novel code-augmented CoT data sythesis method, which performs extensive MCTS rollouts to generate step-by-step verified reasoning trajectories used to train the policy SLM; (2) a novel process reward model training method that avoids na\"ive step-level score annotation, yielding a more effective process preference model (PPM); (3) a self-evolution recipe in which the policy SLM and PPM are built from scratch and iteratively evolved to improve reasoning capabilities. Through 4 rounds of self-evolution with millions of synthesized solutions for 747k math problems, rStar-Math boosts SLMs' math reasoning to state-of-the-art levels. On the MATH benchmark, it improves Qwen2.5-Math-7B from 58.8% to 90.0% and Phi3-mini-3.8B from 41.4% to 86.4%, surpassing o1-preview by +4.5% and +0.9%. On the USA Math Olympiad (AIME), rStar-Math solves an average of 53.3% (8/15) of problems, ranking among the top 20% the brightest high school math students. Code and data will be available at https://github.com/microsoft/rStar.

Large language models (LLMs) are leading significant progress in code generation. Beyond one-pass code generation, recent works further integrate unit tests and program verifiers into LLMs to iteratively refine the generated programs. However, these works consider the generated programs as an indivisible entity, which falls short for LLMs in debugging the programs, especially when the programs contain complex logic flows and data operations. In contrast, when human developers debug programs, they typically set breakpoints and selectively examine runtime execution information. The execution flow and the intermediate variables play a crucial role in the debugging process, yet they are underutilized in the existing literature on code generation. In this study, we introduce Large Language Model Debugger (LDB), a novel debugging framework that enables LLMs to refine their generated programs with the runtime execution information. Specifically, LDB segments the programs into basic blocks and tracks the values of intermediate variables after each block throughout the runtime execution. This allows LLMs to concentrate on simpler code units within the overall execution flow, verify their correctness against the task description block by block, and efficiently pinpoint any potential errors. Experiments demonstrate that LDB consistently enhances the baseline performance by up to 9.8% across the HumanEval, MBPP, and TransCoder benchmarks, archiving new state-of-the-art performance in code debugging for various LLM selections.

Large language models have achieved remarkable success, but their extensive parameter size necessitates substantial memory for training, thereby setting a high threshold. While the recently proposed low-memory optimization (LOMO) reduces memory footprint, its optimization technique, akin to stochastic gradient descent, is sensitive to hyper-parameters and exhibits suboptimal convergence, failing to match the performance of the prevailing optimizer for large language models, AdamW. Through empirical analysis of the Adam optimizer, we found that, compared to momentum, the adaptive learning rate is more critical for bridging the gap. Building on this insight, we introduce the low-memory optimization with adaptive learning rate (AdaLomo), which offers an adaptive learning rate for each parameter. To maintain memory efficiency, we employ non-negative matrix factorization for the second-order moment estimation in the optimizer state. Additionally, we suggest the use of a grouped update normalization to stabilize convergence. Our experiments with instruction-tuning and further pre-training demonstrate that AdaLomo achieves results on par with AdamW, while significantly reducing memory requirements, thereby lowering the hardware barrier to training large language models.

LLMs have seen rapid adoption in all domains. They need to be trained on high-end high-performance computing (HPC) infrastructures and ingest massive amounts of input data. Unsurprisingly, at such a large scale, unexpected events (e.g., failures of components, instability of the software, undesirable learning patterns, etc.), are frequent and typically impact the training in a negative fashion. Thus, LLMs need to be checkpointed frequently so that they can be rolled back to a stable state and subsequently fine-tuned. However, given the large sizes of LLMs, a straightforward checkpointing solution that directly writes the model parameters and optimizer state to persistent storage (e.g., a parallel file system), incurs significant I/O overheads. To address this challenge, in this paper we study how to reduce the I/O overheads for enabling fast and scalable checkpointing for LLMs that can be applied at high frequency (up to the granularity of individual iterations) without significant impact on the training process. Specifically, we introduce a lazy asynchronous multi-level approach that takes advantage of the fact that the tensors making up the model and optimizer state shards remain immutable for extended periods of time, which makes it possible to copy their content in the background with minimal interference during the training process. We evaluate our approach at scales of up to 180 GPUs using different model sizes, parallelism settings, and checkpointing frequencies. The results show up to 48times faster checkpointing and 2.2times faster end-to-end training runtime compared with the state-of-art checkpointing approaches.

Self-Correction aims to enable large language models (LLMs) to self-verify and self-refine their initial responses without external feedback. However, LLMs often fail to effectively self-verify and generate correct feedback, further misleading refinement and leading to the failure of self-correction, especially in complex reasoning tasks. In this paper, we propose Program-driven Self-Correction (ProgCo). First, program-driven verification (ProgVe) achieves complex verification logic and extensive validation through self-generated, self-executing verification pseudo-programs. Then, program-driven refinement (ProgRe) receives feedback from ProgVe, conducts dual reflection and refinement on both responses and verification programs to mitigate misleading of incorrect feedback in complex reasoning tasks. Experiments on three instruction-following and mathematical benchmarks indicate that ProgCo achieves effective self-correction, and can be further enhance performance when combined with real program tools.

The application of large-language models (LLMs) to digital hardware code generation is an emerging field. Most LLMs are primarily trained on natural language and software code. Hardware code, such as Verilog, represents only a small portion of the training data and few hardware benchmarks exist. To address this gap, the open-source VerilogEval benchmark was released in 2023, providing a consistent evaluation framework for LLMs on code completion tasks. It was tested on state-of-the-art models at the time including GPT-4. However, VerilogEval and other Verilog generation benchmarks lack failure analysis and, in present form, are not conducive to exploring prompting techniques. Also, since VerilogEval's release, both commercial and open-source models have seen continued development. In this work, we evaluate new commercial and open-source models of varying sizes against an improved VerilogEval benchmark suite. We enhance VerilogEval's infrastructure and dataset by automatically classifying failures, introduce new prompts for supporting in-context learning (ICL) examples, and extend the supported tasks to specification-to-RTL translation. We find a measurable improvement in commercial state-of-the-art models, with GPT-4 Turbo achieving a 59% pass rate on spec-to-RTL tasks. We also study the performance of open-source and domain-specific models that have emerged, and demonstrate that models can benefit substantially from ICL. We find that recently-released Llama 3.1 405B achieves a pass rate of 58%, effectively matching that of GPT-4 Turbo, and that the much smaller domain-specific RTL-Coder 6.7B models achieve an impressive 37% pass rate. However, prompt engineering is key to achieving good pass rates, and varies widely with model and task. A benchmark infrastructure that allows for prompt engineering and failure analysis is key to continued model development and deployment.

Large Language Models (LLMs) are widely adopted for assisting in software development tasks, yet their performance evaluations have narrowly focused on the functional correctness of generated code. Human programmers, however, require LLM-generated code to be not only correct but also optimally efficient. We propose PerfCodeGen, a training-free framework that enhances the performance of LLM-generated code by incorporating feedback based on runtime during test case execution into the self-refinement iterations. With PerfCodeGen, we achieve speedups for a significantly higher proportion of problems compared to using the base LLM with sophisticated prompting techniques. Applied to open language models like Phi-3-mini, PerfCodeGen achieves runtime efficiency comparable to prompting powerful closed models like GPT-4. We achieve state-of-the-art runtime efficiency on benchmarks such as HumanEval, MBPP, and APPS, frequently surpassing the ground truth reference solutions with PerfCodeGen using GPT-3.5 and GPT-4. Additionally, we demonstrate the effectiveness of our approach in enhancing code quality across a range of open LLMs of varying sizes including Phi-3-mini, Llama 3 8B, Mixtral 8x7B, Command R, and Llama 3 70B.

Program synthesis with language models (LMs) has unlocked a large set of reasoning abilities; code-tuned LMs have proven adept at generating programs that solve a wide variety of algorithmic symbolic manipulation tasks (e.g. word concatenation). However, not all reasoning tasks are easily expressible as code, e.g. tasks involving commonsense reasoning, moral decision-making, and sarcasm understanding. Our goal is to extend an LM's program synthesis skills to such tasks and evaluate the results via pseudo-programs, namely Python programs where some leaf function calls are left undefined. To that end, we propose, Code Generation and Emulated EXecution (CoGEX). CoGEX works by (1) training LMs to generate their own pseudo-programs, (2) teaching them to emulate their generated program's execution, including those leaf functions, allowing the LM's knowledge to fill in the execution gaps; and (3) using them to search over many programs to find an optimal one. To adapt the CoGEX model to a new task, we introduce a method for performing program search to find a single program whose pseudo-execution yields optimal performance when applied to all the instances of a given dataset. We show that our approach yields large improvements compared to standard in-context learning approaches on a battery of tasks, both algorithmic and soft reasoning. This result thus demonstrates that code synthesis can be applied to a much broader class of problems than previously considered. Our released dataset, fine-tuned models, and implementation can be found at https://github.com/nweir127/CoGEX.

Recent advances in real-world applications of reinforcement learning (RL) have relied on the ability to accurately simulate systems at scale. However, domains such as fluid dynamical systems exhibit complex dynamic phenomena that are hard to simulate at high integration rates, limiting the direct application of modern deep RL algorithms to often expensive or safety critical hardware. In this work, we introduce "Box o Flows", a novel benchtop experimental control system for systematically evaluating RL algorithms in dynamic real-world scenarios. We describe the key components of the Box o Flows, and through a series of experiments demonstrate how state-of-the-art model-free RL algorithms can synthesize a variety of complex behaviors via simple reward specifications. Furthermore, we explore the role of offline RL in data-efficient hypothesis testing by reusing past experiences. We believe that the insights gained from this preliminary study and the availability of systems like the Box o Flows support the way forward for developing systematic RL algorithms that can be generally applied to complex, dynamical systems. Supplementary material and videos of experiments are available at https://sites.google.com/view/box-o-flows/home.

Large language models (LLMs) have demonstrated remarkable potential in solving complex tasks across diverse domains, typically by employing agentic workflows that follow detailed instructions and operational sequences. However, constructing these workflows requires significant human effort, limiting scalability and generalizability. Recent research has sought to automate the generation and optimization of these workflows, but existing methods still rely on initial manual setup and fall short of achieving fully automated and effective workflow generation. To address this challenge, we reformulate workflow optimization as a search problem over code-represented workflows, where LLM-invoking nodes are connected by edges. We introduce AFlow, an automated framework that efficiently explores this space using Monte Carlo Tree Search, iteratively refining workflows through code modification, tree-structured experience, and execution feedback. Empirical evaluations across six benchmark datasets demonstrate AFlow's efficacy, yielding a 5.7% average improvement over state-of-the-art baselines. Furthermore, AFlow enables smaller models to outperform GPT-4o on specific tasks at 4.55% of its inference cost in dollars. The code will be available at https://github.com/geekan/MetaGPT.

Large Language Models (LLMs) have exhibited an impressive ability to perform In-Context Learning (ICL) from only a few examples. Recent works have indicated that the functions learned by ICL can be represented through compressed vectors derived from the transformer. However, the working mechanisms and optimization of these vectors are yet to be thoroughly explored. In this paper, we address this gap by presenting a comprehensive analysis of these compressed vectors, drawing parallels to the parameters trained with gradient descent, and introduce the concept of state vector. Inspired by the works on model soup and momentum-based gradient descent, we propose inner and momentum optimization methods that are applied to refine the state vector progressively as test-time adaptation. Moreover, we simulate state vector aggregation in the multiple example setting, where demonstrations comprising numerous examples are usually too lengthy for regular ICL, and further propose a divide-and-conquer aggregation method to address this challenge. We conduct extensive experiments using Llama-2 and GPT-J in both zero-shot setting and few-shot setting. The experimental results show that our optimization method effectively enhances the state vector and achieves the state-of-the-art performance on diverse tasks. Code is available at https://github.com/HITsz-TMG/ICL-State-Vector

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

We present a trainable framework for efficiently generating gauge configurations, and discuss ongoing work in this direction. In particular, we consider the problem of sampling configurations from a 4D SU(3) lattice gauge theory, and consider a generalized leapfrog integrator in the molecular dynamics update that can be trained to improve sampling efficiency. Code is available online at https://github.com/saforem2/l2hmc-qcd.

The K-core of a graph is the unique maximum subgraph within which each vertex connects to at least K other vertices. The K-core optimal attack problem asks to construct a minimum-sized set of vertices whose removal results in the complete collapse of the K-core. In this paper, we construct a hierarchical cycle-tree packing model which converts a long-range correlated K-core pruning process into static patterns and analyze this model through the replica-symmetric (RS) cavity method of statistical physics. The cycle-tree guided attack (CTGA) message-passing algorithm exhibits superior performance on random regular and Erdos-Renyi graphs. It provides new upper bounds on the minimal cardinality of the K-core attack set. The model of this work may be extended to construct optimal initial conditions for other irreversible dynamical processes.

We present SmolTulu-1.7b-Instruct, referenced in this report as SmolTulu-DPO-1130, an instruction-tuned language model that adapts AllenAI's Tulu 3 post-training pipeline to enhance Huggingface's SmolLM2-1.7B base model. Through comprehensive empirical analysis using a 135M parameter model, we demonstrate that the relationship between learning rate and batch size significantly impacts model performance in a task-dependent manner. Our findings reveal a clear split: reasoning tasks like ARC and GSM8K benefit from higher learning rate to batch size ratios, while pattern recognition tasks such as HellaSwag and IFEval show optimal performance with lower ratios. These insights informed the development of SmolTulu, which achieves state-of-the-art performance among sub-2B parameter models on instruction following, scoring 67.7% on IFEval (Delta11%), and mathematical reasoning with 51.6% on GSM8K (Delta3.4%), with an alternate version achieving scoring 57.1% on ARC (Delta5.4%). We release our model, training recipes, and ablation studies to facilitate further research in efficient model alignment, demonstrating that careful adaptation of optimization dynamics can help bridge the capability gap between small and large language models.

AdamW has been the default optimizer for transformer pretraining. For many years, our community searches for faster and more stable optimizers with only constraint positive outcomes. In this work, we propose a single-line modification in Pytorch to any momentum-based optimizer, which we rename Cautious Optimizer, e.g. C-AdamW and C-Lion. Our theoretical result shows that this modification preserves Adam's Hamiltonian function and it does not break the convergence guarantee under the Lyapunov analysis. In addition, a whole new family of optimizers is revealed by our theoretical insight. Among them, we pick the simplest one for empirical experiments, showing speed-up on Llama and MAE pretraining up to 1.47times. Code is available at https://github.com/kyleliang919/C-Optim

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

We introduce self-invoking code generation, a new task designed to evaluate the progressive reasoning and problem-solving capabilities of LLMs. In this task, models are presented with a base problem and a related, more complex problem. They must solve the base problem and then utilize its solution to address the more complex one. This work features three key contributions. First, we propose a general recipe for generating more challenging versions of existing benchmarks, resulting in three new benchmarks: HumanEval Pro, MBPP Pro, and BigCodeBench-Lite Pro, specifically designed to assess LLMs on self-invoking code generation. Second, from the analysis of experimental results over twenty LLMs on our benchmarks, we have two important observations: (i) Most LLMs excel in traditional code generation benchmarks like HumanEval and MBPP, but their performance declines on self-invoking tasks. For example, o1-mini achieves 96.2% pass@1 on HumanEval but only 76.2% on HumanEval Pro. (ii) On self-invoking code generation task, the instruction-tuned models demonstrate only marginal improvements compared to the base models. Third, we disclose the types of failure modes that exist in our evaluation results. All these results underscore the need for further advancements in self-invoking code generation tasks and provide a new direction for future research on enhancing LLMs' code reasoning capabilities.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

Scaling model size significantly challenges the deployment and inference of Large Language Models (LLMs). Due to the redundancy in LLM weights, recent research has focused on pushing weight-only quantization to extremely low-bit (even down to 2 bits). It reduces memory requirements, optimizes storage costs, and decreases memory bandwidth needs during inference. However, due to numerical representation limitations, traditional scalar-based weight quantization struggles to achieve such extreme low-bit. Recent research on Vector Quantization (VQ) for LLMs has demonstrated the potential for extremely low-bit model quantization by compressing vectors into indices using lookup tables. In this paper, we introduce Vector Post-Training Quantization (VPTQ) for extremely low-bit quantization of LLMs. We use Second-Order Optimization to formulate the LLM VQ problem and guide our quantization algorithm design by solving the optimization. We further refine the weights using Channel-Independent Second-Order Optimization for a granular VQ. In addition, by decomposing the optimization problem, we propose a brief and effective codebook initialization algorithm. We also extend VPTQ to support residual and outlier quantization, which enhances model accuracy and further compresses the model. Our experimental results show that VPTQ reduces model quantization perplexity by 0.01-0.34 on LLaMA-2, 0.38-0.68 on Mistral-7B, 4.41-7.34 on LLaMA-3 over SOTA at 2-bit, with an average accuracy improvement of 0.79-1.5% on LLaMA-2, 1% on Mistral-7B, 11-22% on LLaMA-3 on QA tasks on average. We only utilize 10.4-18.6% of the quantization algorithm execution time, resulting in a 1.6-1.8times increase in inference throughput compared to SOTA.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

In multi-goal Reinforcement Learning, an agent can share experience between related training tasks, resulting in better generalization for new tasks at test time. However, when the goal space has discontinuities and the reward is sparse, a majority of goals are difficult to reach. In this context, a curriculum over goals helps agents learn by adapting training tasks to their current capabilities. In this work we propose Stein Variational Goal Generation (SVGG), which samples goals of intermediate difficulty for the agent, by leveraging a learned predictive model of its goal reaching capabilities. The distribution of goals is modeled with particles that are attracted in areas of appropriate difficulty using Stein Variational Gradient Descent. We show that SVGG outperforms state-of-the-art multi-goal Reinforcement Learning methods in terms of success coverage in hard exploration problems, and demonstrate that it is endowed with a useful recovery property when the environment changes.

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.