Daily Papers

In recent years, the rapid advancement of large-scale pre-trained language models based on transformer architectures has revolutionized natural language processing tasks. Among these, ChatGPT has gained widespread popularity, demonstrating human-level conversational abilities and attracting over 100 million monthly users by late 2022. Concurrently, Baidu's commercial deployment of the Ernie Wenxin model has significantly enhanced marketing effectiveness through AI-driven technologies. This paper focuses on optimizing high-performance inference for Ernie models, emphasizing GPU acceleration and leveraging the Paddle inference framework. We employ techniques such as Faster Transformer for efficient model processing, embedding layer pruning to reduce computational overhead, and FP16 half-precision inference for enhanced computational efficiency. Additionally, our approach integrates efficient data handling strategies using multi-process parallel processing to minimize latency. Experimental results demonstrate that our optimized solution achieves up to an 8.96x improvement in inference speed compared to standard methods, while maintaining competitive performance.

This paper presents the first comprehensive empirical study demonstrating the efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep Learning training across image classification, speech recognition, language modeling, generative networks and industrial recommendation systems. BFLOAT16 is attractive for Deep Learning training for two reasons: the range of values it can represent is the same as that of IEEE 754 floating-point format (FP32) and conversion to/from FP32 is simple. Maintaining the same range as FP32 is important to ensure that no hyper-parameter tuning is required for convergence; e.g., IEEE 754 compliant half-precision floating point (FP16) requires hyper-parameter tuning. In this paper, we discuss the flow of tensors and various key operations in mixed precision training, and delve into details of operations, such as the rounding modes for converting FP32 tensors to BFLOAT16. We have implemented a method to emulate BFLOAT16 operations in Tensorflow, Caffe2, IntelCaffe, and Neon for our experiments. Our results show that deep learning training using BFLOAT16 tensors achieves the same state-of-the-art (SOTA) results across domains as FP32 tensors in the same number of iterations and with no changes to hyper-parameters.

Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models also increases. We introduce a technique to train deep neural networks using half precision floating point numbers. In our technique, weights, activations and gradients are stored in IEEE half-precision format. Half-precision floating numbers have limited numerical range compared to single-precision numbers. We propose two techniques to handle this loss of information. Firstly, we recommend maintaining a single-precision copy of the weights that accumulates the gradients after each optimizer step. This single-precision copy is rounded to half-precision format during training. Secondly, we propose scaling the loss appropriately to handle the loss of information with half-precision gradients. We demonstrate that this approach works for a wide variety of models including convolution neural networks, recurrent neural networks and generative adversarial networks. This technique works for large scale models with more than 100 million parameters trained on large datasets. Using this approach, we can reduce the memory consumption of deep learning models by nearly 2x. In future processors, we can also expect a significant computation speedup using half-precision hardware units.

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision (16-bit floating points) and can be naturally extended to work with even lower precision such as 8-bit. Experimental results show that pre-training using Collage removes the requirement of using 32-bit floating-point copies of the model and attains similar/better training performance compared to (16, 32)-bit mixed-precision strategy, with up to 3.7times speedup and sim 15% to 23% less memory usage in practice.

The massive computational costs associated with large language model (LLM) pretraining have spurred great interest in reduced-precision floating-point representations to accelerate the process. As a result, the BrainFloat16 (BF16) precision has become the de facto standard for LLM training, with hardware support included in recent accelerators. This trend has gone even further in the latest processors, where FP8 has recently been introduced. However, prior experience with FP16, which was found to be less stable than BF16, raises concerns as to whether FP8, with even fewer bits than FP16, can be a cost-effective option for LLM training. We argue that reduced-precision training schemes must have similar training stability and hyperparameter sensitivities to their higher-precision counterparts in order to be cost-effective. However, we find that currently available methods for FP8 training are not robust enough to allow their use as economical replacements. This prompts us to investigate the stability of reduced-precision LLM training in terms of robustness across random seeds and learning rates. To this end, we propose new evaluation techniques and a new metric for quantifying loss landscape sharpness in autoregressive language models. By simulating incremental bit reductions in floating-point representations, we analyze the relationship between representational power and training stability with the intent of aiding future research into the field.

Six-bit quantization (FP6) can effectively reduce the size of large language models (LLMs) and preserve the model quality consistently across varied applications. However, existing systems do not provide Tensor Core support for FP6 quantization and struggle to achieve practical performance improvements during LLM inference. It is challenging to support FP6 quantization on GPUs due to (1) unfriendly memory access of model weights with irregular bit-width and (2) high runtime overhead of weight de-quantization. To address these problems, we propose TC-FPx, the first full-stack GPU kernel design scheme with unified Tensor Core support of float-point weights for various quantization bit-width. We integrate TC-FPx kernel into an existing inference system, providing new end-to-end support (called FP6-LLM) for quantized LLM inference, where better trade-offs between inference cost and model quality are achieved. Experiments show that FP6-LLM enables the inference of LLaMA-70b using only a single GPU, achieving 1.69x-2.65x higher normalized inference throughput than the FP16 baseline. The source code will be publicly available soon.

The state-of-the-art (SOTA) for mixed precision training is dominated by variants of low precision floating point operations, and in particular, FP16 accumulating into FP32 Micikevicius et al. (2017). On the other hand, while a lot of research has also happened in the domain of low and mixed-precision Integer training, these works either present results for non-SOTA networks (for instance only AlexNet for ImageNet-1K), or relatively small datasets (like CIFAR-10). In this work, we train state-of-the-art visual understanding neural networks on the ImageNet-1K dataset, with Integer operations on General Purpose (GP) hardware. In particular, we focus on Integer Fused-Multiply-and-Accumulate (FMA) operations which take two pairs of INT16 operands and accumulate results into an INT32 output.We propose a shared exponent representation of tensors and develop a Dynamic Fixed Point (DFP) scheme suitable for common neural network operations. The nuances of developing an efficient integer convolution kernel is examined, including methods to handle overflow of the INT32 accumulator. We implement CNN training for ResNet-50, GoogLeNet-v1, VGG-16 and AlexNet; and these networks achieve or exceed SOTA accuracy within the same number of iterations as their FP32 counterparts without any change in hyper-parameters and with a 1.8X improvement in end-to-end training throughput. To the best of our knowledge these results represent the first INT16 training results on GP hardware for ImageNet-1K dataset using SOTA CNNs and achieve highest reported accuracy using half-precision

FP8 is a natural progression for accelerating deep learning training inference beyond the 16-bit formats common in modern processors. In this paper we propose an 8-bit floating point (FP8) binary interchange format consisting of two encodings - E4M3 (4-bit exponent and 3-bit mantissa) and E5M2 (5-bit exponent and 2-bit mantissa). While E5M2 follows IEEE 754 conventions for representatio of special values, E4M3's dynamic range is extended by not representing infinities and having only one mantissa bit-pattern for NaNs. We demonstrate the efficacy of the FP8 format on a variety of image and language tasks, effectively matching the result quality achieved by 16-bit training sessions. Our study covers the main modern neural network architectures - CNNs, RNNs, and Transformer-based models, leaving all the hyperparameters unchanged from the 16-bit baseline training sessions. Our training experiments include large, up to 175B parameter, language models. We also examine FP8 post-training-quantization of language models trained using 16-bit formats that resisted fixed point int8 quantization.

The demand for inference on extremely large scale LLMs has seen enormous growth in the recent months. It made evident the colossal shortage of dedicated hardware capable of efficient and fast processing of the involved compute and memory movement. The problem is aggravated by the exploding raise in the lengths of the sequences being processed, since those require efficient on-chip storage of the KV-cache of size proportional to the sequence length. To make the required compute feasible and fit the involved data into available memory, numerous quantization techniques have been proposed that allow accurate quantization for both weights and activations. One of the main recent breakthroughs in this direction was introduction of the family of Block Floating Point (BFP) formats characterized by a block of mantissas with a shared scale factor. These enable memory- power-, and compute- efficient hardware support of the tensor operations and provide extremely good quantization accuracy. The main issues preventing widespread application of block formats is caused by the presence of outliers in weights and activations since those affect the accuracy of the other values in the same block. In this paper, we focus on the most critical problem of limited KV-cache storage. We propose a novel approach enabling usage of low precision BFP formats without compromising the resulting model accuracy. We exploit the common channel-wise patterns exhibited by the outliers to rearrange them in such a way, that their quantization quality is significantly improved. The methodology yields 2x savings in the memory footprint without significant degradation of the model's accuracy. Importantly, the rearrangement of channels happens at the compile time and thus has no impact on the inference latency.

Extreme edge platforms, such as in-vehicle smart devices, require efficient deployment of quantized deep neural networks (DNNs) to enable intelligent applications with limited amounts of energy, memory, and computing resources. However, many edge devices struggle to boost inference throughput of various quantized DNNs due to the varying quantization levels, and these devices lack floating-point (FP) support for on-device learning, which prevents them from improving model accuracy while ensuring data privacy. To tackle the challenges above, we propose a precision-scalable RISC-V DNN processor with on-device learning capability. It facilitates diverse precision levels of fixed-point DNN inference, spanning from 2-bit to 16-bit, and enhances on-device learning through improved support with FP16 operations. Moreover, we employ multiple methods such as FP16 multiplier reuse and multi-precision integer multiplier reuse, along with balanced mapping of FPGA resources, to significantly improve hardware resource utilization. Experimental results on the Xilinx ZCU102 FPGA show that our processor significantly improves inference throughput by 1.6sim14.6times and energy efficiency by 1.1sim14.6times across various DNNs, compared to the prior art, XpulpNN. Additionally, our processor achieves a 16.5times higher FP throughput for on-device learning.

Deep learning techniques are increasingly applied to scientific problems, where the precision of networks is crucial. Despite being deemed as universal function approximators, neural networks, in practice, struggle to reduce the prediction errors below O(10^{-5}) even with large network size and extended training iterations. To address this issue, we developed the multi-stage neural networks that divides the training process into different stages, with each stage using a new network that is optimized to fit the residue from the previous stage. Across successive stages, the residue magnitudes decreases substantially and follows an inverse power-law relationship with the residue frequencies. The multi-stage neural networks effectively mitigate the spectral biases associated with regular neural networks, enabling them to capture the high frequency feature of target functions. We demonstrate that the prediction error from the multi-stage training for both regression problems and physics-informed neural networks can nearly reach the machine-precision O(10^{-16}) of double-floating point within a finite number of iterations. Such levels of accuracy are rarely attainable using single neural networks alone.

The introduction of 8-bit floating-point (FP8) computation units in modern AI accelerators has generated significant interest in FP8-based large language model (LLM) inference. Unlike 16-bit floating-point formats, FP8 in deep learning requires a shared scaling factor. Additionally, while E4M3 and E5M2 are well-defined at the individual value level, their scaling and accumulation methods remain unspecified and vary across hardware and software implementations. As a result, FP8 behaves more like a quantization format than a standard numeric representation. In this work, we provide the first comprehensive analysis of FP8 computation and acceleration on two AI accelerators: the NVIDIA H100 and Intel Gaudi 2. Our findings highlight that the Gaudi 2, by leveraging FP8, achieves higher throughput-to-power efficiency during LLM inference, offering valuable insights into the practical implications of FP8 adoption for datacenter-scale LLM serving.

Recently, the idea of using FP8 as a number format for neural network training has been floating around the deep learning world. Given that most training is currently conducted with entire networks in FP32, or sometimes FP16 with mixed-precision, the step to having some parts of a network run in FP8 with 8-bit weights is an appealing potential speed-up for the generally costly and time-intensive training procedures in deep learning. A natural question arises regarding what this development means for efficient inference on edge devices. In the efficient inference device world, workloads are frequently executed in INT8. Sometimes going even as low as INT4 when efficiency calls for it. In this whitepaper, we compare the performance for both the FP8 and INT formats for efficient on-device inference. We theoretically show the difference between the INT and FP formats for neural networks and present a plethora of post-training quantization and quantization-aware-training results to show how this theory translates to practice. We also provide a hardware analysis showing that the FP formats are somewhere between 50-180% less efficient in terms of compute in dedicated hardware than the INT format. Based on our research and a read of the research field, we conclude that although the proposed FP8 format could be good for training, the results for inference do not warrant a dedicated implementation of FP8 in favor of INT8 for efficient inference. We show that our results are mostly consistent with previous findings but that important comparisons between the formats have thus far been lacking. Finally, we discuss what happens when FP8-trained networks are converted to INT8 and conclude with a brief discussion on the most efficient way for on-device deployment and an extensive suite of INT8 results for many models.

As recently demonstrated, Deep Neural Networks (DNN), usually trained using single precision IEEE 754 floating point numbers (binary32), can also work using lower precision. Therefore, 16-bit and 8-bit compressed format have attracted considerable attention. In this paper, we focused on two families of formats that have already achieved interesting results in compressing binary32 numbers in machine learning applications, without sensible degradation of the accuracy: bfloat and posit. Even if 16-bit and 8-bit bfloat/posit are routinely used for reducing the storage of the weights/biases of trained DNNs, the inference still often happens on the 32-bit FPU of the CPU (especially if GPUs are not available). In this paper we propose a way to decompress a tensor of bfloat/posits just before computations, i.e., after the compressed operands have been loaded within the vector registers of a vector capable CPU, in order to save bandwidth usage and increase cache efficiency. Finally, we show the architectural parameters and considerations under which this solution is advantageous with respect to the uncompressed one.

Post-Training Quantization (PTQ) is a powerful technique for model compression, reducing the precision of neural networks without additional training overhead. Recent works have investigated adopting 8-bit floating-point quantization (FP8) in the context of PTQ for model inference. However, the exploration of floating-point formats smaller than 8 bits and their comparison with integer quantization remains relatively limited. In this work, we present minifloats, which are reduced-precision floating-point formats capable of further reducing the memory footprint, latency, and energy cost of a model while approaching full-precision model accuracy. Our work presents a novel PTQ design-space exploration, comparing minifloat and integer quantization schemes across a range of 3 to 8 bits for both weights and activations. We examine the applicability of various PTQ techniques to minifloats, including weight equalization, bias correction, SmoothQuant, gradient-based learned rounding, and the GPTQ method. Our experiments validate the effectiveness of low-precision minifloats when compared to their integer counterparts across a spectrum of accuracy-precision trade-offs on a set of reference deep learning vision workloads. Finally, we evaluate our results against an FPGA-based hardware cost model, showing that integer quantization often remains the Pareto-optimal option, given its relatively smaller hardware resource footprint.

The recent surge of open-source large language models (LLMs) enables developers to create AI-based solutions while maintaining control over aspects such as privacy and compliance, thereby providing governance and ownership of the model deployment process. To utilize these LLMs, inference engines are needed. These engines load the model's weights onto available resources, such as GPUs, and process queries to generate responses. The speed of inference, or performance, of the LLM, is critical for real-time applications, as it computes millions or billions of floating point operations per inference. Recently, advanced inference engines such as vLLM have emerged, incorporating novel mechanisms such as efficient memory management to achieve state-of-the-art performance. In this paper, we analyze the performance, particularly the throughput (tokens generated per unit of time), of 20 LLMs using two inference libraries: vLLM and HuggingFace's pipelines. We investigate how various hyperparameters, which developers must configure, influence inference performance. Our results reveal that throughput landscapes are irregular, with distinct peaks, highlighting the importance of hyperparameter optimization to achieve maximum performance. We also show that applying hyperparameter optimization when upgrading or downgrading the GPU model used for inference can improve throughput from HuggingFace pipelines by an average of 9.16% and 13.7%, respectively.

This study examines 4-bit quantization methods like GPTQ in large language models (LLMs), highlighting GPTQ's overfitting and limited enhancement in Zero-Shot tasks. While prior works merely focusing on zero-shot measurement, we extend task scope to more generative categories such as code generation and abstractive summarization, in which we found that INT4 quantization can significantly underperform. However, simply shifting to higher precision formats like FP6 has been particularly challenging, thus overlooked, due to poor performance caused by the lack of sophisticated integration and system acceleration strategies on current AI hardware. Our results show that FP6, even with a coarse-grain quantization scheme, performs robustly across various algorithms and tasks, demonstrating its superiority in accuracy and versatility. Notably, with the FP6 quantization, \codestar-15B model performs comparably to its FP16 counterpart in code generation, and for smaller models like the 406M it closely matches their baselines in summarization. Neither can be achieved by INT4. To better accommodate various AI hardware and achieve the best system performance, we propose a novel 4+2 design for FP6 to achieve similar latency to the state-of-the-art INT4 fine-grain quantization. With our design, FP6 can become a promising solution to the current 4-bit quantization methods used in LLMs.

We propose LLM-FP4 for quantizing both weights and activations in large language models (LLMs) down to 4-bit floating-point values, in a post-training manner. Existing post-training quantization (PTQ) solutions are primarily integer-based and struggle with bit widths below 8 bits. Compared to integer quantization, floating-point (FP) quantization is more flexible and can better handle long-tail or bell-shaped distributions, and it has emerged as a default choice in many hardware platforms. One characteristic of FP quantization is that its performance largely depends on the choice of exponent bits and clipping range. In this regard, we construct a strong FP-PTQ baseline by searching for the optimal quantization parameters. Furthermore, we observe a high inter-channel variance and low intra-channel variance pattern in activation distributions, which adds activation quantization difficulty. We recognize this pattern to be consistent across a spectrum of transformer models designed for diverse tasks, such as LLMs, BERT, and Vision Transformer models. To tackle this, we propose per-channel activation quantization and show that these additional scaling factors can be reparameterized as exponential biases of weights, incurring a negligible cost. Our method, for the first time, can quantize both weights and activations in the LLaMA-13B to only 4-bit and achieves an average score of 63.1 on the common sense zero-shot reasoning tasks, which is only 5.8 lower than the full-precision model, significantly outperforming the previous state-of-the-art by 12.7 points. Code is available at: https://github.com/nbasyl/LLM-FP4.

In this paper, we explore FP8 low-bit data formats for efficient training of large language models (LLMs). Our key insight is that most variables, such as gradients and optimizer states, in LLM training can employ low-precision data formats without compromising model accuracy and requiring no changes to hyper-parameters. Specifically, we propose a new FP8 automatic mixed-precision framework for training LLMs. This framework offers three levels of FP8 utilization to streamline mixed-precision and distributed parallel training for LLMs. It gradually incorporates 8-bit gradients, optimizer states, and distributed learning in an incremental manner. Experiment results show that, during the training of GPT-175B model on H100 GPU platform, our FP8 mixed-precision training framework not only achieved a remarkable 42% reduction in real memory usage but also ran 64% faster than the widely adopted BF16 framework (i.e., Megatron-LM), surpassing the speed of Nvidia Transformer Engine by 17%. This largely reduces the training costs for large foundation models. Furthermore, our FP8 mixed-precision training methodology is generic. It can be seamlessly applied to other tasks such as LLM instruction tuning and reinforcement learning with human feedback, offering savings in fine-tuning expenses. Our FP8 low-precision training framework is open-sourced at {https://github.com/Azure/MS-AMP}{aka.ms/MS.AMP}.

Quantizing the activations of large language models (LLMs) has been a significant challenge due to the presence of structured outliers. Most existing methods focus on the per-token or per-tensor quantization of activations, making it difficult to achieve both accuracy and hardware efficiency. To address this problem, we propose OutlierTune, an efficient per-channel post-training quantization (PTQ) method for the activations of LLMs. OutlierTune consists of two components: pre-execution of dequantization and symmetrization. The pre-execution of dequantization updates the model weights by the activation scaling factors, avoiding the internal scaling and costly additional computational overheads brought by the per-channel activation quantization. The symmetrization further reduces the quantization differences arising from the weight updates by ensuring the balanced numerical ranges across different activation channels. OutlierTune is easy to implement and hardware-efficient, introducing almost no additional computational overheads during the inference. Extensive experiments show that the proposed framework outperforms existing methods across multiple different tasks. Demonstrating better generalization, this framework improves the Int6 quantization of the instruction-tuning LLMs, such as OPT-IML, to the same level as half-precision (FP16). Moreover, we have shown that the proposed framework is 1.48x faster than the FP16 implementation while reducing approximately 2x memory usage.

Large Mixture of Experts (MoE) models could achieve state-of-the-art quality on various language tasks, including machine translation task, thanks to the efficient model scaling capability with expert parallelism. However, it has brought a fundamental issue of larger memory consumption and increased memory bandwidth bottleneck at deployment time. In this paper, we propose Mixture of Quantized Experts (MoQE) which is a simple weight-only quantization method applying ultra low-bit down to 2-bit quantizations only to expert weights for mitigating the increased memory and latency issues of MoE models. We show that low-bit quantization together with the MoE architecture delivers a reliable model performance while reducing the memory size significantly even without any additional training in most cases. In particular, expert layers in MoE models are much more robust to the quantization than conventional feedforward networks (FFN) layers. In our comprehensive analysis, we show that MoE models with 2-bit expert weights can deliver better model performance than the dense model trained on the same dataset. As a result of low-bit quantization, we show the model size can be reduced by 79.6% of the original half precision floating point (fp16) MoE model. Combined with an optimized GPU runtime implementation, it also achieves 1.24X speed-up on A100 GPUs.

The growing computational demands of training large language models (LLMs) necessitate more efficient methods. Quantized training presents a promising solution by enabling low-bit arithmetic operations to reduce these costs. While FP8 precision has demonstrated feasibility, leveraging FP4 remains a challenge due to significant quantization errors and limited representational capacity. This work introduces the first FP4 training framework for LLMs, addressing these challenges with two key innovations: a differentiable quantization estimator for precise weight updates and an outlier clamping and compensation strategy to prevent activation collapse. To ensure stability, the framework integrates a mixed-precision training scheme and vector-wise quantization. Experimental results demonstrate that our FP4 framework achieves accuracy comparable to BF16 and FP8, with minimal degradation, scaling effectively to 13B-parameter LLMs trained on up to 100B tokens. With the emergence of next-generation hardware supporting FP4, our framework sets a foundation for efficient ultra-low precision training.

When quantizing neural networks for efficient inference, low-bit integers are the go-to format for efficiency. However, low-bit floating point numbers have an extra degree of freedom, assigning some bits to work on an exponential scale instead. This paper in-depth investigates this benefit of the floating point format for neural network inference. We detail the choices that can be made for the FP8 format, including the important choice of the number of bits for the mantissa and exponent, and show analytically in which settings these choices give better performance. Then we show how these findings translate to real networks, provide an efficient implementation for FP8 simulation, and a new algorithm that enables the learning of both the scale parameters and the number of exponent bits in the FP8 format. Our chief conclusion is that when doing post-training quantization for a wide range of networks, the FP8 format is better than INT8 in terms of accuracy, and the choice of the number of exponent bits is driven by the severity of outliers in the network. We also conduct experiments with quantization-aware training where the difference in formats disappears as the network is trained to reduce the effect of outliers.

We present unit scaling, a paradigm for designing deep learning models that simplifies the use of low-precision number formats. Training in FP16 or the recently proposed FP8 formats offers substantial efficiency gains, but can lack sufficient range for out-of-the-box training. Unit scaling addresses this by introducing a principled approach to model numerics: seeking unit variance of all weights, activations and gradients at initialisation. Unlike alternative methods, this approach neither requires multiple training runs to find a suitable scale nor has significant computational overhead. We demonstrate the efficacy of unit scaling across a range of models and optimisers. We further show that existing models can be adapted to be unit-scaled, training BERT-Large in FP16 and then FP8 with no degradation in accuracy.

We train, for the first time, large language models using FP8 precision on datasets up to 2 trillion tokens -- a 20-fold increase over previous limits. Through these extended training runs, we uncover critical instabilities in FP8 training that were not observable in earlier works with shorter durations. We trace these instabilities to outlier amplification by the SwiGLU activation function. Interestingly, we show, both analytically and empirically, that this amplification happens only over prolonged training periods, and link it to a SwiGLU weight alignment process. To address this newly identified issue, we introduce Smooth-SwiGLU, a novel modification that ensures stable FP8 training without altering function behavior. We also demonstrate, for the first time, FP8 quantization of both Adam optimizer moments. Combining these innovations, we successfully train a 7B parameter model using FP8 precision on 256 Intel Gaudi2 accelerators, achieving on-par results with the BF16 baseline while delivering up to a sim 34 % throughput improvement.

The burgeoning computational demands for training large language models (LLMs) necessitate efficient methods, including quantized training, which leverages low-bit arithmetic operations to reduce costs. While FP8 precision has shown potential, leveraging FP4 remains challenging due to inherent quantization errors and limited representation capability. Based on the Transformer architecture, we present an FP4 training scheme for LLMs, overcoming these obstacles through mixed-precision quantization strategies tailed for different modules and training stages. This allows us to apply the precision level suitable to distinct components within the model, ensuring that multi-head attention and linear layers are handled appropriately. Our pretraining recipe ensures stability in backpropagation by incorporating fine-grained quantization methods with a target precision training schedule. Experimental results demonstrate that our FP4 training scheme achieves accuracy comparable to BF16 and FP8, with smaller theoretical computational cost. With the advent of next-generation hardware supporting FP4, our method sets the foundation for efficient ultra-low precision training.

LLM inference for popular enterprise use cases, such as summarization, RAG, and code-generation, typically observes orders of magnitude longer prompt lengths than generation lengths. This characteristic leads to high cost of prefill and increased response latency. In this paper, we present SwiftKV, a novel model transformation and distillation procedure specifically designed to reduce the time and cost of processing prompt tokens while preserving high quality of generated tokens. SwiftKV combines three key mechanisms: i) SingleInputKV, which prefills later layers' KV cache using a much earlier layer's output, allowing prompt tokens to skip much of the model computation, ii) AcrossKV, which merges the KV caches of neighboring layers to reduce the memory footprint and support larger batch size for higher throughput, and iii) a knowledge-preserving distillation procedure that can adapt existing LLMs for SwiftKV with minimal accuracy impact and low compute and data requirement. For Llama-3.1-8B and 70B, SwiftKV reduces the compute requirement of prefill by 50% and the memory requirement of the KV cache by 62.5% while incurring minimum quality degradation across a wide range of tasks. In the end-to-end inference serving using an optimized vLLM implementation, SwiftKV realizes up to 2x higher aggregate throughput and 60% lower time per output token. It can achieve a staggering 560 TFlops/GPU of normalized inference throughput, which translates to 16K tokens/s for Llama-3.1-70B in 16-bit precision on 4x H100 GPUs.

Quantization is a widely-used compression technology to reduce the overhead of serving large language models (LLMs) on terminal devices and in cloud data centers. However, prevalent quantization methods, such as 8-bit weight-activation or 4-bit weight-only quantization, achieve limited performance improvements due to poor support for low-precision (e.g., 4-bit) activation. This work, for the first time, realizes practical W4A4KV4 serving for LLMs, fully utilizing the INT4 tensor cores on modern GPUs and reducing the memory bottleneck caused by the KV cache. Specifically, we propose a novel fine-grained mixed-precision quantization algorithm (FMPQ) that compresses most activations into 4-bit with negligible accuracy loss. To support mixed-precision matrix multiplication for W4A4 and W4A8, we develop a highly optimized W4Ax kernel. Our approach introduces a novel mixed-precision data layout to facilitate access and fast dequantization for activation and weight tensors, utilizing the GPU's software pipeline to hide the overhead of data loading and conversion. Additionally, we propose fine-grained streaming multiprocessor (SM) scheduling to achieve load balance across different SMs. We integrate the optimized W4Ax kernel into our inference framework, COMET, and provide efficient management to support popular LLMs such as LLaMA-3-70B. Extensive evaluations demonstrate that, when running LLaMA family models on a single A100-80G-SMX4, COMET achieves a kernel-level speedup of 2.88times over cuBLAS and a 2.02 times throughput improvement compared to TensorRT-LLM from an end-to-end framework perspective.

Post-training quantization is the leading method for addressing memory-related bottlenecks in LLM inference, but unfortunately, it suffers from significant performance degradation below 4-bit precision. An alternative approach involves training compressed models directly at a low bitwidth (e.g., binary or ternary models). However, the performance, training dynamics, and scaling trends of such models are not yet well understood. To address this issue, we train and openly release the Spectra LLM suite consisting of 54 language models ranging from 99M to 3.9B parameters, trained on 300B tokens. Spectra includes FloatLMs, post-training quantized QuantLMs (3, 4, 6, and 8 bits), and ternary LLMs (TriLMs) - our improved architecture for ternary language modeling, which significantly outperforms previously proposed ternary models of a given size (in bits), matching half-precision models at scale. For example, TriLM 3.9B is (bit-wise) smaller than the half-precision FloatLM 830M, but matches half-precision FloatLM 3.9B in commonsense reasoning and knowledge benchmarks. However, TriLM 3.9B is also as toxic and stereotyping as FloatLM 3.9B, a model six times larger in size. Additionally, TriLM 3.9B lags behind FloatLM in perplexity on validation splits and web-based corpora but performs better on less noisy datasets like Lambada and PennTreeBank. To enhance understanding of low-bitwidth models, we are releasing 500+ intermediate checkpoints of the Spectra suite at https://github.com/NolanoOrg/SpectraSuite{https://github.com/NolanoOrg/SpectraSuite}.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Transformer based models, like BERT and RoBERTa, have achieved state-of-the-art results in many Natural Language Processing tasks. However, their memory footprint, inference latency, and power consumption are prohibitive efficient inference at the edge, and even at the data center. While quantization can be a viable solution for this, previous work on quantizing Transformer based models use floating-point arithmetic during inference, which cannot efficiently utilize integer-only logical units such as the recent Turing Tensor Cores, or traditional integer-only ARM processors. In this work, we propose I-BERT, a novel quantization scheme for Transformer based models that quantizes the entire inference with integer-only arithmetic. Based on lightweight integer-only approximation methods for nonlinear operations, e.g., GELU, Softmax, and Layer Normalization, I-BERT performs an end-to-end integer-only BERT inference without any floating point calculation. We evaluate our approach on GLUE downstream tasks using RoBERTa-Base/Large. We show that for both cases, I-BERT achieves similar (and slightly higher) accuracy as compared to the full-precision baseline. Furthermore, our preliminary implementation of I-BERT shows a speedup of 2.4-4.0x for INT8 inference on a T4 GPU system as compared to FP32 inference. The framework has been developed in PyTorch and has been open-sourced.

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point quantization and thus cannot well fit the LLM losses in this scenario. In contrast, while floating-point quantization training is more commonly implemented in production, the research on it has been relatively superficial. In this paper, we thoroughly explore the effects of floating-point quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in floating-point quantization training performance of LLM models. While presenting an accurate floating-point quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal floating-point quantization precision is directly proportional to the computational power, but within a wide computational power range, we estimate that the best cost-performance precision lies between 4-8 bits.

Recently developed large language models (LLMs) such as ChatGPT, Claude, and Llama have demonstrated impressive abilities, and even surpass human-level performance in several tasks. Despite their success, the resource-intensive demands of these models, requiring significant computational power for both training and inference, limit their deployment to high-performance servers. Additionally, the extensive calculation requirements of the models often lead to increased latency in response times. With the increasing need for LLMs to operate efficiently on CPUs, research about lightweight models that are optimized for CPU inference has emerged. In this work, we introduce GEB-1.3B, a lightweight LLM trained on 550 billion tokens in both Chinese and English languages. We employ novel training techniques, including ROPE, Group-Query-Attention, and FlashAttention-2, to accelerate training while maintaining model performance. Additionally, we fine-tune the model using 10 million samples of instruction data to enhance alignment. GEB-1.3B exhibits outstanding performance on general benchmarks such as MMLU, C-Eval, and CMMLU, outperforming comparative models such as MindLLM-1.3B and TinyLLaMA-1.1B. Notably, the FP32 version of GEB-1.3B achieves commendable inference times on CPUs, with ongoing efforts to further enhance speed through advanced quantization techniques. The release of GEB-1.3B as an open-source model marks a significant contribution to the development of lightweight LLMs, promising to foster further research and innovation in the field.

As large language models gain widespread adoption, running them efficiently becomes crucial. Recent works on LLM inference use speculative decoding to achieve extreme speedups. However, most of these works implicitly design their algorithms for high-end datacenter hardware. In this work, we ask the opposite question: how fast can we run LLMs on consumer machines? Consumer GPUs can no longer fit the largest available models (50B+ parameters) and must offload them to RAM or SSD. When running with offloaded parameters, the inference engine can process batches of hundreds or thousands of tokens at the same time as just one token, making it a natural fit for speculative decoding. We propose SpecExec (Speculative Execution), a simple parallel decoding method that can generate up to 20 tokens per target model iteration for popular LLM families. It utilizes the high spikiness of the token probabilities distribution in modern LLMs and a high degree of alignment between model output probabilities. SpecExec takes the most probable tokens continuation from the draft model to build a "cache" tree for the target model, which then gets validated in a single pass. Using SpecExec, we demonstrate inference of 50B+ parameter LLMs on consumer GPUs with RAM offloading at 4-6 tokens per second with 4-bit quantization or 2-3 tokens per second with 16-bit weights.

The large language model era urges faster and less costly inference. Prior model compression works on LLMs tend to undertake a software-centric approach primarily focused on the simulated quantization performance. By neglecting the feasibility of deployment, these approaches are typically disabled in real practice. They used to drastically push down the quantization bit range for a reduced computation which might not be supported by the mainstream hardware, or involve sophisticated algorithms that introduce extra computation or memory access overhead. We argue that pursuing a hardware-centric approach in the construction of quantization algorithms is crucial. In this regard, we are driven to build our compression method on top of hardware awareness, eliminating impractical algorithm choices while maximizing the benefit of hardware acceleration. Our method, OdysseyLLM, comes with a novel W4A8 kernel implementation called FastGEMM and a combined recipe of quantization strategies. Extensive experiments manifest the superiority of our W4A8 method which brings the actual speed boosting up to 4times compared to Hugging Face FP16 inference and 2.23times vs. the state-of-the-art inference engine TensorRT-LLM in FP16, and 1.45times vs. TensorRT-LLM in INT8, yet without substantially harming the performance.

In the complex domain of large language models (LLMs), striking a balance between computational efficiency and maintaining model quality is a formidable challenge. Navigating the inherent limitations of uniform quantization, particularly when dealing with outliers, and motivated by the launch of NVIDIA's H100 hardware, this study delves into the viability of floating-point (FP) quantization, particularly focusing on FP8 and FP4, as a potential solution. Our comprehensive investigation reveals that for LLMs, FP8 activation consistently outshines its integer (INT8) equivalent, with the performance edge becoming more noticeable in models possessing parameters beyond one billion. For weight quantization, our findings indicate that FP4 exhibits comparable, if not superior, performance to INT4, simplifying deployment on FP-supported hardware like H100. To mitigate the overhead from precision alignment caused by the disparity between weights and activations, we propose two scaling constraints for weight quantization that negligibly impact the performance compared to the standard W4A8 model. We additionally enhance our quantization methods by integrating the Low Rank Compensation (LoRC) strategy, yielding improvements especially in smaller models. The results of our investigation emphasize the immense potential of FP quantization for LLMs, paving the way for high-efficiency deployment in resource-limited settings.

Large language models (LLMs) are rapidly increasing in size, with the number of parameters becoming a key factor in the success of many commercial models, such as ChatGPT, Claude, and Bard. Even the recently released publicly accessible models for commercial usage, such as Falcon and Llama2, come equipped with billions of parameters. This significant increase in the number of parameters makes deployment and operation very costly. The remarkable progress in the field of quantization for large neural networks in general and LLMs in particular, has made these models more accessible by enabling them to be deployed on consumer-grade GPUs. Quantized models generally demonstrate comparable performance levels to their unquantized base counterparts. Nonetheless, there exists a notable gap in our comprehensive understanding of how these quantized models respond to hyperparameters, such as temperature, max new tokens, and topk, particularly for next word prediction. The present analysis reveals that nf4 and fp4 are equally proficient 4-bit quantization techniques, characterized by similar attributes such as inference speed, memory consumption, and the quality of generated content. the study identifies nf4 as displaying greater resilience to temperature variations in the case of the llama2 series of models at lower temperature, while fp4 and fp4-dq proves to be a more suitable choice for falcon series of models. It is noteworthy that, in general, 4-bit quantized models of varying sizes exhibit higher sensitivity to temperature in the range of 0.5 to 0.8, unlike their unquantized counterparts. Additionally, int8 quantization is associated with significantly slower inference speeds, whereas unquantized bfloat16 models consistently yield the fastest inference speeds across models of all sizes.

The deployment of Large Language Models (LLMs) on edge devices is increasingly important to enhance on-device intelligence. Weight quantization is crucial for reducing the memory footprint of LLMs on devices. However, low-bit LLMs necessitate mixed precision matrix multiplication (mpGEMM) of low precision weights and high precision activations during inference. Existing systems, lacking native support for mpGEMM, resort to dequantize weights for high precision computation. Such an indirect way can lead to a significant inference overhead. In this paper, we introduce T-MAC, an innovative lookup table(LUT)-based method designed for efficient low-bit LLM (i.e., weight-quantized LLM) inference on CPUs. T-MAC directly supports mpGEMM without dequantization, while simultaneously eliminating multiplications and reducing additions required. Specifically, T-MAC transforms the traditional data-type-centric multiplication to bit-wise table lookup, and enables a unified and scalable mpGEMM solution. Our LUT-based kernels scale linearly to the weight bit-width. Evaluated on low-bit Llama and BitNet models, T-MAC demonstrates up to 4x increase in throughput and 70% reduction in energy consumption compared to llama.cpp. For BitNet-b1.58-3B, T-MAC delivers a token generation throughput of 30 tokens/s with a single core and 71 tokens/s with eight cores on M2-Ultra, and 11 tokens/s on lower-end devices like Raspberry Pi 5, which significantly exceeds the adult average reading speed. T-MAC with LUT-based computing paradigm, paves the way for the practical deployment of low-bit LLMs on resource-constrained edge devices without compromising computational efficiency. The system is open-sourced at https://github.com/microsoft/T-MAC.

Quantization methods reduce the number of bits required to represent each parameter in a model, trading accuracy for smaller memory footprints and inference latencies. However, the final model size depends on both the number of parameters of the original model and the rate of compression. For example, a 30B 8-bit model and a 60B 4-bit model have the same number of bits but may have very different zero-shot accuracies. In this work, we study this trade-off by developing inference scaling laws of zero-shot performance in Large Language Models (LLMs) to determine the bit-precision and model size that maximizes zero-shot performance. We run more than 35,000 experiments with 16-bit inputs and k-bit parameters to examine which zero-shot quantization methods improve scaling for 3 to 8-bit precision at scales of 19M to 176B parameters across the LLM families BLOOM, OPT, NeoX/Pythia, and GPT-2. We find that it is challenging to improve the bit-level scaling trade-off, with the only improvements being the use of a small block size -- splitting the parameters into small independently quantized blocks -- and the quantization data type being used (e.g., Int vs Float). Overall, our findings show that {4-bit} precision is almost universally optimal for total model bits and zero-shot accuracy.

The recent rise of large language models (LLMs) has resulted in increased efforts towards running LLMs at reduced precision. Running LLMs at lower precision supports resource constraints and furthers their democratization, enabling users to run billion-parameter LLMs on their personal devices. To supplement this ongoing effort, we propose INT-FP-QSim: an open-source simulator that enables flexible evaluation of LLMs and vision transformers at various numerical precisions and formats. INT-FP-QSim leverages existing open-source repositories such as TensorRT, QPytorch and AIMET for a combined simulator that supports various floating point and integer formats. With the help of our simulator, we survey the impact of different numerical formats on the performance of LLMs and vision transformers at 4-bit weights and 4-bit or 8-bit activations. We also compare recently proposed methods like Adaptive Block Floating Point, SmoothQuant, GPTQ and RPTQ on the model performances. We hope INT-FP-QSim will enable researchers to flexibly simulate models at various precisions to support further research in quantization of LLMs and vision transformers.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing to tune various hyperparameters, reduce model scale, or accept the overhead of computing dynamic scale factors. We demonstrate simple, scalable FP8 training that requires no dynamic scaling factors or special hyperparameters, even at large model sizes. Our method, munit Scaling (muS), also enables simple hyperparameter transfer across model widths, matched numerics across training and inference, and other desirable properties. munit Scaling is straightforward to implement, consisting of a set of minimal interventions based on a first-principles analysis of common transformer operations. We validate our method by training models from 1B to 13B parameters, performing all hidden linear layer computations in FP8. We achieve quality equal to higher precision baselines while also training up to 33% faster.

Large language models (LLMs) show great performance in various tasks, but face deployment challenges from limited memory capacity and bandwidth. Low-bit weight quantization can save memory and accelerate inference. Although floating-point (FP) formats show good performance in LLM quantization, they tend to perform poorly with small group sizes or sub-4 bits. We find the reason is that the absence of asymmetry in previous FP quantization makes it unsuitable for handling asymmetric value distribution of LLM weight tensors. In this work, we propose asymmetric FP quantization (AFPQ), which sets separate scales for positive and negative values. Our method leads to large accuracy improvements and can be easily plugged into other quantization methods, including GPTQ and AWQ, for better performance. Besides, no additional storage is needed compared with asymmetric integer (INT) quantization. The code is available at https://github.com/zhangsichengsjtu/AFPQ.

Current low-precision quantization algorithms often have the hidden cost of conversion back and forth from floating point to quantized integer values. This hidden cost limits the latency improvement realized by quantizing Neural Networks. To address this, we present HAWQV3, a novel mixed-precision integer-only quantization framework. The contributions of HAWQV3 are the following: (i) An integer-only inference where the entire computational graph is performed only with integer multiplication, addition, and bit shifting, without any floating point operations or even integer division; (ii) A novel hardware-aware mixed-precision quantization method where the bit-precision is calculated by solving an integer linear programming problem that balances the trade-off between model perturbation and other constraints, e.g., memory footprint and latency; (iii) Direct hardware deployment and open source contribution for 4-bit uniform/mixed-precision quantization in TVM, achieving an average speed up of 1.45times for uniform 4-bit, as compared to uniform 8-bit for ResNet50 on T4 GPUs; and (iv) extensive evaluation of the proposed methods on ResNet18/50 and InceptionV3, for various model compression levels with/without mixed precision. For ResNet50, our INT8 quantization achieves an accuracy of 77.58%, which is 2.68% higher than prior integer-only work, and our mixed-precision INT4/8 quantization can reduce INT8 latency by 23% and still achieve 76.73% accuracy. Our framework and the TVM implementation have been open sourced.

This research aims to accelerate the inference speed of large language models (LLMs) with billions of parameters. We propose Smart Parallel Auto-Correct dEcoding (SPACE), an innovative approach designed for achieving lossless acceleration of LLMs. By integrating semi-autoregressive inference and speculative decoding capabilities, SPACE uniquely enables autoregressive LLMs to parallelize token generation and verification. This is realized through a specialized semi-autoregressive supervised fine-tuning process that equips existing LLMs with the ability to simultaneously predict multiple tokens. Additionally, an auto-correct decoding algorithm facilitates the simultaneous generation and verification of token sequences within a single model invocation. Through extensive experiments on a range of LLMs, SPACE has demonstrated inference speedup ranging from 2.7x-4.0x on HumanEval-X while maintaining output quality.

Large language models have been widely adopted but require significant GPU memory for inference. We develop a procedure for Int8 matrix multiplication for feed-forward and attention projection layers in transformers, which cut the memory needed for inference by half while retaining full precision performance. With our method, a 175B parameter 16/32-bit checkpoint can be loaded, converted to Int8, and used immediately without performance degradation. This is made possible by understanding and working around properties of highly systematic emergent features in transformer language models that dominate attention and transformer predictive performance. To cope with these features, we develop a two-part quantization procedure, LLM.int8(). We first use vector-wise quantization with separate normalization constants for each inner product in the matrix multiplication, to quantize most of the features. However, for the emergent outliers, we also include a new mixed-precision decomposition scheme, which isolates the outlier feature dimensions into a 16-bit matrix multiplication while still more than 99.9% of values are multiplied in 8-bit. Using LLM.int8(), we show empirically it is possible to perform inference in LLMs with up to 175B parameters without any performance degradation. This result makes such models much more accessible, for example making it possible to use OPT-175B/BLOOM on a single server with consumer GPUs. We open-source our software.

Low precision training and inference affect both the quality and cost of language models, but current scaling laws do not account for this. In this work, we devise "precision-aware" scaling laws for both training and inference. We propose that training in lower precision reduces the model's "effective parameter count," allowing us to predict the additional loss incurred from training in low precision and post-train quantization. For inference, we find that the degradation introduced by post-training quantization increases as models are trained on more data, eventually making additional pretraining data actively harmful. For training, our scaling laws allow us to predict the loss of a model with different parts in different precisions, and suggest that training larger models in lower precision may be compute optimal. We unify the scaling laws for post and pretraining quantization to arrive at a single functional form that predicts degradation from training and inference in varied precisions. We fit on over 465 pretraining runs and validate our predictions on model sizes up to 1.7B parameters trained on up to 26B tokens.

The past several years have witnessed the success of transformer-based models, and their scale and application scenarios continue to grow aggressively. The current landscape of transformer models is increasingly diverse: the model size varies drastically with the largest being of hundred-billion parameters; the model characteristics differ due to the sparsity introduced by the Mixture-of-Experts; the target application scenarios can be latency-critical or throughput-oriented; the deployment hardware could be single- or multi-GPU systems with different types of memory and storage, etc. With such increasing diversity and the fast-evolving pace of transformer models, designing a highly performant and efficient inference system is extremely challenging. In this paper, we present DeepSpeed Inference, a comprehensive system solution for transformer model inference to address the above-mentioned challenges. DeepSpeed Inference consists of (1) a multi-GPU inference solution to minimize latency while maximizing the throughput of both dense and sparse transformer models when they fit in aggregate GPU memory, and (2) a heterogeneous inference solution that leverages CPU and NVMe memory in addition to the GPU memory and compute to enable high inference throughput with large models which do not fit in aggregate GPU memory. DeepSpeed Inference reduces latency by up to 7.3X over the state-of-the-art for latency-oriented scenarios and increases throughput by over 1.5x for throughput-oriented scenarios. Moreover, it enables trillion parameter scale inference under real-time latency constraints by leveraging hundreds of GPUs, an unprecedented scale for inference. It can inference 25x larger models than with GPU-only solutions, while delivering a high throughput of 84 TFLOPS (over 50% of A6000 peak).

Quantization emerges as one of the most promising approaches for deploying advanced deep models on resource-constrained hardware. Mixed-precision quantization leverages multiple bit-width architectures to unleash the accuracy and efficiency potential of quantized models. However, existing mixed-precision quantization suffers exhaustive search space that causes immense computational overhead. The quantization process thus relies on separate high-performance devices rather than locally, which also leads to a significant gap between the considered hardware metrics and the real deployment.In this paper, we propose an On-chip Hardware-aware Quantization (OHQ) framework that performs hardware-aware mixed-precision quantization without accessing online devices. First, we construct the On-chip Quantization Awareness (OQA) pipeline, enabling perceive the actual efficiency metrics of the quantization operator on the hardware.Second, we propose Mask-guided Quantization Estimation (MQE) technique to efficiently estimate the accuracy metrics of operators under the constraints of on-chip-level computing power.By synthesizing network and hardware insights through linear programming, we obtain optimized bit-width configurations. Notably, the quantization process occurs on-chip entirely without any additional computing devices and data access. We demonstrate accelerated inference after quantization for various architectures and compression ratios, achieving 70% and 73% accuracy for ResNet-18 and MobileNetV3, respectively. OHQ improves latency by 15~30% compared to INT8 on deployment.

Quantized training of Large Language Models (LLMs) remains an open challenge, as maintaining accuracy while performing all matrix multiplications in low precision has proven difficult. This is particularly the case when fine-tuning pre-trained models, which often already have large weight and activation outlier values that render quantized optimization difficult. We present HALO, a novel quantization-aware training approach for Transformers that enables accurate and efficient low-precision training by combining 1) strategic placement of Hadamard rotations in both forward and backward passes, to mitigate outliers during the low-precision computation, 2) FSDP integration for low-precision communication, and 3) high-performance kernel support. Our approach ensures that all large matrix multiplications during the forward and backward passes are executed in lower precision. Applied to LLAMA-family models, HALO achieves near-full-precision-equivalent results during fine-tuning on various tasks, while delivering up to 1.31x end-to-end speedup for full fine-tuning on RTX 4090 GPUs. Our method supports both standard and parameter-efficient fine-tuning (PEFT) methods, both backed by efficient kernel implementations. Our results demonstrate the first practical approach to fully quantized LLM fine-tuning that maintains accuracy in FP8 precision, while delivering performance benefits.

We present miniF2F, a dataset of formal Olympiad-level mathematics problems statements intended to provide a unified cross-system benchmark for neural theorem proving. The miniF2F benchmark currently targets Metamath, Lean, Isabelle (partially) and HOL Light (partially) and consists of 488 problem statements drawn from the AIME, AMC, and the International Mathematical Olympiad (IMO), as well as material from high-school and undergraduate mathematics courses. We report baseline results using GPT-f, a neural theorem prover based on GPT-3 and provide an analysis of its performance. We intend for miniF2F to be a community-driven effort and hope that our benchmark will help spur advances in neural theorem proving.

The optimal training configurations of large language models (LLMs) with respect to model sizes and compute budgets have been extensively studied. But how to optimally configure LLMs during inference has not been explored in sufficient depth. We study compute-optimal inference: designing models and inference strategies that optimally trade off additional inference-time compute for improved performance. As a first step towards understanding and designing compute-optimal inference methods, we assessed the effectiveness and computational efficiency of multiple inference strategies such as Greedy Search, Majority Voting, Best-of-N, Weighted Voting, and their variants on two different Tree Search algorithms, involving different model sizes and computational budgets. We found that a smaller language model with a novel tree search algorithm typically achieves a Pareto-optimal trade-off. These results highlight the potential benefits of deploying smaller models equipped with more sophisticated decoding algorithms in budget-constrained scenarios, e.g., on end-devices, to enhance problem-solving accuracy. For instance, we show that the Llemma-7B model can achieve competitive accuracy to a Llemma-34B model on MATH500 while using 2times less FLOPs. Our findings could potentially apply to any generation task with a well-defined measure of success.

Inference of Large Language Models (LLMs) across computer clusters has become a focal point of research in recent times, with many acceleration techniques taking inspiration from CPU speculative execution. These techniques reduce bottlenecks associated with memory bandwidth, but also increase end-to-end latency per inference run, requiring high speculation acceptance rates to improve performance. Combined with a variable rate of acceptance across tasks, speculative inference techniques can result in reduced performance. Additionally, pipeline-parallel designs require many user requests to maintain maximum utilization. As a remedy, we propose PipeInfer, a pipelined speculative acceleration technique to reduce inter-token latency and improve system utilization for single-request scenarios while also improving tolerance to low speculation acceptance rates and low-bandwidth interconnects. PipeInfer exhibits up to a 2.15times improvement in generation speed over standard speculative inference. PipeInfer achieves its improvement through Continuous Asynchronous Speculation and Early Inference Cancellation, the former improving latency and generation speed by running single-token inference simultaneously with several speculative runs, while the latter improves speed and latency by skipping the computation of invalidated runs, even in the middle of inference.

Generative Large Language Models (LLMs) have demonstrated remarkable results for a wide range of tasks. However, deploying these models for inference has been a significant challenge due to their unprecedented resource requirements. This has forced existing deployment frameworks to use multi-GPU inference pipelines, which are often complex and costly, or to use smaller and less performant models. In this work, we demonstrate that the main bottleneck for generative inference with LLMs is memory bandwidth, rather than compute, specifically for single batch inference. While quantization has emerged as a promising solution by representing model weights with reduced precision, previous efforts have often resulted in notable performance degradation. To address this, we introduce SqueezeLLM, a post-training quantization framework that not only enables lossless compression to ultra-low precisions of up to 3-bit, but also achieves higher quantization performance under the same memory constraint. Our framework incorporates two novel ideas: (i) sensitivity-based non-uniform quantization, which searches for the optimal bit precision assignment based on second-order information; and (ii) the Dense-and-Sparse decomposition that stores outliers and sensitive weight values in an efficient sparse format. When applied to the LLaMA models, our 3-bit quantization significantly reduces the perplexity gap from the FP16 baseline by up to 2.1x as compared to the state-of-the-art methods with the same memory requirement. Furthermore, when deployed on an A6000 GPU, our quantized models achieve up to 2.3x speedup compared to the baseline. Our code is open-sourced and available online.

Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to automate proofs in languages such as F*. Seeking to spur research on using AI to automate the construction of proof-oriented programs, we curate a dataset of 600K lines of open-source F* programs and proofs, including software used in production systems ranging from Windows and Linux, to Python and Firefox. Our dataset includes around 32K top-level F* definitions, each representing a type-directed program and proof synthesis problem -- producing a definition given a formal specification expressed as an F* type. We provide a program-fragment checker that queries F* to check the correctness of candidate solutions. We believe this is the largest corpus of SMT-assisted program proofs coupled with a reproducible program-fragment checker. Grounded in this dataset, we investigate the use of AI to synthesize programs and their proofs in F*, with promising results. Our main finding in that the performance of fine-tuned smaller language models (such as Phi-2 or StarCoder) compare favorably with large language models (such as GPT-4), at a much lower computational cost. We also identify various type-based retrieval augmentation techniques and find that they boost performance significantly. With detailed error analysis and case studies, we identify potential strengths and weaknesses of models and techniques and suggest directions for future improvements.

Quantization has become a mainstream compression technique for reducing model size, computational requirements, and energy consumption for modern deep neural networks (DNNs). With the improved numerical support in recent hardware, including multiple variants of integer and floating point, mixed-precision quantization has become necessary to achieve high-quality results with low model cost. Prior mixed-precision quantization methods have performed a post-training quantization search, which compromises on accuracy, or a differentiable quantization search, which leads to high memory usage from branching. Therefore, we propose the first one-shot mixed-precision quantization search that eliminates the need for retraining in both integer and low-precision floating point models. We evaluate our floating-point and integer quantization search (FLIQS) on multiple convolutional networks and vision transformer models to discover Pareto-optimal models. Our approach discovers models that improve upon uniform precision, manual mixed-precision, and recent integer quantization search methods. With the proposed integer quantization search, we increase the accuracy of ResNet-18 on ImageNet by 1.31% points and ResNet-50 by 0.90% points with equivalent model cost over previous methods. Additionally, for the first time, we explore a novel mixed-precision floating-point search and improve MobileNetV2 by up to 0.98% points compared to prior state-of-the-art FP8 models. Finally, we extend FLIQS to simultaneously search a joint quantization and neural architecture space and improve the ImageNet accuracy by 2.69% points with similar model cost on a MobileNetV2 search space.

We propose a framework for robust evaluation of reasoning capabilities of language models, using functional variants of benchmarks. Models that solve a reasoning test should exhibit no difference in performance over the static version of a problem compared to a snapshot of the functional variant. We have rewritten the relevant fragment of the MATH benchmark into its functional variant MATH(), with functionalization of other benchmarks to follow. When evaluating current state-of-the-art models over snapshots of MATH(), we find a reasoning gap -- the percentage difference between the static and functional accuracies. We find reasoning gaps from 58.35% to 80.31% among the state-of-the-art closed and open weights models that perform well on static benchmarks, with the caveat that the gaps are likely to be smaller with more sophisticated prompting strategies. Here we show that models which anecdotally have good reasoning performance over real-world tasks, have quantifiable lower gaps, motivating the open problem of building "gap 0" models. Code for evaluation and new evaluation datasets, three MATH() snapshots, are publicly available at https://github.com/consequentai/fneval/.

Recent advancements in large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, single-shot inference often yields unreliable results for complex reasoning tasks, leading researchers to explore multiple reasoning paths through methods such as perplexity and self-consistency. In this paper, we present the first theoretical error decomposition analysis of these techniques, breaking down their error into estimation error and model error. Our analysis reveals a fundamental trade-off: perplexity methods suffer from substantial model error due to the absence of a proper consistency function, while self-consistency exhibits high estimation error due to a slow error convergence rate. To overcome these limitations, we propose Reasoning-Pruning Perplexity Consistency (RPC). This approach combines Perplexity Consistency, which seamlessly integrates LLM perplexity with self-consistency, and Reasoning Pruning, which eliminates low-probability reasoning paths to effectively prevent the degeneration of estimation error reduction. Theoretical analysis demonstrates that RPC not only accelerates the convergence rate of estimation error to an exponential level but also holds strong potential for further reducing model error. Extensive empirical evaluations on seven benchmark datasets confirm that RPC can significantly improve reasoning performance, sample efficiency, and confidence reliability.

Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor Core support and inefficient memory management, leading to suboptimal acceleration. To address these challenges, we propose a comprehensive acceleration scheme for arbitrary precision LLMs. At its core, we introduce a novel bipolar-INT data format that facilitates parallel computing and supports symmetric quantization, effectively reducing data redundancy. Building on this, we implement an arbitrary precision matrix multiplication scheme that decomposes and recovers matrices at the bit level, enabling flexible precision while maximizing GPU Tensor Core utilization. Furthermore, we develop an efficient matrix preprocessing method that optimizes data layout for subsequent computations. Finally, we design a data recovery-oriented memory management system that strategically utilizes fast shared memory, significantly enhancing kernel execution speed and minimizing memory access latency. Experimental results demonstrate our approach's effectiveness, with up to 2.4\times speedup in matrix multiplication compared to NVIDIA's CUTLASS. When integrated into LLMs, we achieve up to 6.7\times inference acceleration. These improvements significantly enhance LLM inference efficiency, enabling broader and more responsive applications of LLMs.

Model quantization is widely applied for compressing and accelerating deep neural networks (DNNs). However, conventional Quantization-Aware Training (QAT) focuses on training DNNs with uniform bit-width. The bit-width settings vary across different hardware and transmission demands, which induces considerable training and storage costs. Hence, the scheme of one-shot joint training multiple precisions is proposed to address this issue. Previous works either store a larger FP32 model to switch between different precision models for higher accuracy or store a smaller INT8 model but compromise accuracy due to using shared quantization parameters. In this paper, we introduce the Double Rounding quantization method, which fully utilizes the quantized representation range to accomplish nearly lossless bit-switching while reducing storage by using the highest integer precision instead of full precision. Furthermore, we observe a competitive interference among different precisions during one-shot joint training, primarily due to inconsistent gradients of quantization scales during backward propagation. To tackle this problem, we propose an Adaptive Learning Rate Scaling (ALRS) technique that dynamically adapts learning rates for various precisions to optimize the training process. Additionally, we extend our Double Rounding to one-shot mixed precision training and develop a Hessian-Aware Stochastic Bit-switching (HASB) strategy. Experimental results on the ImageNet-1K classification demonstrate that our methods have enough advantages to state-of-the-art one-shot joint QAT in both multi-precision and mixed-precision. We also validate the feasibility of our method on detection and segmentation tasks, as well as on LLMs task. Our codes are available at https://github.com/haiduo/Double-Rounding.

Large Language Model (LLM) inference consists of two distinct phases - prefill phase which processes the input prompt and decode phase which generates output tokens autoregressively. While the prefill phase effectively saturates GPU compute at small batch sizes, the decode phase results in low compute utilization as it generates one token at a time per request. The varying prefill and decode times also lead to imbalance across micro-batches when using pipeline parallelism, resulting in further inefficiency due to bubbles. We present SARATHI to address these challenges. SARATHI employs chunked-prefills, which splits a prefill request into equal sized chunks, and decode-maximal batching, which constructs a batch using a single prefill chunk and populates the remaining slots with decodes. During inference, the prefill chunk saturates GPU compute, while the decode requests 'piggyback' and cost up to an order of magnitude less compared to a decode-only batch. Chunked-prefills allows constructing multiple decode-maximal batches from a single prefill request, maximizing coverage of decodes that can piggyback. Furthermore, the uniform compute design of these batches ameliorates the imbalance between micro-batches, significantly reducing pipeline bubbles. Our techniques yield significant improvements in inference performance across models and hardware. For the LLaMA-13B model on A6000 GPU, SARATHI improves decode throughput by up to 10x, and accelerates end-to-end throughput by up to 1.33x. For LLaMa-33B on A100 GPU, we achieve 1.25x higher end-to-end-throughput and up to 4.25x higher decode throughput. When used with pipeline parallelism on GPT-3, SARATHI reduces bubbles by 6.29x, resulting in an end-to-end throughput improvement of 1.91x.

As the usage of large language models (LLMs) grows, performing efficient inference with these models becomes increasingly important. While speculative decoding has recently emerged as a promising direction for speeding up inference, existing methods are limited in their ability to scale to larger speculation budgets, and adapt to different hyperparameters and hardware. This paper introduces Sequoia, a scalable, robust, and hardware-aware algorithm for speculative decoding. To attain better scalability, Sequoia introduces a dynamic programming algorithm to find the optimal tree structure for the speculated tokens. To achieve robust speculative performance, Sequoia uses a novel sampling and verification method that outperforms prior work across different decoding temperatures. Finally, Sequoia introduces a hardware-aware tree optimizer that maximizes speculative performance by automatically selecting the token tree size and depth for a given hardware platform. Evaluation shows that Sequoia improves the decoding speed of Llama2-7B, Llama2-13B, and Vicuna-33B on an A100 by up to 4.04times, 3.84times, and 2.37times, and Llama2-70B offloading by up to 10.33times on L40.

The softmax (also called softargmax) function is widely used in machine learning models to normalize real-valued scores into a probability distribution. To avoid floating-point overflow, the softmax function is conventionally implemented in three passes: the first pass to compute the normalization constant, and two other passes to compute outputs from normalized inputs. We analyze two variants of the Three-Pass algorithm and demonstrate that in a well-optimized implementation on HPC-class processors performance of all three passes is limited by memory bandwidth. We then present a novel algorithm for softmax computation in just two passes. The proposed Two-Pass algorithm avoids both numerical overflow and the extra normalization pass by employing an exotic representation for intermediate values, where each value is represented as a pair of floating-point numbers: one representing the "mantissa" and another representing the "exponent". Performance evaluation demonstrates that on out-of-cache inputs on an Intel Skylake-X processor the new Two-Pass algorithm outperforms the traditional Three-Pass algorithm by up to 28% in AVX512 implementation, and by up to 18% in AVX2 implementation. The proposed Two-Pass algorithm also outperforms the traditional Three-Pass algorithm on Intel Broadwell and AMD Zen 2 processors. To foster reproducibility, we released an open-source implementation of the new Two-Pass Softmax algorithm and other experiments in this paper as a part of XNNPACK library at GitHub.com/google/XNNPACK.

We show that the majority of the inference computations for large generative models such as LLaMA and OPT can be performed with both weights and activations being cast to 4 bits, in a way that leads to practical speedups while at the same time maintaining good accuracy. We achieve this via a hybrid quantization strategy called QUIK, which compresses most of the weights and activations to 4-bit, while keeping some outlier weights and activations in higher-precision. Crucially, our scheme is designed with computational efficiency in mind: we provide GPU kernels with highly-efficient layer-wise runtimes, which lead to practical end-to-end throughput improvements of up to 3.1x relative to FP16 execution. Code and models are provided at https://github.com/IST-DASLab/QUIK.

Large language models (LLMs) have shown remarkable capabilities in various tasks. However their huge model size and the consequent demand for computational and memory resources also pose challenges to model deployment. Currently, 4-bit post-training quantization (PTQ) has achieved some success in LLMs, reducing the memory footprint by approximately 75% compared to FP16 models, albeit with some accuracy loss. In this paper, we propose SmoothQuant+, an accurate and efficient 4-bit weight-only PTQ that requires no additional training, which enables lossless in accuracy for LLMs for the first time. Based on the fact that the loss of weight quantization is amplified by the activation outliers, SmoothQuant+ smoothes the activation outliers by channel before quantization, while adjusting the corresponding weights for mathematical equivalence, and then performs group-wise 4-bit weight quantization for linear layers. We have integrated SmoothQuant+ into the vLLM framework, an advanced high-throughput inference engine specially developed for LLMs, and equipped it with an efficient W4A16 CUDA kernels, so that vLLM can seamlessly support SmoothQuant+ 4-bit weight quantization. Our results show that, with SmoothQuant+, the Code Llama-34B model can be quantized and deployed on a A100 40GB GPU, achieving lossless accuracy and a throughput increase of 1.9 to 4.0 times compared to the FP16 model deployed on two A100 40GB GPUs. Moreover, the latency per token is only 68% of the FP16 model deployed on two A100 40GB GPUs. This is the state-of-the-art 4-bit weight quantization for LLMs as we know.

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.

Post-training quantization~(PTQ) of transformer language models faces significant challenges due to the existence of detrimental outliers in activations. We observe that these outliers are concentrated in specific channels and are asymmetric across channels. To address this issue, we propose the Outlier Suppression+~(OS+) framework, which contains the channel-wise shifting for asymmetry and channel-wise scaling for concentration. We show that these operations can be seamlessly migrated into subsequent modules while maintaining equivalence. Second, we propose a fast and stable scheme to calculate effective shifting and scaling values. The channel-wise shifting aligns the center of each channel for removal of outlier asymmetry. The channel-wise scaling quantitatively evaluates changes brought by migration and quantization for better quantization burden balance. We validate our OS+ under both standard and fine-grained quantization settings with models including BERT, OPT, BLOOM, BLOOMZ, and LLaMA. Comprehensive results across various tasks demonstrate the superiority of our approach. Especially, with standard quantization, OS+ can achieve near-floating-point performance on both small models and large language models on 8-bit and 6-bit. Besides, we establish a new state-of-the-art for 4-bit BERT with 15.5\% improvement. Our code is available at https://github.com/ModelTC/Outlier_Suppression_Plus.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Enabling On-Device Learning (ODL) for Ultra-Low-Power Micro-Controller Units (MCUs) is a key step for post-deployment adaptation and fine-tuning of Deep Neural Network (DNN) models in future TinyML applications. This paper tackles this challenge by introducing a novel reduced precision optimization technique for ODL primitives on MCU-class devices, leveraging the State-of-Art advancements in RISC-V RV32 architectures with support for vectorized 16-bit floating-point (FP16) Single-Instruction Multiple-Data (SIMD) operations. Our approach for the Forward and Backward steps of the Back-Propagation training algorithm is composed of specialized shape transform operators and Matrix Multiplication (MM) kernels, accelerated with parallelization and loop unrolling. When evaluated on a single training step of a 2D Convolution layer, the SIMD-optimized FP16 primitives result up to 1.72times faster than the FP32 baseline on a RISC-V-based 8+1-core MCU. An average computing efficiency of 3.11 Multiply and Accumulate operations per clock cycle (MAC/clk) and 0.81 MAC/clk is measured for the end-to-end training tasks of a ResNet8 and a DS-CNN for Image Classification and Keyword Spotting, respectively -- requiring 17.1 ms and 6.4 ms on the target platform to compute a training step on a single sample. Overall, our approach results more than two orders of magnitude faster than existing ODL software frameworks for single-core MCUs and outperforms by 1.6 times previous FP32 parallel implementations on a Continual Learning setup.

Recent advances with large language models (LLM) illustrate their diverse capabilities. We propose a novel algorithm, staged speculative decoding, to accelerate LLM inference in small-batch, on-device scenarios. We address the low arithmetic intensity of small-batch inference by improving upon previous work in speculative decoding. First, we restructure the speculative batch as a tree, which reduces generation costs and increases the expected tokens per batch. Second, we add a second stage of speculative decoding. Taken together, we reduce single-batch decoding latency by 3.16x with a 762M parameter GPT-2-L model while perfectly preserving output quality.

Model size and inference speed/power have become a major challenge in the deployment of Neural Networks for many applications. A promising approach to address these problems is quantization. However, uniformly quantizing a model to ultra low precision leads to significant accuracy degradation. A novel solution for this is to use mixed-precision quantization, as some parts of the network may allow lower precision as compared to other layers. However, there is no systematic way to determine the precision of different layers. A brute force approach is not feasible for deep networks, as the search space for mixed-precision is exponential in the number of layers. Another challenge is a similar factorial complexity for determining block-wise fine-tuning order when quantizing the model to a target precision. Here, we introduce Hessian AWare Quantization (HAWQ), a novel second-order quantization method to address these problems. HAWQ allows for the automatic selection of the relative quantization precision of each layer, based on the layer's Hessian spectrum. Moreover, HAWQ provides a deterministic fine-tuning order for quantizing layers, based on second-order information. We show the results of our method on Cifar-10 using ResNet20, and on ImageNet using Inception-V3, ResNet50 and SqueezeNext models. Comparing HAWQ with state-of-the-art shows that we can achieve similar/better accuracy with 8times activation compression ratio on ResNet20, as compared to DNAS~wu2018mixed, and up to 1% higher accuracy with up to 14% smaller models on ResNet50 and Inception-V3, compared to recently proposed methods of RVQuant~park2018value and HAQ~wang2018haq. Furthermore, we show that we can quantize SqueezeNext to just 1MB model size while achieving above 68% top1 accuracy on ImageNet.

Accelerating the inference of large language models (LLMs) is an important challenge in artificial intelligence. This paper introduces distributed speculative inference (DSI), a novel distributed inference algorithm that is provably faster than speculative inference (SI) [leviathan2023fast, chen2023accelerating, miao2023specinfer] and traditional autoregressive inference (non-SI). Like other SI algorithms, DSI works on frozen LLMs, requiring no training or architectural modifications, and it preserves the target distribution. Prior studies on SI have demonstrated empirical speedups (compared to non-SI) but require a fast and accurate drafter LLM. In practice, off-the-shelf LLMs often do not have matching drafters that are sufficiently fast and accurate. We show a gap: SI gets slower than non-SI when using slower or less accurate drafters. We close this gap by proving that DSI is faster than both SI and non-SI given any drafters. By orchestrating multiple instances of the target and drafters, DSI is not only faster than SI but also supports LLMs that cannot be accelerated with SI. Our simulations show speedups of off-the-shelf LLMs in realistic settings: DSI is 1.29-1.92x faster than SI.

Fully quantized training (FQT) accelerates the training of deep neural networks by quantizing the activations, weights, and gradients into lower precision. To explore the ultimate limit of FQT (the lowest achievable precision), we make a first attempt to 1-bit FQT. We provide a theoretical analysis of FQT based on Adam and SGD, revealing that the gradient variance influences the convergence of FQT. Building on these theoretical results, we introduce an Activation Gradient Pruning (AGP) strategy. The strategy leverages the heterogeneity of gradients by pruning less informative gradients and enhancing the numerical precision of remaining gradients to mitigate gradient variance. Additionally, we propose Sample Channel joint Quantization (SCQ), which utilizes different quantization strategies in the computation of weight gradients and activation gradients to ensure that the method is friendly to low-bitwidth hardware. Finally, we present a framework to deploy our algorithm. For fine-tuning VGGNet-16 and ResNet-18 on multiple datasets, our algorithm achieves an average accuracy improvement of approximately 6%, compared to per-sample quantization. Moreover, our training speedup can reach a maximum of 5.13x compared to full precision training.

The large number of parameters of some prominent language models, such as BERT, makes their fine-tuning on downstream tasks computationally intensive and energy hungry. Previously researchers were focused on lower bit-width integer data types for the forward propagation of language models to save memory and computation. As for the backward propagation, however, only 16-bit floating-point data type has been used for the fine-tuning of BERT. In this work, we use integer arithmetic for both forward and back propagation in the fine-tuning of BERT. We study the effects of varying the integer bit-width on the model's metric performance. Our integer fine-tuning uses integer arithmetic to perform forward propagation and gradient computation of linear, layer-norm, and embedding layers of BERT. We fine-tune BERT using our integer training method on SQuAD v1.1 and SQuAD v2., and GLUE benchmark. We demonstrate that metric performance of fine-tuning 16-bit integer BERT matches both 16-bit and 32-bit floating-point baselines. Furthermore, using the faster and more memory efficient 8-bit integer data type, integer fine-tuning of BERT loses an average of 3.1 points compared to the FP32 baseline.

Large language models (LLMs) have shown exceptional performance and vast potential across diverse tasks. However, the deployment of LLMs with high performance in low-resource environments has garnered significant attention in the industry. When GPU hardware resources are limited, we can explore alternative options on CPUs. To mitigate the financial burden and alleviate constraints imposed by hardware resources, optimizing inference performance is necessary. In this paper, we introduce an easily deployable inference performance optimization solution aimed at accelerating LLMs on CPUs. In this solution, we implement an effective way to reduce the KV cache size while ensuring precision. We propose a distributed inference optimization approach and implement it based on oneAPI Collective Communications Library. Furthermore, we propose optimization approaches for LLMs on CPU, and conduct tailored optimizations for the most commonly used models. The code is open-sourced at https://github.com/intel/xFasterTransformer.

Generative Pre-trained Transformer models, known as GPT or OPT, set themselves apart through breakthrough performance across complex language modelling tasks, but also by their extremely high computational and storage costs. Specifically, due to their massive size, even inference for large, highly-accurate GPT models may require multiple performant GPUs, which limits the usability of such models. While there is emerging work on relieving this pressure via model compression, the applicability and performance of existing compression techniques is limited by the scale and complexity of GPT models. In this paper, we address this challenge, and propose GPTQ, a new one-shot weight quantization method based on approximate second-order information, that is both highly-accurate and highly-efficient. Specifically, GPTQ can quantize GPT models with 175 billion parameters in approximately four GPU hours, reducing the bitwidth down to 3 or 4 bits per weight, with negligible accuracy degradation relative to the uncompressed baseline. Our method more than doubles the compression gains relative to previously-proposed one-shot quantization methods, preserving accuracy, allowing us for the first time to execute an 175 billion-parameter model inside a single GPU for generative inference. Moreover, we also show that our method can still provide reasonable accuracy in the extreme quantization regime, in which weights are quantized to 2-bit or even ternary quantization levels. We show experimentally that these improvements can be leveraged for end-to-end inference speedups over FP16, of around 3.25x when using high-end GPUs (NVIDIA A100) and 4.5x when using more cost-effective ones (NVIDIA A6000). The implementation is available at https://github.com/IST-DASLab/gptq.

The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point arithmetic. However, conventional floating-point implementations can be power hungry. This paper proposes a method to improve the energy efficiency of the matrix engines used in machine learning algorithm acceleration. Our approach leverages approximate normalization within the floating-point multiply-add units as a means to reduce their hardware complexity, without sacrificing overall machine-learning model accuracy. Hardware synthesis results show that this technique reduces area and power consumption roughly by 16% and 13% on average for Bfloat16 format. Also, the error introduced in transformer model accuracy is 1% on average, for the most efficient configuration of the proposed approach.

Large Language Models (LLMs), despite their recent impressive accomplishments, are notably cost-prohibitive to deploy, particularly for applications involving long-content generation, such as dialogue systems and story writing. Often, a large amount of transient state information, referred to as the KV cache, is stored in GPU memory in addition to model parameters, scaling linearly with the sequence length and batch size. In this paper, we introduce a novel approach for implementing the KV cache which significantly reduces its memory footprint. Our approach is based on the noteworthy observation that a small portion of tokens contributes most of the value when computing attention scores. We call these tokens Heavy Hitters (H_2). Through a comprehensive investigation, we find that (i) the emergence of H_2 is natural and strongly correlates with the frequent co-occurrence of tokens in the text, and (ii) removing them results in significant performance degradation. Based on these insights, we propose Heavy Hitter Oracle (H_2O), a KV cache eviction policy that dynamically retains a balance of recent and H_2 tokens. We formulate the KV cache eviction as a dynamic submodular problem and prove (under mild assumptions) a theoretical guarantee for our novel eviction algorithm which could help guide future work. We validate the accuracy of our algorithm with OPT, LLaMA, and GPT-NeoX across a wide range of tasks. Our implementation of H_2O with 20% heavy hitters improves the throughput over three leading inference systems DeepSpeed Zero-Inference, Hugging Face Accelerate, and FlexGen by up to 29times, 29times, and 3times on OPT-6.7B and OPT-30B. With the same batch size, H2O can reduce the latency by up to 1.9times. The code is available at https://github.com/FMInference/H2O.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization parameters and evaluate their choices on a wide range of neural network models for different application domains, including vision, speech, and language. We focus on quantization techniques that are amenable to acceleration by processors with high-throughput integer math pipelines. We also present a workflow for 8-bit quantization that is able to maintain accuracy within 1% of the floating-point baseline on all networks studied, including models that are more difficult to quantize, such as MobileNets and BERT-large.

This paper presents a configurable Convolutional Neural Network Accelerator (CNNA) for a System on Chip design (SoC). The goal was to accelerate inference of different deep learning networks on an embedded SoC platform. The presented CNNA has a scalable architecture which uses High Level Synthesis (HLS) and SystemC for the hardware accelerator. It is able to accelerate any Convolutional Neural Network (CNN) exported from Python and supports a combination of convolutional, max-pooling, and fully connected layers. A training method with fixed-point quantized weights is proposed and presented in the paper. The CNNA is template-based, enabling it to scale for different targets of the Xilinx Zynq platform. This approach enables design space exploration, which makes it possible to explore several configurations of the CNNA during C- and RTL-simulation, fitting it to the desired platform and model. The CNN VGG16 was used to test the solution on a Xilinx Ultra96 board using PYNQ. The result gave a high level of accuracy in training with an auto-scaled fixed-point Q2.14 format compared to a similar floating-point model. It was able to perform inference in 2.0 seconds, while having an average power consumption of 2.63 W, which corresponds to a power efficiency of 6.0 GOPS/W.

Accelerating inference in Large Language Models (LLMs) is critical for real-time interactions, as they have been widely incorporated into real-world services. Speculative decoding, a fully algorithmic solution, has gained attention for improving inference speed by drafting and verifying tokens, thereby generating multiple tokens in a single forward pass. However, current drafting strategies usually require significant fine-tuning or have inconsistent performance across tasks. To address these challenges, we propose Hierarchy Drafting (HD), a novel lossless drafting approach that organizes various token sources into multiple databases in a hierarchical framework based on temporal locality. In the drafting step, HD sequentially accesses multiple databases to obtain draft tokens from the highest to the lowest locality, ensuring consistent acceleration across diverse tasks and minimizing drafting latency. Our experiments on Spec-Bench using LLMs with 7B and 13B parameters demonstrate that HD outperforms existing database drafting methods, achieving robust inference speedups across model sizes, tasks, and temperatures.

We present speculative sampling, an algorithm for accelerating transformer decoding by enabling the generation of multiple tokens from each transformer call. Our algorithm relies on the observation that the latency of parallel scoring of short continuations, generated by a faster but less powerful draft model, is comparable to that of sampling a single token from the larger target model. This is combined with a novel modified rejection sampling scheme which preserves the distribution of the target model within hardware numerics. We benchmark speculative sampling with Chinchilla, a 70 billion parameter language model, achieving a 2-2.5x decoding speedup in a distributed setup, without compromising the sample quality or making modifications to the model itself.

The rising popularity of intelligent mobile devices and the daunting computational cost of deep learning-based models call for efficient and accurate on-device inference schemes. We propose a quantization scheme that allows inference to be carried out using integer-only arithmetic, which can be implemented more efficiently than floating point inference on commonly available integer-only hardware. We also co-design a training procedure to preserve end-to-end model accuracy post quantization. As a result, the proposed quantization scheme improves the tradeoff between accuracy and on-device latency. The improvements are significant even on MobileNets, a model family known for run-time efficiency, and are demonstrated in ImageNet classification and COCO detection on popular CPUs.

The inference process for large language models is slow and memory-intensive, with one of the most critical bottlenecks being excessive Key-Value (KV) cache accesses. This paper introduces "Double Sparsity," a novel post-training sparse attention technique designed to alleviate this bottleneck by reducing KV cache access. Double Sparsity combines token sparsity, which focuses on utilizing only the important tokens for computing self-attention, with channel sparsity, an approach that uses important feature channels for identifying important tokens. Our key insight is that the pattern of channel sparsity is relatively static, allowing us to use offline calibration to make it efficient at runtime, thereby enabling accurate and efficient identification of important tokens. Moreover, this method can be combined with offloading to achieve significant memory usage reduction. Experimental results demonstrate that Double Sparsity can achieve 1{16} token and channel sparsity with minimal impact on accuracy across various tasks, including wiki-2 perplexity, key-value retrieval, and long context benchmarks with models including Llama-2-7B, Llama-2-70B, and Mixtral-8x7B. It brings up to a 14.1times acceleration in attention operations and a 1.9times improvement in end-to-end inference on GPUs. With offloading, it achieves a decoding speed acceleration of 16.3times compared to state-of-the-art solutions at a sequence length of 256K. Our code is publicly available at https://github.com/andy-yang-1/DoubleSparse.

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 5% absolute performance improvement on Leandojo benchmark. Additionally, our synthetic data achieve a 2.5% absolute performance gain on the out-of-distribution miniF2F benchmark. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

Large language models (LLMs) have revolutionized the field of AI, demonstrating unprecedented capacity across various tasks. However, the inference process for LLMs comes with significant computational costs. In this paper, we propose an efficient LLM inference pipeline that harnesses the power of LLMs. Our approach begins by tapping into the potential of LLMs to accurately perceive and predict the response length with minimal overhead. By leveraging this information, we introduce an efficient sequence scheduling technique that groups queries with similar response lengths into micro-batches. We evaluate our approach on real-world instruction datasets using the LLaMA-based model, and our results demonstrate an impressive 86% improvement in inference throughput without compromising effectiveness. Notably, our method is orthogonal to other inference acceleration techniques, making it a valuable addition to many existing toolkits (e.g., FlashAttention, Quantization) for LLM inference.

Recent research, such as BitNet, is paving the way for a new era of 1-bit Large Language Models (LLMs). In this work, we introduce a 1-bit LLM variant, namely BitNet b1.58, in which every single parameter (or weight) of the LLM is ternary {-1, 0, 1}. It matches the full-precision (i.e., FP16 or BF16) Transformer LLM with the same model size and training tokens in terms of both perplexity and end-task performance, while being significantly more cost-effective in terms of latency, memory, throughput, and energy consumption. More profoundly, the 1.58-bit LLM defines a new scaling law and recipe for training new generations of LLMs that are both high-performance and cost-effective. Furthermore, it enables a new computation paradigm and opens the door for designing specific hardware optimized for 1-bit LLMs.

We present APQ for efficient deep learning inference on resource-constrained hardware. Unlike previous methods that separately search the neural architecture, pruning policy, and quantization policy, we optimize them in a joint manner. To deal with the larger design space it brings, a promising approach is to train a quantization-aware accuracy predictor to quickly get the accuracy of the quantized model and feed it to the search engine to select the best fit. However, training this quantization-aware accuracy predictor requires collecting a large number of quantized <model, accuracy> pairs, which involves quantization-aware finetuning and thus is highly time-consuming. To tackle this challenge, we propose to transfer the knowledge from a full-precision (i.e., fp32) accuracy predictor to the quantization-aware (i.e., int8) accuracy predictor, which greatly improves the sample efficiency. Besides, collecting the dataset for the fp32 accuracy predictor only requires to evaluate neural networks without any training cost by sampling from a pretrained once-for-all network, which is highly efficient. Extensive experiments on ImageNet demonstrate the benefits of our joint optimization approach. With the same accuracy, APQ reduces the latency/energy by 2x/1.3x over MobileNetV2+HAQ. Compared to the separate optimization approach (ProxylessNAS+AMC+HAQ), APQ achieves 2.3% higher ImageNet accuracy while reducing orders of magnitude GPU hours and CO2 emission, pushing the frontier for green AI that is environmental-friendly. The code and video are publicly available.

Speculative Decoding is a widely used technique to speed up inference for Large Language Models (LLMs) without sacrificing quality. When performing inference, speculative decoding uses a smaller draft model to generate speculative tokens and then uses the target LLM to verify those draft tokens. The speedup provided by speculative decoding heavily depends on the choice of the draft model. In this work, we perform a detailed study comprising over 350 experiments with LLaMA-65B and OPT-66B using speculative decoding and delineate the factors that affect the performance gain provided by speculative decoding. Our experiments indicate that the performance of speculative decoding depends heavily on the latency of the draft model, and the draft model's capability in language modeling does not correlate strongly with its performance in speculative decoding. Based on these insights we explore a new design space for draft models and design hardware-efficient draft models for speculative decoding. Our newly designed draft model for LLaMA-65B can provide 60% higher throughput than existing draft models and can generalize further to the LLaMA-2 model family and supervised fine-tuned models.

The autoregressive nature of conventional large language models (LLMs) inherently limits inference speed, as tokens are generated sequentially. While speculative and parallel decoding techniques attempt to mitigate this, they face limitations: either relying on less accurate smaller models for generation or failing to fully leverage the base LLM's representations. We introduce a novel architecture, Tandem transformers, to address these issues. This architecture uniquely combines (1) a small autoregressive model and (2) a large model operating in block mode (processing multiple tokens simultaneously). The small model's predictive accuracy is substantially enhanced by granting it attention to the large model's richer representations. On the PaLM2 pretraining dataset, a tandem of PaLM2-Bison and PaLM2-Gecko demonstrates a 3.3% improvement in next-token prediction accuracy over a standalone PaLM2-Gecko, offering a 1.16x speedup compared to a PaLM2-Otter model with comparable downstream performance. We further incorporate the tandem model within the speculative decoding (SPEED) framework where the large model validates tokens from the small model. This ensures that the Tandem of PaLM2-Bison and PaLM2-Gecko achieves substantial speedup (around 1.14x faster than using vanilla PaLM2-Gecko in SPEED) while maintaining identical downstream task accuracy.

The increasing use of foundation models highlights the urgent need to address and eliminate implicit biases present in them that arise during pretraining. In this paper, we introduce PEFTDebias, a novel approach that employs parameter-efficient fine-tuning (PEFT) to mitigate the biases within foundation models. PEFTDebias consists of two main phases: an upstream phase for acquiring debiasing parameters along a specific bias axis, and a downstream phase where these parameters are incorporated into the model and frozen during the fine-tuning process. By evaluating on four datasets across two bias axes namely gender and race, we find that downstream biases can be effectively reduced with PEFTs. In addition, we show that these parameters possess axis-specific debiasing characteristics, enabling their effective transferability in mitigating biases in various downstream tasks. To ensure reproducibility, we release the code to do our experiments.

Despite the popularity of large language model (LLM) quantization for inference acceleration, significant uncertainty remains regarding the accuracy-performance trade-offs associated with various quantization formats. We present a comprehensive empirical study of quantized accuracy, evaluating popular quantization formats (FP8, INT8, INT4) across academic benchmarks and real-world tasks, on the entire Llama-3.1 model family. Additionally, our study examines the difference in text generated by quantized models versus their uncompressed counterparts. Beyond benchmarks, we also present a couple of quantization improvements which allowed us to obtain state-of-the-art accuracy recovery results. Our investigation, encompassing over 500,000 individual evaluations, yields several key findings: (1) FP8 weight and activation quantization (W8A8-FP) is lossless across all model scales, (2) INT8 weight and activation quantization (W8A8-INT), when properly tuned, incurs surprisingly low 1-3% accuracy degradation, and (3) INT4 weight-only quantization (W4A16-INT) is competitive with 8-bit integer weight and activation quantization. To address the question of the "best" format for a given deployment environment, we conduct inference performance analysis using the popular open-source vLLM framework on various GPU architectures. We find that W4A16 offers the best cost-efficiency for synchronous deployments, and for asynchronous deployment on mid-tier GPUs. At the same time, W8A8 formats excel in asynchronous "continuous batching" deployment of mid- and large-size models on high-end GPUs. Our results provide a set of practical guidelines for deploying quantized LLMs across scales and performance requirements.

Diffusion Transformers (DiTs) have recently gained substantial attention in both industrial and academic fields for their superior visual generation capabilities, outperforming traditional diffusion models that use U-Net. However,the enhanced performance of DiTs also comes with high parameter counts and implementation costs, seriously restricting their use on resource-limited devices such as mobile phones. To address these challenges, we introduce the Hybrid Floating-point Quantization for DiT(HQ-DiT), an efficient post-training quantization method that utilizes 4-bit floating-point (FP) precision on both weights and activations for DiT inference. Compared to fixed-point quantization (e.g., INT8), FP quantization, complemented by our proposed clipping range selection mechanism, naturally aligns with the data distribution within DiT, resulting in a minimal quantization error. Furthermore, HQ-DiT also implements a universal identity mathematical transform to mitigate the serious quantization error caused by the outliers. The experimental results demonstrate that DiT can achieve extremely low-precision quantization (i.e., 4 bits) with negligible impact on performance. Our approach marks the first instance where both weights and activations in DiTs are quantized to just 4 bits, with only a 0.12 increase in sFID on ImageNet.

Vision Transformers (ViTs) have achieved state-of-the-art performance on various computer vision applications. However, these models have considerable storage and computational overheads, making their deployment and efficient inference on edge devices challenging. Quantization is a promising approach to reducing model complexity, and the dyadic arithmetic pipeline can allow the quantized models to perform efficient integer-only inference. Unfortunately, dyadic arithmetic is based on the homogeneity condition in convolutional neural networks, which is not applicable to the non-linear components in ViTs, making integer-only inference of ViTs an open issue. In this paper, we propose I-ViT, an integer-only quantization scheme for ViTs, to enable ViTs to perform the entire computational graph of inference with integer arithmetic and bit-shifting, and without any floating-point arithmetic. In I-ViT, linear operations (e.g., MatMul and Dense) follow the integer-only pipeline with dyadic arithmetic, and non-linear operations (e.g., Softmax, GELU, and LayerNorm) are approximated by the proposed light-weight integer-only arithmetic methods. More specifically, I-ViT applies the proposed Shiftmax and ShiftGELU, which are designed to use integer bit-shifting to approximate the corresponding floating-point operations. We evaluate I-ViT on various benchmark models and the results show that integer-only INT8 quantization achieves comparable (or even slightly higher) accuracy to the full-precision (FP) baseline. Furthermore, we utilize TVM for practical hardware deployment on the GPU's integer arithmetic units, achieving 3.72sim4.11times inference speedup compared to the FP model. Code of both Pytorch and TVM is released at https://github.com/zkkli/I-ViT.

Low-precision formats such as float8 have been introduced in machine learning accelerated hardware to improve computational efficiency for large language models training and inference. Nevertheless, adoption by the ML community has been slowed down by the complex, and sometimes brittle, techniques required to match higher precision training accuracy. In this work, we present Scalify, a end-to-end scale propagation paradigm for computational graphs, generalizing and formalizing existing tensor scaling methods. Experiment results show that Scalify supports out-of-the-box float8 matrix multiplication and gradients representation, as well as float16 optimizer state storage. Our JAX implementation of Scalify is open-sourced at https://github.com/graphcore-research/jax-scalify

The large number of parameters in Pretrained Language Models enhance their performance, but also make them resource-intensive, making it challenging to deploy them on commodity hardware like a single GPU. Due to the memory and power limitations of these devices, model compression techniques are often used to decrease both the model's size and its inference latency. This usually results in a trade-off between model accuracy and efficiency. Therefore, optimizing this balance is essential for effectively deploying LLMs on commodity hardware. A significant portion of the efficiency challenge is the Feed-forward network (FFN) component, which accounts for roughly 2{3} total parameters and inference latency. In this paper, we first observe that only a few neurons of FFN module have large output norm for any input tokens, a.k.a. heavy hitters, while the others are sparsely triggered by different tokens. Based on this observation, we explicitly split the FFN into two parts according to the heavy hitters. We improve the efficiency-accuracy trade-off of existing compression methods by allocating more resource to FFN parts with heavy hitters. In practice, our method can reduce model size by 43.1\% and bring 1.25sim1.56times wall clock time speedup on different hardware with negligible accuracy drop.

Quantization is an effective method for reducing memory footprint and inference time of Neural Networks, e.g., for efficient inference in the cloud, especially at the edge. However, ultra low precision quantization could lead to significant degradation in model generalization. A promising method to address this is to perform mixed-precision quantization, where more sensitive layers are kept at higher precision. However, the search space for a mixed-precision quantization is exponential in the number of layers. Recent work has proposed HAWQ, a novel Hessian based framework, with the aim of reducing this exponential search space by using second-order information. While promising, this prior work has three major limitations: (i) HAWQV1 only uses the top Hessian eigenvalue as a measure of sensitivity and do not consider the rest of the Hessian spectrum; (ii) HAWQV1 approach only provides relative sensitivity of different layers and therefore requires a manual selection of the mixed-precision setting; and (iii) HAWQV1 does not consider mixed-precision activation quantization. Here, we present HAWQV2 which addresses these shortcomings. For (i), we perform a theoretical analysis showing that a better sensitivity metric is to compute the average of all of the Hessian eigenvalues. For (ii), we develop a Pareto frontier based method for selecting the exact bit precision of different layers without any manual selection. For (iii), we extend the Hessian analysis to mixed-precision activation quantization. We have found this to be very beneficial for object detection. We show that HAWQV2 achieves new state-of-the-art results for a wide range of tasks.

Large language models (LLMs) require immense resources for training and inference. Quantization, a technique that reduces the precision of model parameters, offers a promising solution for improving LLM efficiency and sustainability. While post-training quantization methods typically achieve 4-8 bits per parameter, recent research suggests that training LLMs with 1.58 bits per weight parameter from scratch can maintain model accuracy while greatly reducing memory requirements and energy consumption at inference time. Here, we investigate a training strategy for quantization-aware pre-training, where the models are first trained with 16-bit precision and then transition into 1.58-bit quantization-aware training. Our results on 11 downstream tasks show that this 16-to-1.58-bit training strategy is preferable over full 1.58-bit training and leaves models closer to those which have undergone 16-bit training. We further investigate the effects of retaining the optimizer state at the transition point and gradually phasing in quantization strength -- finding that both techniques alleviate the magnitude of loss spikes, but also that these effects can be compensated through further training.

Post-training quantization of Large Language Models (LLMs) has proven effective in reducing the computational requirements for running inference on these models. In this study, we focus on a straightforward question: When aiming for a specific accuracy or perplexity target for low-precision quantization, how many high-precision numbers or calculations are required to preserve as we scale LLMs to larger sizes? We first introduce a critical metric named the quantization ratio, which compares the number of parameters quantized to low-precision arithmetic against the total parameter count. Through extensive and carefully controlled experiments across different model families, arithmetic types, and quantization granularities (e.g. layer-wise, matmul-wise), we identify two central phenomenons. 1) The larger the models, the better they can preserve performance with an increased quantization ratio, as measured by perplexity in pre-training tasks or accuracy in downstream tasks. 2) The finer the granularity of mixed-precision quantization (e.g., matmul-wise), the more the model can increase the quantization ratio. We believe these observed phenomena offer valuable insights for future AI hardware design and the development of advanced Efficient AI algorithms.

As large language models (LLMs) become more prevalent, there is a growing need for new and improved quantization methods that can meet the computationalast layer demands of these modern architectures while maintaining the accuracy. In this paper, we present TEQ, a trainable equivalent transformation that preserves the FP32 precision of the model output while taking advantage of low-precision quantization, especially 3 and 4 bits weight-only quantization. The training process is lightweight, requiring only 1K steps and fewer than 0.1 percent of the original model's trainable parameters. Furthermore, the transformation does not add any computational overhead during inference. Our results are on-par with the state-of-the-art (SOTA) methods on typical LLMs. Our approach can be combined with other methods to achieve even better performance. The code is available at https://github.com/intel/neural-compressor.

We propose a lightweight scheme where the formation of a data block is changed in such a way that it can tolerate soft errors significantly better than the baseline. The key insight behind our work is that CNN weights are normalized between -1 and 1 after each convolutional layer, and this leaves one bit unused in half-precision floating-point representation. By taking advantage of the unused bit, we create a backup for the most significant bit to protect it against the soft errors. Also, considering the fact that in MLC STT-RAMs the cost of memory operations (read and write), and reliability of a cell are content-dependent (some patterns take larger current and longer time, while they are more susceptible to soft error), we rearrange the data block to minimize the number of costly bit patterns. Combining these two techniques provides the same level of accuracy compared to an error-free baseline while improving the read and write energy by 9% and 6%, respectively.

Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap (Delta), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large Delta values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and Delta = 0. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity multiplication L-Mul algorithm that approximates floating point number multiplication with integer addition operations. The new algorithm costs significantly less computation resource than 8-bit floating point multiplication but achieves higher precision. Compared to 8-bit floating point multiplications, the proposed method achieves higher precision but consumes significantly less bit-level computation. Since multiplying floating point numbers requires substantially higher energy compared to integer addition operations, applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by element-wise floating point tensor multiplications and 80% energy cost of dot products. We calculated the theoretical error expectation of L-Mul, and evaluated the algorithm on a wide range of textual, visual, and symbolic tasks, including natural language understanding, structural reasoning, mathematics, and commonsense question answering. Our numerical analysis experiments agree with the theoretical error estimation, which indicates that L-Mul with 4-bit mantissa achieves comparable precision as float8_e4m3 multiplications, and L-Mul with 3-bit mantissa outperforms float8_e5m2. Evaluation results on popular benchmarks show that directly applying L-Mul to the attention mechanism is almost lossless. We further show that replacing all floating point multiplications with 3-bit mantissa L-Mul in a transformer model achieves equivalent precision as using float8_e4m3 as accumulation precision in both fine-tuning and inference.

Specializing large language models (LLMs) for local deployment in domain-specific use cases is necessary for strong performance while meeting latency and privacy constraints. However, conventional task-specific adaptation approaches do not show simultaneous memory saving and inference speedup at deployment time. Practical compression techniques like quantization and pruning require dedicated hardware or kernel support to achieve measured inference speedup. We develop TrimLLM based on the layer-wise specialization phenomenon we empirically observed and verified on contemporary LLMs. TrimLLM reduces the depth of LLMs via progressive layer dropping. We show it retains LLMs' capacity in specific domains and achieves inference speedup irrespective of hardware and deep learning frameworks. We evaluated TrimLLM on LLMs of various sizes for inference; models adapted on medical, legal, and financial datasets all demonstrate 2.1-5.7times inference speedup on consumer GPUs and up to 3.1times speedup on A100 when compared to state-of-the-art model compression algorithms, with no loss in accuracy at 50sim60\% model compression ratio.

This paper reveals the phenomenon of parameter heterogeneity in large language models (LLMs). We find that a small subset of ``cherry'' parameters exhibit a disproportionately large influence on model performance, while the vast majority of parameters have minimal impact. This heterogeneity is found to be prevalent across different model families, scales, and types. Motivated by this observation, we propose CherryQ, a novel quantization method that unifies the optimization of mixed-precision parameters. CherryQ identifies and preserves the critical cherry parameters in high precision while aggressively quantizing the remaining parameters to low precision. Extensive experiments demonstrate the effectiveness of CherryQ. CherryQ outperforms existing quantization approaches in terms of perplexity and downstream task performance. Notably, our 3-bit quantized Vicuna-1.5 exhibits competitive performance compared to their 16-bit counterparts. These findings highlight the potential of CherryQ for enabling efficient deployment of LLMs by taking advantage of parameter heterogeneity.

Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops and mobile phones, enabling personalized use. However, quantization down to 3-4 bits per parameter usually leads to moderate-to-high accuracy losses, especially for smaller models in the 1-10B parameter range, which are well-suited for edge deployments. To address this accuracy issue, we introduce the Sparse-Quantized Representation (SpQR), a new compressed format and quantization technique which enables for the first time near-lossless compression of LLMs across model scales, while reaching similar compression levels to previous methods. SpQR works by identifying and isolating outlier weights, which cause particularly-large quantization errors, and storing them in higher precision, while compressing all other weights to 3-4 bits, and achieves relative accuracy losses of less than 1% in perplexity for highly-accurate LLaMA and Falcon LLMs. This makes it possible to run 33B parameter LLM on a single 24 GB consumer GPU without any performance degradation at 15% speedup thus making powerful LLMs available to consumer without any downsides. SpQR comes with efficient algorithms for both encoding weights into its format, as well as decoding them efficiently at runtime. Specifically, we provide an efficient GPU inference algorithm for SpQR which yields faster inference than 16-bit baselines at similar accuracy, while enabling memory compression gains of more than 4x.

The simultaneous rise of machine learning as a service and concerns over user privacy have increasingly motivated the need for private inference (PI). While recent work demonstrates PI is possible using cryptographic primitives, the computational overheads render it impractical. The community is largely unprepared to address these overheads, as the source of slowdown in PI stems from the ReLU operator whereas optimizations for plaintext inference focus on optimizing FLOPs. In this paper we re-think the ReLU computation and propose optimizations for PI tailored to properties of neural networks. Specifically, we reformulate ReLU as an approximate sign test and introduce a novel truncation method for the sign test that significantly reduces the cost per ReLU. These optimizations result in a specific type of stochastic ReLU. The key observation is that the stochastic fault behavior is well suited for the fault-tolerant properties of neural network inference. Thus, we provide significant savings without impacting accuracy. We collectively call the optimizations Circa and demonstrate improvements of up to 4.7x storage and 3x runtime over baseline implementations; we further show that Circa can be used on top of recent PI optimizations to obtain 1.8x additional speedup.

Quantization is a crucial technique for deploying deep learning models on resource-constrained devices, such as embedded FPGAs. Prior efforts mostly focus on quantizing matrix multiplications, leaving other layers like BatchNorm or shortcuts in floating-point form, even though fixed-point arithmetic is more efficient on FPGAs. A common practice is to fine-tune a pre-trained model to fixed-point for FPGA deployment, but potentially degrading accuracy. This work presents QFX, a novel trainable fixed-point quantization approach that automatically learns the binary-point position during model training. Additionally, we introduce a multiplier-free quantization strategy within QFX to minimize DSP usage. QFX is implemented as a PyTorch-based library that efficiently emulates fixed-point arithmetic, supported by FPGA HLS, in a differentiable manner during backpropagation. With minimal effort, models trained with QFX can readily be deployed through HLS, producing the same numerical results as their software counterparts. Our evaluation shows that compared to post-training quantization, QFX can quantize models trained with element-wise layers quantized to fewer bits and achieve higher accuracy on both CIFAR-10 and ImageNet datasets. We further demonstrate the efficacy of multiplier-free quantization using a state-of-the-art binarized neural network accelerator designed for an embedded FPGA (AMD Xilinx Ultra96 v2). We plan to release QFX in open-source format.

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.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Transformer-based large language models (LLMs) have achieved remarkable success as model sizes continue to grow, yet their deployment remains challenging due to significant computational and memory demands. Quantization has emerged as a promising solution, and state-of-the-art quantization algorithms for LLMs introduce the need for mixed-precision matrix multiplication (mpGEMM), where lower-precision weights are multiplied with higher-precision activations. Despite its benefits, current hardware accelerators such as GPUs and TPUs lack native support for efficient mpGEMM, leading to inefficient dequantization operations in the main sequential loop. To address this limitation, we introduce MixPE, a specialized mixed-precision processing element designed for efficient low-bit quantization in LLM inference. MixPE leverages two key innovations to minimize dequantization overhead and unlock the full potential of low-bit quantization. First, recognizing that scale and zero point are shared within each quantization group, we propose performing dequantization after per-group mpGEMM, significantly reducing dequantization overhead. Second, instead of relying on conventional multipliers, MixPE utilizes efficient shift\&add operations for multiplication, optimizing both computation and energy efficiency. Our experimental results demonstrate that MixPE surpasses the state-of-the-art quantization accelerators by 2.6times speedup and 1.4times energy reduction.

In recent times, the emergence of Large Language Models (LLMs) has resulted in increasingly larger model size, posing challenges for inference on low-resource devices. Prior approaches have explored offloading to facilitate low-memory inference but often suffer from efficiency due to I/O bottlenecks. To achieve low-latency LLMs inference on resource-constrained devices, we introduce HeteGen, a novel approach that presents a principled framework for heterogeneous parallel computing using CPUs and GPUs. Based on this framework, HeteGen further employs heterogeneous parallel computing and asynchronous overlap for LLMs to mitigate I/O bottlenecks. Our experiments demonstrate a substantial improvement in inference speed, surpassing state-of-the-art methods by over 317% at most.

It is now a common business practice to buy access to large language model (LLM) inference rather than self-host, because of significant upfront hardware infrastructure and energy costs. However, as a buyer, there is no mechanism to verify the authenticity of the advertised service including the serving hardware platform, e.g. that it is actually being served using an NVIDIA H100. Furthermore, there are reports suggesting that model providers may deliver models that differ slightly from the advertised ones, often to make them run on less expensive hardware. That way, a client pays premium for a capable model access on more expensive hardware, yet ends up being served by a (potentially less capable) cheaper model on cheaper hardware. In this paper we introduce \textbf{hardware and software platform inference (HSPI)} -- a method for identifying the underlying architecture and software stack of a (black-box) machine learning model solely based on its input-output behavior. Our method leverages the inherent differences of various architectures and compilers to distinguish between different types and software stacks. By analyzing the numerical patterns in the model's outputs, we propose a classification framework capable of accurately identifying the used for model inference as well as the underlying software configuration. Our findings demonstrate the feasibility of inferring type from black-box models. We evaluate HSPI against models served on different real hardware and find that in a white-box setting we can distinguish between different s with between 83.9% and 100% accuracy. Even in a black-box setting we are able to achieve results that are up to three times higher than random guess accuracy.

Recent advancements in Large Language Model (LLM) compression, such as BitNet and BitNet b1.58, have marked significant strides in reducing the computational demands of LLMs through innovative one-bit quantization techniques. We extend this frontier by looking at Large Inference Models (LIMs) that have become indispensable across various applications. However, their scale and complexity often come at a significant computational cost. We introduce a novel approach that leverages one-bit algorithm unrolling, effectively integrating information from the physical world in the model architecture. Our method achieves a bit-per-link rate significantly lower than the 1.58 bits reported in prior work, thanks to the natural sparsity that emerges in our network architectures. We numerically demonstrate that the proposed one-bit algorithm unrolling scheme can improve both training and test outcomes by effortlessly increasing the number of layers while substantially compressing the network. Additionally, we provide theoretical results on the generalization gap, convergence rate, stability, and sensitivity of our proposed one-bit algorithm unrolling.

In this paper, we present a novel method that reduces model inference latency during distributed deployment of Large Language Models (LLMs). Our contribution is an optimized inference deployment scheme that address the current limitations of state-of-the-art quantization kernels when used in conjunction with Tensor Parallel (TP). Our method preserves data locality in GPU memory access patterns and exploits a priori knowledge of TP to reduce global communication. We demonstrate an up to 1.81x speedup over existing methods for Llama-70B and up to 1.78x speedup for IBM WatsonX's Granite-20B MLP layer problem sizes on A100 and H100 NVIDIA DGX Systems for a variety of TP settings.

Web applications are increasingly becoming the primary platform for AI service delivery, making in-browser deep learning (DL) inference more prominent. However, current in-browser inference systems fail to effectively utilize advanced web programming techniques and customize kernels for various client devices, leading to suboptimal performance. To address the issues, this paper presents the first in-browser inference system, nn-JIT.web, which enables just-in-time (JIT) auto-generation of optimized kernels for both CPUs and GPUs during inference. The system achieves this by using two novel web programming techniques that can significantly reduce kernel generation time, compared to other tensor compilers such as TVM, while maintaining or even improving performance. The first technique, Tensor-Web Compiling Co-Design, lowers compiling costs by unifying tensor and web compiling and eliminating redundant and ineffective compiling passes. The second technique, Web-Specific Lite Kernel Optimization Space Design, reduces kernel tuning costs by focusing on web programming requirements and efficient hardware resource utilization, limiting the optimization space to only dozens. nn-JIT.web is evaluated for modern transformer models on a range of client devices, including the mainstream CPUs and GPUs from ARM, Intel, AMD and Nvidia. Results show that nn-JIT.web can achieve up to 8.2x faster within 30 seconds compared to the baselines across various models.

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.

The performance of neural networks improves when more parameters are used. However, the model sizes are constrained by the available on-device memory during training and inference. Although applying techniques like quantization can alleviate the constraint, they suffer from performance degradation. In this work, we introduce NeuZip, a new weight compression scheme based on the entropy of floating-point numbers in neural networks. With NeuZip, we are able to achieve memory-efficient training and inference without sacrificing performance. Notably, we significantly reduce the memory footprint of training a Llama-3 8B model from 31GB to less than 16GB, while keeping the training dynamics fully unchanged. In inference, our method can reduce memory usage by more than half while maintaining near-lossless performance. Our code is publicly available.

Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training quantization for high-performance inference. Recent works propose low-bitwidth (e.g., 8-bit or 4-bit) quantization for diffusion models, however 4-bit integer quantization typically results in low-quality images. We observe that on several widely used hardware platforms, there is little or no difference in compute capability between floating-point and integer arithmetic operations of the same bitwidth (e.g., 8-bit or 4-bit). Therefore, we propose an effective floating-point quantization method for diffusion models that provides better image quality compared to integer quantization methods. We employ a floating-point quantization method that was effective for other processing tasks, specifically computer vision and natural language tasks, and tailor it for diffusion models by integrating weight rounding learning during the mapping of the full-precision values to the quantized values in the quantization process. We comprehensively study integer and floating-point quantization methods in state-of-the-art diffusion models. Our floating-point quantization method not only generates higher-quality images than that of integer quantization methods, but also shows no noticeable degradation compared to full-precision models (32-bit floating-point), when both weights and activations are quantized to 8-bit floating-point values, while has minimal degradation with 4-bit weights and 8-bit activations.

Speculative decoding (SD) accelerates large language model inference by using a smaller draft model to predict multiple tokens, which are then verified in parallel by the larger target model. However, the limited capacity of the draft model often necessitates tree-based sampling to improve prediction accuracy, where multiple candidates are generated at each step. We identify a key limitation in this approach: the candidates at the same step are derived from the same representation, limiting diversity and reducing overall effectiveness. To address this, we propose Jakiro, leveraging Mixture of Experts (MoE), where independent experts generate diverse predictions, effectively decoupling correlations among candidates. Furthermore, we introduce a hybrid inference strategy, combining autoregressive decoding for initial tokens with parallel decoding for subsequent stages, and enhance the latter with contrastive mechanism in features to improve accuracy. Our method significantly boosts prediction accuracy and achieves higher inference speedups. Extensive experiments across diverse models validate the effectiveness and robustness of our approach, establishing a new SOTA in speculative decoding. Our codes are available at https://github.com/haiduo/Jakiro.

This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical evaluation across models ranging from 10M to 1B parameters, we demonstrate that quantization can achieve up to 68% reduction in model size while maintaining performance within 6% of full-precision baselines when utilizing our proposed scaling factor {\gamma}. Our experiments show that INT8 quantization delivers a 40% reduction in computational cost and power consumption, while INT4 quantization further improves these metrics by 60%. We introduce a novel theoretical framework for mixed-precision quantization, deriving optimal bit allocation strategies based on layer sensitivity and weight variance. Hardware efficiency evaluations on edge devices reveal that our quantization approach enables up to 2.4x throughput improvement for INT8 and 3x for INT4, with 60% power reduction compared to full-precision models.

With the advancement of large language models (LLMs), solving complex reasoning tasks has gained increasing attention. Inference-time computation methods (e.g., Best-of-N, beam search, et al.) are particularly valuable as they can enhance reasoning performance without modifying model parameters or requiring additional training. However, these techniques come with implementation challenges, and most existing methods remain at the proof-of-concept stage with limited practical adoption due to their computational complexity and varying effectiveness across different tasks. In this paper, we investigate and benchmark diverse inference-time computation strategies across reasoning tasks of varying complexity. Since most current methods rely on a proposer-verifier pipeline that first generates candidate solutions (e.g., reasoning solutions) and then selects the best one based on reward signals (e.g., RLHF rewards, process rewards), our research focuses on optimizing both candidate solution generation (e.g., instructing prompts, hyperparameters such as temperature and top-p) and reward mechanisms (e.g., self-evaluation, reward types). Through extensive experiments (more than 20,000 A100-80G GPU hours with over 1,000 experiments) across a variety of models (e.g., Llama, Qwen, and Mistral families) of various sizes, our ablation studies reveal that previously overlooked strategies can significantly enhance performance (e.g., tuning temperature can improve reasoning task performance by up to 5%). Furthermore, we establish a standardized benchmark for inference-time computation by systematically evaluating six representative methods across eight reasoning tasks. These findings provide a stronger foundation for future research. The code is available at https://github.com/usail-hkust/benchmark_inference_time_computation_LLM

Large Language Models (LLMs) have propelled groundbreaking advancements across several domains and are commonly used for text generation applications. However, the computational demands of these complex models pose significant challenges, requiring efficient hardware acceleration. Benchmarking the performance of LLMs across diverse hardware platforms is crucial to understanding their scalability and throughput characteristics. We introduce LLM-Inference-Bench, a comprehensive benchmarking suite to evaluate the hardware inference performance of LLMs. We thoroughly analyze diverse hardware platforms, including GPUs from Nvidia and AMD and specialized AI accelerators, Intel Habana and SambaNova. Our evaluation includes several LLM inference frameworks and models from LLaMA, Mistral, and Qwen families with 7B and 70B parameters. Our benchmarking results reveal the strengths and limitations of various models, hardware platforms, and inference frameworks. We provide an interactive dashboard to help identify configurations for optimal performance for a given hardware platform.

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Learning curve extrapolation aims to predict model performance in later epochs of training, based on the performance in earlier epochs. In this work, we argue that, while the inherent uncertainty in the extrapolation of learning curves warrants a Bayesian approach, existing methods are (i) overly restrictive, and/or (ii) computationally expensive. We describe the first application of prior-data fitted neural networks (PFNs) in this context. A PFN is a transformer, pre-trained on data generated from a prior, to perform approximate Bayesian inference in a single forward pass. We propose LC-PFN, a PFN trained to extrapolate 10 million artificial right-censored learning curves generated from a parametric prior proposed in prior art using MCMC. We demonstrate that LC-PFN can approximate the posterior predictive distribution more accurately than MCMC, while being over 10 000 times faster. We also show that the same LC-PFN achieves competitive performance extrapolating a total of 20 000 real learning curves from four learning curve benchmarks (LCBench, NAS-Bench-201, Taskset, and PD1) that stem from training a wide range of model architectures (MLPs, CNNs, RNNs, and Transformers) on 53 different datasets with varying input modalities (tabular, image, text, and protein data). Finally, we investigate its potential in the context of model selection and find that a simple LC-PFN based predictive early stopping criterion obtains 2 - 6x speed-ups on 45 of these datasets, at virtually no overhead.

The pervasiveness of proprietary language models has raised privacy concerns for users' sensitive data, emphasizing the need for private inference (PI), where inference is performed directly on encrypted inputs. However, current PI methods face prohibitively higher communication and latency overheads, primarily due to nonlinear operations. In this paper, we present a comprehensive analysis to understand the role of nonlinearities in transformer-based decoder-only language models. We introduce AERO, a four-step architectural optimization framework that refines the existing LLM architecture for efficient PI by systematically removing nonlinearities such as LayerNorm and GELU and reducing FLOPs counts. For the first time, we propose a Softmax-only architecture with significantly fewer FLOPs tailored for efficient PI. Furthermore, we devise a novel entropy regularization technique to improve the performance of Softmax-only models. AERO achieves up to 4.23times communication and 1.94times latency reduction. We validate the effectiveness of AERO by benchmarking it against the state-of-the-art.

Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods only compare model outputs to ground-truth answers, obscuring insights into reasoning processes. To address these limitations, we introduce GSM-Ranges, a dataset generator derived from GSM8K that systematically perturbs numerical values in math problems to assess model robustness across varying numerical scales. Additionally, we propose a novel grading methodology that distinguishes between logical and non-logical errors, offering a more precise evaluation of reasoning processes beyond computational accuracy. Our experiments with various models reveal a significant increase in logical error rates-up to 14 percentage points-as numerical complexity rises, demonstrating a general weakness in reasoning with out-of-distribution numerical values. Moreover, while models demonstrate high accuracy on standalone arithmetic tasks, their performance deteriorates substantially when computations are embedded within word problems. These findings provide a comprehensive evaluation of LLMs' mathematical reasoning capabilities and inform future research directions for improving numerical generalization in language models.

Quantization emerges as one of the most promising compression technologies for deploying efficient large models for various real time application in recent years. Considering that the storage and IO of weights take up the vast majority of the overhead inside a large model, weight only quantization can lead to large gains. However, existing quantization schemes suffer from significant accuracy degradation at very low bits, or require some additional computational overhead when deployed, making it difficult to be applied to large-scale applications in industry. In this paper, we propose decoupleQ, achieving a substantial increase in model accuracy, especially at very low bits. decoupleQ abandons the traditional heuristic quantization paradigm and decouples the model parameters into integer and floating-point parts, thus transforming the quantization problem into a traditional mathematical optimization problem with constraints, which is then solved alternatively by off-the-shelf optimization methods. Quantization via decoupleQ is linear and uniform, making it hardware-friendlier than non-uniform counterpart, and enabling the idea to be migrated to high-bit quantization to enhance its robustness. Our method has achieved well on-line accuracy near fp16/bf16 on the 2-bit quantization of large speech models in ByteDance. The code is available at https://github.com/bytedance/decoupleQ

One approach to reducing the massive costs of large language models (LLMs) is the use of quantized or sparse representations for training or deployment. While post-training compression methods are very popular, the question of obtaining even more accurate compressed models by directly training over such representations, i.e., Quantization-Aware Training (QAT), is still open: for example, a recent study (arXiv:2411.04330v2) put the "optimal" bit-width at which models can be trained using QAT, while staying accuracy-competitive with standard FP16/BF16 precision, at 8-bits weights and activations. We advance this state-of-the-art via a new method called QuEST, which is Pareto-competitive with FP16, i.e., it provides better accuracy at lower model size, while training models with weights and activations in 4-bits or less. Moreover, QuEST allows stable training with 1-bit weights and activations. QuEST achieves this by improving two key aspects of QAT methods: (1) accurate and fast quantization of the (continuous) distributions of weights and activations via Hadamard normalization and MSE-optimal fitting; (2) a new trust gradient estimator based on the idea of explicitly minimizing the error between the noisy gradient computed over quantized states and the "true" (but unknown) full-precision gradient. Experiments on Llama-type architectures show that QuEST induces stable scaling laws across the entire range of hardware-supported precisions, and can be extended to sparse representations. We provide GPU kernel support showing that models produced by QuEST can be executed efficiently. Our code is available at https://github.com/IST-DASLab/QuEST.

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline's main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f. Online training on these unproved theorems increases accuracy to 82.6%. With a similar computational budget, we improve the state of the art on the Lean-based miniF2F-curriculum dataset from 31% to 42% proving accuracy.

As the size of large language models (LLMs) continues to grow, model compression without sacrificing accuracy has become a crucial challenge for deployment. While some quantization methods, such as GPTQ, have made progress in achieving acceptable 4-bit weight-only quantization, attempts at lower bit quantization often result in severe performance degradation. In this paper, we introduce a technique called norm tweaking, which can be used as a plugin in current PTQ methods to achieve high precision while being cost-efficient. Our approach is inspired by the observation that rectifying the quantized activation distribution to match its float counterpart can readily restore accuracy for LLMs. To achieve this, we carefully design a tweaking strategy that includes calibration data generation and channel-wise distance constraint to update the weights of normalization layers for better generalization. We conduct extensive experiments on various datasets using several open-sourced LLMs. Our method demonstrates significant improvements in both weight-only quantization and joint quantization of weights and activations, surpassing existing PTQ methods. On GLM-130B and OPT-66B, our method even achieves the same level of accuracy at 2-bit quantization as their float ones. Our simple and effective approach makes it more practical for real-world applications.

Current inference scaling methods, such as Self-consistency and Best-of-N, have proven effective in improving the accuracy of LLMs on complex reasoning tasks. However, these methods rely heavily on the quality of candidate responses and are unable to produce correct answers when all candidates are incorrect. In this paper, we propose a novel inference scaling strategy, CoT-based Synthesizer, which leverages CoT reasoning to synthesize superior answers by analyzing complementary information from multiple candidate responses, even when all candidate responses are flawed. To enable a lightweight and cost-effective implementation, we introduce an automated data generation pipeline that creates diverse training data. This allows smaller LLMs trained on this data to improve the inference accuracy of larger models, including API-based LLMs. Experimental results across four benchmark datasets with seven policy models demonstrate that our method significantly enhances performance, with gains of 11.8% for Llama3-8B and 10.3% for GPT-4o on the MATH dataset. The corresponding training data and code are publicly available on https://github.com/RUCKBReasoning/CoT-based-Synthesizer.

Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position embedding for extrapolation by kernelizing positional differences. We achieve this goal using conditionally positive definite (CPD) kernels, a class of functions known for generalizing distance metrics. To maintain the inner product interpretation of self-attention, we show that a CPD kernel can be transformed into a PD kernel by adding a constant offset. This offset is implicitly absorbed in the Softmax normalization during self-attention. The diversity of CPD kernels allows us to derive various RPEs that enable length extrapolation in a principled way. Experiments demonstrate that the logarithmic variant achieves excellent extrapolation performance on three large language modeling datasets. Our implementation and pretrained checkpoints are released at https://github.com/chijames/KERPLE.git.

Speculative decoding (SD) has attracted a significant amount of research attention due to the substantial speedup it can achieve for LLM inference. However, despite the high speedups they offer, speculative decoding methods often achieve optimal performance on high-end devices or with a substantial GPU memory overhead. Given limited memory and the necessity of quantization, a high-performing model on a high-end GPU can slow down by up to 7 times. To this end, we propose Skippy Simultaneous Speculative Decoding (or S3D), a cost-effective self-speculative SD method based on simultaneous multi-token decoding and mid-layer skipping. When compared against recent effective open-source SD systems, our method has achieved one of the top performance-memory ratios while requiring minimal architecture changes and training data. Leveraging our memory efficiency, we created a smaller yet more effective SD model based on Phi-3. It is 1.4 to 2 times faster than the quantized EAGLE model and operates in half-precision while using less VRAM.

Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33\% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3\times speedup over 16-bit baseline. Code is available at https://github.com/utkarsh-dmx/project-resq.

Previous studies have typically assumed that large language models are unable to accurately perform arithmetic operations, particularly multiplication of >8 digits, and operations involving decimals and fractions, without the use of calculator tools. This paper aims to challenge this misconception. With sufficient training data, a 2 billion-parameter language model can accurately perform multi-digit arithmetic operations with almost 100% accuracy without data leakage, significantly surpassing GPT-4 (whose multi-digit multiplication accuracy is only 4.3%). We also demonstrate that our MathGLM, fine-tuned from GLM-10B on a dataset with additional multi-step arithmetic operations and math problems described in text, achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set.

Deploying neural networks on microcontroller units (MCUs) presents substantial challenges due to their constrained computation and memory resources. Previous researches have explored patch-based inference as a strategy to conserve memory without sacrificing model accuracy. However, this technique suffers from severe redundant computation overhead, leading to a substantial increase in execution latency. A feasible solution to address this issue is mixed-precision quantization, but it faces the challenges of accuracy degradation and a time-consuming search time. In this paper, we propose QuantMCU, a novel patch-based inference method that utilizes value-driven mixed-precision quantization to reduce redundant computation. We first utilize value-driven patch classification (VDPC) to maintain the model accuracy. VDPC classifies patches into two classes based on whether they contain outlier values. For patches containing outlier values, we apply 8-bit quantization to the feature maps on the dataflow branches that follow. In addition, for patches without outlier values, we utilize value-driven quantization search (VDQS) on the feature maps of their following dataflow branches to reduce search time. Specifically, VDQS introduces a novel quantization search metric that takes into account both computation and accuracy, and it employs entropy as an accuracy representation to avoid additional training. VDQS also adopts an iterative approach to determine the bitwidth of each feature map to further accelerate the search process. Experimental results on real-world MCU devices show that QuantMCU can reduce computation by 2.2x on average while maintaining comparable model accuracy compared to the state-of-the-art patch-based inference methods.

Striking an optimal balance between minimal drafting latency and high speculation accuracy to enhance the inference speed of Large Language Models remains a significant challenge in speculative decoding. In this paper, we introduce Falcon, an innovative semi-autoregressive speculative decoding framework fashioned to augment both the drafter's parallelism and output quality. Falcon incorporates the Coupled Sequential Glancing Distillation technique, which fortifies inter-token dependencies within the same block, leading to increased speculation accuracy. We offer a comprehensive theoretical analysis to illuminate the underlying mechanisms. Additionally, we introduce a Custom-Designed Decoding Tree, which permits the drafter to generate multiple tokens in a single forward pass and accommodates multiple forward passes as needed, thereby boosting the number of drafted tokens and significantly improving the overall acceptance rate. Comprehensive evaluations on benchmark datasets such as MT-Bench, HumanEval, and GSM8K demonstrate Falcon's superior acceleration capabilities. The framework achieves a lossless speedup ratio ranging from 2.91x to 3.51x when tested on the Vicuna and LLaMA2-Chat model series. These results outstrip existing speculative decoding methods for LLMs, including Eagle, Medusa, Lookahead, SPS, and PLD, while maintaining a compact drafter architecture equivalent to merely two Transformer layers.

Speculative decoding emerges as a pivotal technique for enhancing the inference speed of Large Language Models (LLMs). Despite recent research aiming to improve prediction efficiency, multi-sample speculative decoding has been overlooked due to varying numbers of accepted tokens within a batch in the verification phase. Vanilla method adds padding tokens in order to ensure that the number of new tokens remains consistent across samples. However, this increases the computational and memory access overhead, thereby reducing the speedup ratio. We propose a novel method that can resolve the issue of inconsistent tokens accepted by different samples without necessitating an increase in memory or computing overhead. Furthermore, our proposed method can handle the situation where the prediction tokens of different samples are inconsistent without the need to add padding tokens. Sufficient experiments demonstrate the efficacy of our method. Our code is available at https://github.com/niyunsheng/EMS-SD.

Large language models (LLMs) have demonstrated remarkable capabilities across various tasks. However, their widespread application is hindered by the resource-intensive decoding process. To address this challenge, current approaches have incorporated additional decoding heads to enable parallel prediction of multiple subsequent tokens, thereby achieving inference acceleration. Nevertheless, the accuracy of these decoding heads falls short of the auto-regressive decoding approach. In light of these limitations, we propose Chimera, a novel framework specifically designed for speculative sampling. Within this framework, we introduce a lightweight draft model that effectively utilizes previously generated tokens to predict subsequent words. To ensure both accuracy and efficiency, we present two strategies within the lightweight draft model. Firstly, we focus on capturing short-range dependencies at the bottom layer. Secondly, we leverage the readily available representations from the original LLM.Through empirical evaluation on the Vicuna and LlaMA-2 series, Chimera demonstrates impressive results, achieving an average latency speedup ratio of 2.7x compared to the vanilla auto-regressive decoding approach. This highlights the potential of our proposed framework in significantly improving the efficiency of large language models during the decoding process.

The rapid growth in the parameters of large language models (LLMs) has made inference latency a fundamental bottleneck, limiting broader application of LLMs. Speculative decoding represents a lossless approach to accelerate inference through a guess-and-verify paradigm, leveraging the parallel capabilities of modern hardware. Some speculative decoding methods rely on additional structures to guess draft tokens, such as small models or parameter-efficient architectures, which need extra training before use. Alternatively, retrieval-based train-free techniques build libraries from pre-existing corpora or by n-gram generation. However, they face challenges like large storage requirements, time-consuming retrieval, and limited adaptability. Observing that candidate tokens generated during the decoding process are likely to reoccur in future sequences, we propose Token Recycling. This approach stores candidate tokens in an adjacency matrix and employs a breadth-first search (BFS)-like algorithm on the matrix to construct a draft tree. The tree is then validated through tree attention. New candidate tokens from the decoding process are then used to update the matrix. Token Recycling requires \textless2MB of additional storage and achieves approximately 2x speedup across all sizes of LLMs. It significantly outperforms existing train-free methods by 30\% and even a training method by 25\%. It can be directly applied to any existing LLMs and tasks without the need for adaptation.

This paper introduces PowerInfer, a high-speed Large Language Model (LLM) inference engine on a personal computer (PC) equipped with a single consumer-grade GPU. The key underlying the design of PowerInfer is exploiting the high locality inherent in LLM inference, characterized by a power-law distribution in neuron activation. This distribution indicates that a small subset of neurons, termed hot neurons, are consistently activated across inputs, while the majority, cold neurons, vary based on specific inputs. PowerInfer exploits such an insight to design a GPU-CPU hybrid inference engine: hot-activated neurons are preloaded onto the GPU for fast access, while cold-activated neurons are computed on the CPU, thus significantly reducing GPU memory demands and CPU-GPU data transfers. PowerInfer further integrates adaptive predictors and neuron-aware sparse operators, optimizing the efficiency of neuron activation and computational sparsity. Evaluation shows that PowerInfer attains an average token generation rate of 13.20 tokens/s, with a peak of 29.08 tokens/s, across various LLMs (including OPT-175B) on a single NVIDIA RTX 4090 GPU, only 18% lower than that achieved by a top-tier server-grade A100 GPU. This significantly outperforms llama.cpp by up to 11.69x while retaining model accuracy.

Conformal prediction is emerging as a popular paradigm for providing rigorous uncertainty quantification in machine learning since it can be easily applied as a post-processing step to already trained models. In this paper, we extend conformal prediction to the federated learning setting. The main challenge we face is data heterogeneity across the clients - this violates the fundamental tenet of exchangeability required for conformal prediction. We propose a weaker notion of partial exchangeability, better suited to the FL setting, and use it to develop the Federated Conformal Prediction (FCP) framework. We show FCP enjoys rigorous theoretical guarantees and excellent empirical performance on several computer vision and medical imaging datasets. Our results demonstrate a practical approach to incorporating meaningful uncertainty quantification in distributed and heterogeneous environments. We provide code used in our experiments https://github.com/clu5/federated-conformal.

Prior work on Private Inference (PI) -- inferences performed directly on encrypted input -- has focused on minimizing a network's ReLUs, which have been assumed to dominate PI latency rather than FLOPs. Recent work has shown that FLOPs for PI can no longer be ignored and incur high latency penalties. In this paper, we develop DeepReShape, a technique that optimizes neural network architectures under PI's constraints, optimizing for both ReLUs and FLOPs for the first time. The key insight is strategically allocating channels to position the network's ReLUs in order of their criticality to network accuracy, simultaneously optimizes ReLU and FLOPs efficiency. DeepReShape automates network development with an efficient process, and we call generated networks HybReNets. We evaluate DeepReShape using standard PI benchmarks and demonstrate a 2.1% accuracy gain with a 5.2times runtime improvement at iso-ReLU on CIFAR-100 and an 8.7times runtime improvement at iso-accuracy on TinyImageNet. Furthermore, we investigate the significance of network selection in prior ReLU optimizations and shed light on the key network attributes for superior PI performance.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

Deep neural network (DNN) deployment has been confined to larger hardware devices due to their expensive computational requirements. This challenge has recently reached another scale with the emergence of large language models (LLMs). In order to reduce both their memory footprint and latency, a promising technique is quantization. It consists in converting floating point representations to low bit-width fixed point representations, usually by assuming a uniform mapping onto a regular grid. This process, referred to in the literature as uniform quantization, may however be ill-suited as most DNN weights and activations follow a bell-shaped distribution. This is even worse on LLMs whose weight distributions are known to exhibit large, high impact, outlier values. In this work, we propose an improvement over the most commonly adopted way to tackle this limitation in deep learning models quantization, namely, non-uniform quantization. NUPES leverages automorphisms to preserve the scalar multiplications. Such transformations are derived from power functions. However, the optimization of the exponent parameter and weight values remains a challenging and novel problem which could not be solved with previous post training optimization techniques which only learn to round up or down weight values in order to preserve the predictive function. We circumvent this limitation with a new paradigm: learning new quantized weights over the entire quantized space. Similarly, we enable the optimization of the power exponent, i.e. the optimization of the quantization operator itself during training by alleviating all the numerical instabilities. The resulting predictive function is compatible with integer-only low-bit inference. We show the ability of the method to achieve state-of-the-art compression rates in both, data-free and data-driven configurations.

Despite the impressive performance of LLMs, their widespread adoption faces challenges due to substantial computational and memory requirements during inference. Recent advancements in model compression and system-level optimization methods aim to enhance LLM inference. This survey offers an overview of these methods, emphasizing recent developments. Through experiments on LLaMA(/2)-7B, we evaluate various compression techniques, providing practical insights for efficient LLM deployment in a unified setting. The empirical analysis on LLaMA(/2)-7B highlights the effectiveness of these methods. Drawing from survey insights, we identify current limitations and discuss potential future directions to improve LLM inference efficiency. We release the codebase to reproduce the results presented in this paper at https://github.com/nyunAI/Faster-LLM-Survey

As the Large Language Model (LLM) becomes increasingly important in various domains. However, the following challenges still remain unsolved in accelerating LLM inference: (1) Synchronized partial softmax update. The softmax operation requires a synchronized update operation among each partial softmax result, leading to ~20% overheads for the attention computation in LLMs. (2) Under-utilized computation of flat GEMM. The shape of matrices performing GEMM in LLM inference is flat, leading to under-utilized computation and >50% performance loss after padding zeros in previous designs. (3) Performance loss due to static dataflow. Kernel performance in LLM depends on varied input data features, hardware configurations, etc. A single and static dataflow may lead to a 50.25% performance loss for GEMMs of different shapes in LLM inference. We present FlashDecoding++, a fast LLM inference engine supporting mainstream LLMs and hardware back-ends. To tackle the above challenges, FlashDecoding++ creatively proposes: (1) Asynchronized softmax with unified max value. FlashDecoding++ introduces a unified max value technique for different partial softmax computations to avoid synchronization. (2) Flat GEMM optimization with double buffering. FlashDecoding++ points out that flat GEMMs with different shapes face varied bottlenecks. Then, techniques like double buffering are introduced. (3) Heuristic dataflow with hardware resource adaptation. FlashDecoding++ heuristically optimizes dataflow using different hardware resource considering input dynamics. Due to the versatility of optimizations in FlashDecoding++, FlashDecoding++ can achieve up to 4.86x and 2.18x speedup on both NVIDIA and AMD GPUs compared to Hugging Face implementations. FlashDecoding++ also achieves an average speedup of 1.37x compared to state-of-the-art LLM inference engines on mainstream LLMs.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

In recent years, large language models have demonstrated remarkable performance across various natural language processing (NLP) tasks. However, deploying these models for real-world applications often requires efficient inference solutions to handle the computational demands. In this paper, we explore the utilization of CPUs for accelerating the inference of large language models. Specifically, we introduce a parallelized approach to enhance throughput by 1) Exploiting the parallel processing capabilities of modern CPU architectures, 2) Batching the inference request. Our evaluation shows the accelerated inference engine gives an 18-22x improvement in the generated token per sec. The improvement is more with longer sequence and larger models. In addition to this, we can also run multiple workers in the same machine with NUMA node isolation to further improvement in tokens/s. Table 2, we have received 4x additional improvement with 4 workers. This would also make Gen-AI based products and companies environment friendly, our estimates shows that CPU usage for Inference could reduce the power consumption of LLMs by 48.9% while providing production ready throughput and latency.

We present a novel inference scheme, self-speculative decoding, for accelerating Large Language Models (LLMs) without the need for an auxiliary model. This approach is characterized by a two-stage process: drafting and verification. The drafting stage generates draft tokens at a slightly lower quality but more quickly, which is achieved by selectively skipping certain intermediate layers during drafting Subsequently, the verification stage employs the original LLM to validate those draft output tokens in one forward pass. This process ensures the final output remains identical to that produced by the unaltered LLM, thereby maintaining output quality. The proposed method requires no additional neural network training and no extra memory footprint, making it a plug-and-play and cost-effective solution for inference acceleration. Benchmarks with LLaMA-2 and its fine-tuned models demonstrated a speedup up to 1.73times.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

To tackle the high inference latency exhibited by autoregressive language models, previous studies have proposed an early-exiting framework that allocates adaptive computation paths for each token based on the complexity of generating the subsequent token. However, we observed several shortcomings, including performance degradation caused by a state copying mechanism or numerous exit paths, and sensitivity to exit confidence thresholds. Consequently, we propose a Fast and Robust Early-Exiting (FREE) framework, which incorporates a shallow-deep module and a synchronized parallel decoding. Our framework enables faster inference by synchronizing the decoding process of the current token with previously stacked early-exited tokens. Furthermore, as parallel decoding allows us to observe predictions from both shallow and deep models, we present a novel adaptive threshold estimator that exploits a Beta mixture model to determine suitable confidence thresholds. We empirically demonstrated the superiority of our proposed framework on extensive generation tasks.

Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when the order v is large, and GPU-specific implementations are limited. We address the precision limitations of current numerical implementations while dramatically improving the runtime. We propose two novel algorithms for computing the logarithm of modified Bessel functions of the first and second kinds by computing intermediate values on a logarithmic scale. Our algorithms are robust and never have issues with underflows or overflows while having relative errors on the order of machine precision, even for inputs where existing libraries fail. In C++/CUDA, our algorithms have median and maximum speedups of 45x and 6150x for GPU and 17x and 3403x for CPU, respectively, over the ranges of inputs and third-party libraries tested. Compared to SciPy, the algorithms have median and maximum speedups of 77x and 300x for GPU and 35x and 98x for CPU, respectively, over the tested inputs. The ability to robustly compute a solution and the low relative errors allow us to fit von Mises-Fisher, vMF, distributions to high-dimensional neural network features. This is, e.g., relevant for uncertainty quantification in metric learning. We obtain image feature data by processing CIFAR10 training images with the convolutional layers of a pre-trained ResNet50. We successfully fit vMF distributions to 2048-, 8192-, and 32768-dimensional image feature data using our algorithms. Our approach provides fast and accurate results while existing implementations in SciPy and mpmath fail to fit successfully. Our approach is readily implementable on GPUs, and we provide a fast open-source implementation alongside this paper.

Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples are able to manipulate conformal methods to construct prediction sets with invalid coverage rates, as the i.i.d. assumption is violated. To address this issue, a recent work, Randomized Smoothed Conformal Prediction (RSCP), was first proposed to certify the robustness of conformal prediction methods to adversarial noise. However, RSCP has two major limitations: (i) its robustness guarantee is flawed when used in practice and (ii) it tends to produce large uncertainty sets. To address these limitations, we first propose a novel framework called RSCP+ to provide provable robustness guarantee in evaluation, which fixes the issues in the original RSCP method. Next, we propose two novel methods, Post-Training Transformation (PTT) and Robust Conformal Training (RCT), to effectively reduce prediction set size with little computation overhead. Experimental results in CIFAR10, CIFAR100, and ImageNet suggest the baseline method only yields trivial predictions including full label set, while our methods could boost the efficiency by up to 4.36times, 5.46times, and 16.9times respectively and provide practical robustness guarantee. Our codes are available at https://github.com/Trustworthy-ML-Lab/Provably-Robust-Conformal-Prediction.

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (an additional 7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively.

A lot of recent progress has been made in ultra low-bit quantization, promising significant improvements in latency, memory footprint and energy consumption on edge devices. Quantization methods such as Learned Step Size Quantization can achieve model accuracy that is comparable to full-precision floating-point baselines even with sub-byte quantization. However, it is extremely challenging to deploy these ultra low-bit quantized models on mainstream CPU devices because commodity SIMD (Single Instruction, Multiple Data) hardware typically supports no less than 8-bit precision. To overcome this limitation, we propose DeepGEMM, a lookup table based approach for the execution of ultra low-precision convolutional neural networks on SIMD hardware. The proposed method precomputes all possible products of weights and activations, stores them in a lookup table, and efficiently accesses them at inference time to avoid costly multiply-accumulate operations. Our 2-bit implementation outperforms corresponding 8-bit integer kernels in the QNNPACK framework by up to 1.74x on x86 platforms.

The performance of large language models (LLMs) is closely linked to their underlying size, leading to ever-growing networks and hence slower inference. Speculative decoding has been proposed as a technique to accelerate autoregressive generation, leveraging a fast draft model to propose candidate tokens, which are then verified in parallel based on their likelihood under the target model. While this approach guarantees to reproduce the target output, it incurs a substantial penalty: many high-quality draft tokens are rejected, even when they represent objectively valid continuations. Indeed, we show that even powerful draft models such as GPT-4o, as well as human text cannot achieve high acceptance rates under the standard verification scheme. This severely limits the speedup potential of current speculative decoding methods, as an early rejection becomes overwhelmingly likely when solely relying on alignment of draft and target. We thus ask the following question: Can we adapt verification to recognize correct, but non-aligned replies? To this end, we draw inspiration from the LLM-as-a-judge framework, which demonstrated that LLMs are able to rate answers in a versatile way. We carefully design a dataset to elicit the same capability in the target model by training a compact module on top of the embeddings to produce ``judgements" of the current continuation. We showcase our strategy on the Llama-3.1 family, where our 8b/405B-Judge achieves a speedup of 9x over Llama-405B, while maintaining its quality on a large range of benchmarks. These benefits remain present even in optimized inference frameworks, where our method reaches up to 141 tokens/s for 8B/70B-Judge and 129 tokens/s for 8B/405B on 2 and 8 H100s respectively.

With the widespread deployment of long-context large language models (LLMs), there has been a growing demand for efficient support of high-throughput inference. However, as the key-value (KV) cache expands with the sequence length, the increasing memory footprint and the need to access it for each token generation both result in low throughput when serving long-context LLMs. While various dynamic sparse attention methods have been proposed to speed up inference while maintaining generation quality, they either fail to sufficiently reduce GPU memory consumption or introduce significant decoding latency by offloading the KV cache to the CPU. We present ShadowKV, a high-throughput long-context LLM inference system that stores the low-rank key cache and offloads the value cache to reduce the memory footprint for larger batch sizes and longer sequences. To minimize decoding latency, ShadowKV employs an accurate KV selection strategy that reconstructs minimal sparse KV pairs on-the-fly. By evaluating ShadowKV on a broad range of benchmarks, including RULER, LongBench, and Needle In A Haystack, and models like Llama-3.1-8B, Llama-3-8B-1M, GLM-4-9B-1M, Yi-9B-200K, Phi-3-Mini-128K, and Qwen2-7B-128K, we demonstrate that it can support up to 6times larger batch sizes and boost throughput by up to 3.04times on an A100 GPU without sacrificing accuracy, even surpassing the performance achievable with infinite batch size under the assumption of infinite GPU memory. The code is available at https://github.com/bytedance/ShadowKV.

This technical report describes the design and training of novel speculative decoding draft models, for accelerating the inference speeds of large language models in a production environment. By conditioning draft predictions on both context vectors and sampled tokens, we can train our speculators to efficiently predict high-quality n-grams, which the base model then accepts or rejects. This allows us to effectively predict multiple tokens per inference forward pass, accelerating wall-clock inference speeds of highly optimized base model implementations by a factor of 2-3x. We explore these initial results and describe next steps for further improvements.

In recent years, the advent of foundation models (FM) for digital pathology has relied heavily on scaling the pre-training datasets and the model size, yielding large and powerful models. While it resulted in improving the performance on diverse downstream tasks, it also introduced increased computational cost and inference time. In this work, we explore the distillation of a large foundation model into a smaller one, reducing the number of parameters by several orders of magnitude. Leveraging distillation techniques, our distilled model, H0-mini, achieves nearly comparable performance to large FMs at a significantly reduced inference cost. It is evaluated on several public benchmarks, achieving 3rd place on the HEST benchmark and 5th place on the EVA benchmark. Additionally, a robustness analysis conducted on the PLISM dataset demonstrates that our distilled model reaches excellent robustness to variations in staining and scanning conditions, significantly outperforming other state-of-the art models. This opens new perspectives to design lightweight and robust models for digital pathology, without compromising on performance.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

Leveraging recent advancements in large language models, modern neural code completion models have demonstrated the capability to generate highly accurate code suggestions. However, their massive size poses challenges in terms of computational costs and environmental impact, hindering their widespread adoption in practical scenarios. Dynamic inference emerges as a promising solution, as it allocates minimal computation during inference while maintaining the model's performance. In this research, we explore dynamic inference within the context of code completion. Initially, we conducted an empirical investigation on GPT-2, focusing on the inference capabilities of intermediate layers for code completion. We found that 54.4% of tokens can be accurately generated using just the first layer, signifying significant computational savings potential. Moreover, despite using all layers, the model still fails to predict 14.5% of tokens correctly, and the subsequent completions continued from them are rarely considered helpful, with only a 4.2% Acceptance Rate. These findings motivate our exploration of dynamic inference in code completion and inspire us to enhance it with a decision-making mechanism that stops the generation of incorrect code. We thus propose a novel dynamic inference method specifically tailored for code completion models. This method aims not only to produce correct predictions with largely reduced computation but also to prevent incorrect predictions proactively. Our extensive evaluation shows that it can averagely skip 1.7 layers out of 16 layers in the models, leading to an 11.2% speedup with only a marginal 1.1% reduction in ROUGE-L.

Large language models (LLMs) have shown remarkable capabilities in code generation. However, the effects of hallucinations (e.g., output noise) make it particularly challenging for LLMs to generate high-quality code in one pass. In this work, we propose a simple and effective uncertainty-aware selective contrastive decoding (USCD) mechanism to improve the quality of one-pass code generation in LLMs and reduce the impact of output noise. To be specific, we first elaborately designed a negative prompt (namely lame prompt) to output noise by removing input-output examples from the standard few-shot prompt. Our preliminary study shows that the Jensen-Shannon divergence (JS divergence) between token distribution uncertainty and the output noise is relatively low (approximately 0.25), indicating their high relevance. Then, we selectively eliminate output noise induced by lame prompts based on the uncertainty of the prediction distribution from the standard prompt. Notably, our proposed plug-and-play mechanism is an inference-only method, enjoying appealing flexibility. Extensive experiments on widely used benchmarks, e.g., HumanEval, MBPP, and MultiPL-E, upon several LLMs (i.e., Inocder-6b, CodeLlama-7b, WizardCoder-15b, StarCoder, and Llama2-7b), demonstrate that our proposed USCD significantly improves one-pass code generation, with an average pass@1 scores increase of 16.59\%. We will release code and data on GitHub.

Large language models (LLMs) have demonstrated remarkable capabilities, but their adoption is limited by high computational costs during inference. While increasing parameter counts enhances accuracy, it also widens the gap between state-of-the-art capabilities and practical deployability. We present Puzzle, a framework to accelerate LLM inference on specific hardware while preserving their capabilities. Through an innovative application of neural architecture search (NAS) at an unprecedented scale, Puzzle systematically optimizes models with tens of billions of parameters under hardware constraints. Our approach utilizes blockwise local knowledge distillation (BLD) for parallel architecture exploration and employs mixed-integer programming for precise constraint optimization. We demonstrate the real-world impact of our framework through Llama-3.1-Nemotron-51B-Instruct (Nemotron-51B), a publicly available model derived from Llama-3.1-70B-Instruct. Nemotron-51B achieves a 2.17x inference throughput speedup, fitting on a single NVIDIA H100 GPU while preserving 98.4% of the original model's capabilities. Nemotron-51B currently stands as the most accurate language model capable of inference on a single GPU with large batch sizes. Remarkably, this transformation required just 45B training tokens, compared to over 15T tokens used for the 70B model it was derived from. This establishes a new paradigm where powerful models can be optimized for efficient deployment with only negligible compromise of their capabilities, demonstrating that inference performance, not parameter count alone, should guide model selection. With the release of Nemotron-51B and the presentation of the Puzzle framework, we provide practitioners immediate access to state-of-the-art language modeling capabilities at significantly reduced computational costs.

Recent advances in deep learning methods such as LLMs and Diffusion models have created a need for improved quantization methods that can meet the computational demands of these modern architectures while maintaining accuracy. Towards this goal, we study the advantages of FP8 data formats for post-training quantization across 75 unique network architectures covering a wide range of tasks, including machine translation, language modeling, text generation, image classification, generation, and segmentation. We examine three different FP8 representations (E5M2, E4M3, and E3M4) to study the effects of varying degrees of trade-off between dynamic range and precision on model accuracy. Based on our extensive study, we developed a quantization workflow that generalizes across different network architectures. Our empirical results show that FP8 formats outperform INT8 in multiple aspects, including workload coverage (92.64% vs. 65.87%), model accuracy and suitability for a broader range of operations. Furthermore, our findings suggest that E4M3 is better suited for NLP models, whereas E3M4 performs marginally better than E4M3 on computer vision tasks. The code is publicly available on Intel Neural Compressor: https://github.com/intel/neural-compressor.