Daily Papers

Autoregressive (AR) Large Language Models (LLMs) have demonstrated significant success across numerous tasks. However, the AR modeling paradigm presents certain limitations; for instance, contemporary autoregressive LLMs are trained to generate one token at a time, which can result in noticeable latency. Recent advances have indicated that search and repeated sampling can enhance performance in various applications, such as theorem proving, code generation, and alignment, by utilizing greater computational resources during inference. In this study, we demonstrate that diffusion language models are capable of generating at least 32 tokens simultaneously, while exceeding the performance of AR models in text quality and on the LAMBADA natural language understanding benchmark. This outcome is achieved through a novel distillation method for discrete diffusion models, which reduces the number of inference steps by a factor of 32-64. Practically, our models, even without caching, can generate tokens at a rate that is up to 8 times faster than AR models employing KV caching, and we anticipate further improvements with the inclusion of caching. Moreover, we demonstrate the efficacy of our approach for diffusion language models with up to 860M parameters.

Autoregressive language models, despite their impressive capabilities, struggle with complex reasoning and long-term planning tasks. We introduce discrete diffusion models as a novel solution to these challenges. Through the lens of subgoal imbalance, we demonstrate how diffusion models effectively learn difficult subgoals that elude autoregressive approaches. We propose Multi-granularity Diffusion Modeling (MDM), which prioritizes subgoals based on difficulty during learning. On complex tasks like Countdown, Sudoku, and Boolean Satisfiability Problems, MDM significantly outperforms autoregressive models without using search techniques. For instance, MDM achieves 91.5\% and 100\% accuracy on Countdown and Sudoku, respectively, compared to 45.8\% and 20.7\% for autoregressive models. Our work highlights the potential of diffusion-based approaches in advancing AI capabilities for sophisticated language understanding and problem-solving tasks.

We present JanusFlow, a powerful framework that unifies image understanding and generation in a single model. JanusFlow introduces a minimalist architecture that integrates autoregressive language models with rectified flow, a state-of-the-art method in generative modeling. Our key finding demonstrates that rectified flow can be straightforwardly trained within the large language model framework, eliminating the need for complex architectural modifications. To further improve the performance of our unified model, we adopt two key strategies: (i) decoupling the understanding and generation encoders, and (ii) aligning their representations during unified training. Extensive experiments show that JanusFlow achieves comparable or superior performance to specialized models in their respective domains, while significantly outperforming existing unified approaches across standard benchmarks. This work represents a step toward more efficient and versatile vision-language models.

We propose Heterogeneous Masked Autoregression (HMA) for modeling action-video dynamics to generate high-quality data and evaluation in scaling robot learning. Building interactive video world models and policies for robotics is difficult due to the challenge of handling diverse settings while maintaining computational efficiency to run in real time. HMA uses heterogeneous pre-training from observations and action sequences across different robotic embodiments, domains, and tasks. HMA uses masked autoregression to generate quantized or soft tokens for video predictions. \ourshort achieves better visual fidelity and controllability than the previous robotic video generation models with 15 times faster speed in the real world. After post-training, this model can be used as a video simulator from low-level action inputs for evaluating policies and generating synthetic data. See this link https://liruiw.github.io/hma for more information.

In "Embers of Autoregression" (McCoy et al., 2023), we showed that several large language models (LLMs) have some important limitations that are attributable to their origins in next-word prediction. Here we investigate whether these issues persist with o1, a new system from OpenAI that differs from previous LLMs in that it is optimized for reasoning. We find that o1 substantially outperforms previous LLMs in many cases, with particularly large improvements on rare variants of common tasks (e.g., forming acronyms from the second letter of each word in a list, rather than the first letter). Despite these quantitative improvements, however, o1 still displays the same qualitative trends that we observed in previous systems. Specifically, o1 - like previous LLMs - is sensitive to the probability of examples and tasks, performing better and requiring fewer "thinking tokens" in high-probability settings than in low-probability ones. These results show that optimizing a language model for reasoning can mitigate but might not fully overcome the language model's probability sensitivity.

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.

Most existing multimodality methods use separate backbones for autoregression-based discrete text generation and diffusion-based continuous visual generation, or the same backbone by discretizing the visual data to use autoregression for both text and visual generation. In this paper, we propose to study a simple idea: share one transformer for both autoregression and diffusion. The feasibility comes from two main aspects: (i) Transformer is successfully applied to diffusion for visual generation, and (ii) transformer training for autoregression and diffusion is very similar, and the difference merely lies in that diffusion uses bidirectional attention mask and autoregression uses causal attention mask. Experimental results show that our approach achieves comparable image generation performance to current state-of-the-art methods as well as maintains the text generation capability. The project is publicly available at https://monoformer.github.io/.

We introduce V-AURA, the first autoregressive model to achieve high temporal alignment and relevance in video-to-audio generation. V-AURA uses a high-framerate visual feature extractor and a cross-modal audio-visual feature fusion strategy to capture fine-grained visual motion events and ensure precise temporal alignment. Additionally, we propose VisualSound, a benchmark dataset with high audio-visual relevance. VisualSound is based on VGGSound, a video dataset consisting of in-the-wild samples extracted from YouTube. During the curation, we remove samples where auditory events are not aligned with the visual ones. V-AURA outperforms current state-of-the-art models in temporal alignment and semantic relevance while maintaining comparable audio quality. Code, samples, VisualSound and models are available at https://v-aura.notion.site

Training general-purpose vision models on purely sequential visual data, eschewing linguistic inputs, has heralded a new frontier in visual understanding. These models are intended to not only comprehend but also seamlessly transit to out-of-domain tasks. However, current endeavors are hamstrung by an over-reliance on colossal models, exemplified by models with upwards of 3B parameters, and the necessity for an extensive corpus of visual data, often comprising a staggering 400B tokens. In this paper, we delve into the development of an efficient, autoregression-based vision model, innovatively architected to operate on a limited dataset. We meticulously demonstrate how this model achieves proficiency in a spectrum of visual tasks spanning both high-level and low-level semantic understanding during the testing phase. Our empirical evaluations underscore the model's agility in adapting to various tasks, heralding a significant reduction in the parameter footprint, and a marked decrease in training data requirements, thereby paving the way for more sustainable and accessible advancements in the field of generalist vision models. The code is available at https://github.com/ggjy/DeLVM.

In this paper, we present DiffusionVLA, a novel framework that seamlessly combines the autoregression model with the diffusion model for learning visuomotor policy. Central to our approach is a next-token prediction objective, enabling the model to reason effectively over the user's query in the context of current observations. Subsequently, a diffusion model is attached to generate robust action outputs. To enhance policy learning through self-reasoning, we introduce a novel reasoning injection module that integrates reasoning phrases directly into the policy learning process. The whole framework is simple and flexible, making it easy to deploy and upgrade. We conduct extensive experiments using multiple real robots to validate the effectiveness of DiffusionVLA. Our tests include a challenging factory sorting task, where DiffusionVLA successfully categorizes objects, including those not seen during training. We observe that the reasoning module makes the model interpretable. It allows observers to understand the model thought process and identify potential causes of policy failures. Additionally, we test DiffusionVLA on a zero-shot bin-picking task, achieving 63.7\% accuracy on 102 previously unseen objects. Our method demonstrates robustness to visual changes, such as distractors and new backgrounds, and easily adapts to new embodiments. Furthermore, DiffusionVLA can follow novel instructions and retain conversational ability. Notably, DiffusionVLA is data-efficient and fast at inference; our smallest DiffusionVLA-2B runs 82Hz on a single A6000 GPU and can train from scratch on less than 50 demonstrations for a complex task. Finally, we scale the model from 2B to 72B parameters, showcasing improved generalization capabilities with increased model size.

This work studies training instabilities of behavior cloning with deep neural networks. We observe that minibatch SGD updates to the policy network during training result in sharp oscillations in long-horizon rewards, despite negligibly affecting the behavior cloning loss. We empirically disentangle the statistical and computational causes of these oscillations, and find them to stem from the chaotic propagation of minibatch SGD noise through unstable closed-loop dynamics. While SGD noise is benign in the single-step action prediction objective, it results in catastrophic error accumulation over long horizons, an effect we term gradient variance amplification (GVA). We show that many standard mitigation techniques do not alleviate GVA, but find an exponential moving average (EMA) of iterates to be surprisingly effective at doing so. We illustrate the generality of this phenomenon by showing the existence of GVA and its amelioration by EMA in both continuous control and autoregressive language generation. Finally, we provide theoretical vignettes that highlight the benefits of EMA in alleviating GVA and shed light on the extent to which classical convex models can help in understanding the benefits of iterate averaging in deep learning.

Auto-regressive models have achieved impressive results in 2D image generation by modeling joint distributions in grid space. In this paper, we extend auto-regressive models to 3D domains, and seek a stronger ability of 3D shape generation by improving auto-regressive models at capacity and scalability simultaneously. Firstly, we leverage an ensemble of publicly available 3D datasets to facilitate the training of large-scale models. It consists of a comprehensive collection of approximately 900,000 objects, with multiple properties of meshes, points, voxels, rendered images, and text captions. This diverse labeled dataset, termed Objaverse-Mix, empowers our model to learn from a wide range of object variations. However, directly applying 3D auto-regression encounters critical challenges of high computational demands on volumetric grids and ambiguous auto-regressive order along grid dimensions, resulting in inferior quality of 3D shapes. To this end, we then present a novel framework Argus3D in terms of capacity. Concretely, our approach introduces discrete representation learning based on a latent vector instead of volumetric grids, which not only reduces computational costs but also preserves essential geometric details by learning the joint distributions in a more tractable order. The capacity of conditional generation can thus be realized by simply concatenating various conditioning inputs to the latent vector, such as point clouds, categories, images, and texts. In addition, thanks to the simplicity of our model architecture, we naturally scale up our approach to a larger model with an impressive 3.6 billion parameters, further enhancing the quality of versatile 3D generation. Extensive experiments on four generation tasks demonstrate that Argus3D can synthesize diverse and faithful shapes across multiple categories, achieving remarkable performance.

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

Autoregressive modeling has been a huge success in the field of natural language processing (NLP). Recently, autoregressive models have emerged as a significant area of focus in computer vision, where they excel in producing high-quality visual content. Autoregressive models in NLP typically operate on subword tokens. However, the representation strategy in computer vision can vary in different levels, i.e., pixel-level, token-level, or scale-level, reflecting the diverse and hierarchical nature of visual data compared to the sequential structure of language. This survey comprehensively examines the literature on autoregressive models applied to vision. To improve readability for researchers from diverse research backgrounds, we start with preliminary sequence representation and modeling in vision. Next, we divide the fundamental frameworks of visual autoregressive models into three general sub-categories, including pixel-based, token-based, and scale-based models based on the strategy of representation. We then explore the interconnections between autoregressive models and other generative models. Furthermore, we present a multi-faceted categorization of autoregressive models in computer vision, including image generation, video generation, 3D generation, and multi-modal generation. We also elaborate on their applications in diverse domains, including emerging domains such as embodied AI and 3D medical AI, with about 250 related references. Finally, we highlight the current challenges to autoregressive models in vision with suggestions about potential research directions. We have also set up a Github repository to organize the papers included in this survey at: https://github.com/ChaofanTao/Autoregressive-Models-in-Vision-Survey.

Autoregressive models have achieved impressive results over a wide range of domains in terms of generation quality and downstream task performance. In the continuous domain, a key factor behind this success is the usage of quantized latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for dimensionality reduction and faster inference times. However, using existing pre-trained models to perform new non-trivial tasks is difficult since it requires additional fine-tuning or extensive training to elicit prompting. This paper introduces LASS as a way to perform vector-quantized Latent Autoregressive Source Separation (i.e., de-mixing an input signal into its constituent sources) without requiring additional gradient-based optimization or modifications of existing models. Our separation method relies on the Bayesian formulation in which the autoregressive models are the priors, and a discrete (non-parametric) likelihood function is constructed by performing frequency counts over latent sums of addend tokens. We test our method on images and audio with several sampling strategies (e.g., ancestral, beam search) showing competitive results with existing approaches in terms of separation quality while offering at the same time significant speedups in terms of inference time and scalability to higher dimensional data.

Autoregressive models are typically applied to sequences of discrete tokens, but recent research indicates that generating sequences of continuous embeddings in an autoregressive manner is also feasible. However, such Continuous Autoregressive Models (CAMs) can suffer from a decline in generation quality over extended sequences due to error accumulation during inference. We introduce a novel method to address this issue by injecting random noise into the input embeddings during training. This procedure makes the model robust against varying error levels at inference. We further reduce error accumulation through an inference procedure that introduces low-level noise. Experiments on musical audio generation show that CAM substantially outperforms existing autoregressive and non-autoregressive approaches while preserving audio quality over extended sequences. This work paves the way for generating continuous embeddings in a purely autoregressive setting, opening new possibilities for real-time and interactive generative applications.

In this paper we construct an inferential procedure for Granger causality in high-dimensional non-stationary vector autoregressive (VAR) models. Our method does not require knowledge of the order of integration of the time series under consideration. We augment the VAR with at least as many lags as the suspected maximum order of integration, an approach which has been proven to be robust against the presence of unit roots in low dimensions. We prove that we can restrict the augmentation to only the variables of interest for the testing, thereby making the approach suitable for high dimensions. We combine this lag augmentation with a post-double-selection procedure in which a set of initial penalized regressions is performed to select the relevant variables for both the Granger causing and caused variables. We then establish uniform asymptotic normality of a second-stage regression involving only the selected variables. Finite sample simulations show good performance, an application to investigate the (predictive) causes and effects of economic uncertainty illustrates the need to allow for unknown orders of integration.

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional encoding for the output, this order can be modulated on-the-fly per-sample which offers key advantageous properties. It allows for the sampling of and conditioning on arbitrary subsets of tokens, and it also allows sampling in one shot multiple tokens dynamically according to a rejection strategy, leading to a sub-linear number of model evaluations. We evaluate our method across various domains, including language modeling, path-solving, and aircraft vertical rate prediction, decreasing the number of steps required for generation by an order of magnitude.

We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special cases of ARDMs under mild assumptions. ARDMs are simple to implement and easy to train. Unlike standard ARMs, they do not require causal masking of model representations, and can be trained using an efficient objective similar to modern probabilistic diffusion models that scales favourably to highly-dimensional data. At test time, ARDMs support parallel generation which can be adapted to fit any given generation budget. We find that ARDMs require significantly fewer steps than discrete diffusion models to attain the same performance. Finally, we apply ARDMs to lossless compression, and show that they are uniquely suited to this task. Contrary to existing approaches based on bits-back coding, ARDMs obtain compelling results not only on complete datasets, but also on compressing single data points. Moreover, this can be done using a modest number of network calls for (de)compression due to the model's adaptable parallel generation.

This paper introduces a novel training methodology that enables a small Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at: https://github.com/AGPatriota/ALGA-R/.

Conventional wisdom holds that autoregressive models for image generation are typically accompanied by vector-quantized tokens. We observe that while a discrete-valued space can facilitate representing a categorical distribution, it is not a necessity for autoregressive modeling. In this work, we propose to model the per-token probability distribution using a diffusion procedure, which allows us to apply autoregressive models in a continuous-valued space. Rather than using categorical cross-entropy loss, we define a Diffusion Loss function to model the per-token probability. This approach eliminates the need for discrete-valued tokenizers. We evaluate its effectiveness across a wide range of cases, including standard autoregressive models and generalized masked autoregressive (MAR) variants. By removing vector quantization, our image generator achieves strong results while enjoying the speed advantage of sequence modeling. We hope this work will motivate the use of autoregressive generation in other continuous-valued domains and applications.

There exists recent work in computer vision, named VAR, that proposes a new autoregressive paradigm for image generation. Diverging from the vanilla next-token prediction, VAR structurally reformulates the image generation into a coarse to fine next-scale prediction. In this paper, we show that this scale-wise autoregressive framework can be effectively decoupled into intra-scale modeling, which captures local spatial dependencies within each scale, and inter-scale modeling, which models cross-scale relationships progressively from coarse-to-fine scales. This decoupling structure allows to rebuild VAR in a more computationally efficient manner. Specifically, for intra-scale modeling -- crucial for generating high-fidelity images -- we retain the original bidirectional self-attention design to ensure comprehensive modeling; for inter-scale modeling, which semantically connects different scales but is computationally intensive, we apply linear-complexity mechanisms like Mamba to substantially reduce computational overhead. We term this new framework M-VAR. Extensive experiments demonstrate that our method outperforms existing models in both image quality and generation speed. For example, our 1.5B model, with fewer parameters and faster inference speed, outperforms the largest VAR-d30-2B. Moreover, our largest model M-VAR-d32 impressively registers 1.78 FID on ImageNet 256times256 and outperforms the prior-art autoregressive models LlamaGen/VAR by 0.4/0.19 and popular diffusion models LDM/DiT by 1.82/0.49, respectively. Code is avaiable at https://github.com/OliverRensu/MVAR.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Autoregressive (AR) models have reformulated image generation as next-token prediction, demonstrating remarkable potential and emerging as strong competitors to diffusion models. However, control-to-image generation, akin to ControlNet, remains largely unexplored within AR models. Although a natural approach, inspired by advancements in Large Language Models, is to tokenize control images into tokens and prefill them into the autoregressive model before decoding image tokens, it still falls short in generation quality compared to ControlNet and suffers from inefficiency. To this end, we introduce ControlAR, an efficient and effective framework for integrating spatial controls into autoregressive image generation models. Firstly, we explore control encoding for AR models and propose a lightweight control encoder to transform spatial inputs (e.g., canny edges or depth maps) into control tokens. Then ControlAR exploits the conditional decoding method to generate the next image token conditioned on the per-token fusion between control and image tokens, similar to positional encodings. Compared to prefilling tokens, using conditional decoding significantly strengthens the control capability of AR models but also maintains the model's efficiency. Furthermore, the proposed ControlAR surprisingly empowers AR models with arbitrary-resolution image generation via conditional decoding and specific controls. Extensive experiments can demonstrate the controllability of the proposed ControlAR for the autoregressive control-to-image generation across diverse inputs, including edges, depths, and segmentation masks. Furthermore, both quantitative and qualitative results indicate that ControlAR surpasses previous state-of-the-art controllable diffusion models, e.g., ControlNet++. Code, models, and demo will soon be available at https://github.com/hustvl/ControlAR.

This paper presents Randomized AutoRegressive modeling (RAR) for visual generation, which sets a new state-of-the-art performance on the image generation task while maintaining full compatibility with language modeling frameworks. The proposed RAR is simple: during a standard autoregressive training process with a next-token prediction objective, the input sequence-typically ordered in raster form-is randomly permuted into different factorization orders with a probability r, where r starts at 1 and linearly decays to 0 over the course of training. This annealing training strategy enables the model to learn to maximize the expected likelihood over all factorization orders and thus effectively improve the model's capability of modeling bidirectional contexts. Importantly, RAR preserves the integrity of the autoregressive modeling framework, ensuring full compatibility with language modeling while significantly improving performance in image generation. On the ImageNet-256 benchmark, RAR achieves an FID score of 1.48, not only surpassing prior state-of-the-art autoregressive image generators but also outperforming leading diffusion-based and masked transformer-based methods. Code and models will be made available at https://github.com/bytedance/1d-tokenizer

We present Visual AutoRegressive modeling (VAR), a new generation paradigm that redefines the autoregressive learning on images as coarse-to-fine "next-scale prediction" or "next-resolution prediction", diverging from the standard raster-scan "next-token prediction". This simple, intuitive methodology allows autoregressive (AR) transformers to learn visual distributions fast and generalize well: VAR, for the first time, makes AR models surpass diffusion transformers in image generation. On ImageNet 256x256 benchmark, VAR significantly improve AR baseline by improving Frechet inception distance (FID) from 18.65 to 1.80, inception score (IS) from 80.4 to 356.4, with around 20x faster inference speed. It is also empirically verified that VAR outperforms the Diffusion Transformer (DiT) in multiple dimensions including image quality, inference speed, data efficiency, and scalability. Scaling up VAR models exhibits clear power-law scaling laws similar to those observed in LLMs, with linear correlation coefficients near -0.998 as solid evidence. VAR further showcases zero-shot generalization ability in downstream tasks including image in-painting, out-painting, and editing. These results suggest VAR has initially emulated the two important properties of LLMs: Scaling Laws and zero-shot task generalization. We have released all models and codes to promote the exploration of AR/VAR models for visual generation and unified learning.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

In this note we examine the autoregressive generalization of the FNet algorithm, in which self-attention layers from the standard Transformer architecture are substituted with a trivial sparse-uniformsampling procedure based on Fourier transforms. Using the Wikitext-103 benchmark, we demonstratethat FNetAR retains state-of-the-art performance (25.8 ppl) on the task of causal language modelingcompared to a Transformer-XL baseline (24.2 ppl) with only half the number self-attention layers,thus providing further evidence for the superfluity of deep neural networks with heavily compoundedattention mechanisms. The autoregressive Fourier transform could likely be used for parameterreduction on most Transformer-based time-series prediction models.

This work tackles the information loss bottleneck of vector-quantization (VQ) autoregressive image generation by introducing a novel model architecture called the 2-Dimensional Autoregression (DnD) Transformer. The DnD-Transformer predicts more codes for an image by introducing a new autoregression direction, model depth, along with the sequence length direction. Compared to traditional 1D autoregression and previous work utilizing similar 2D image decomposition such as RQ-Transformer, the DnD-Transformer is an end-to-end model that can generate higher quality images with the same backbone model size and sequence length, opening a new optimization perspective for autoregressive image generation. Furthermore, our experiments reveal that the DnD-Transformer's potential extends beyond generating natural images. It can even generate images with rich text and graphical elements in a self-supervised manner, demonstrating an understanding of these combined modalities. This has not been previously demonstrated for popular vision generative models such as diffusion models, showing a spark of vision-language intelligence when trained solely on images. Code, datasets and models are open at https://github.com/chenllliang/DnD-Transformer.

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Flow models are effective at progressively generating realistic images, but they generally struggle to capture long-range dependencies during the generation process as they compress all the information from previous time steps into a single corrupted image. To address this limitation, we propose integrating autoregressive modeling -- known for its excellence in modeling complex, high-dimensional joint probability distributions -- into flow models. During training, at each step, we construct causally-ordered sequences by sampling multiple images from the same semantic category and applying different levels of noise, where images with higher noise levels serve as causal predecessors to those with lower noise levels. This design enables the model to learn broader category-level variations while maintaining proper causal relationships in the flow process. During generation, the model autoregressively conditions the previously generated images from earlier denoising steps, forming a contextual and coherent generation trajectory. Additionally, we design a customized hybrid linear attention mechanism tailored to our modeling approach to enhance computational efficiency. Our approach, termed ARFlow, under 400k training steps, achieves 14.08 FID scores on ImageNet at 128 * 128 without classifier-free guidance, reaching 4.34 FID with classifier-free guidance 1.5, significantly outperforming the previous flow-based model SiT's 9.17 FID. Extensive ablation studies demonstrate the effectiveness of our modeling strategy and chunk-wise attention design.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Time series analysis and forecasting of stock market prices has been a very active area of research over the last two decades. Availability of extremely fast and parallel architecture of computing and sophisticated algorithms has made it possible to extract, store, process and analyze high volume stock market time series data very efficiently. In this paper, we have used time series data of the two sectors of the Indian economy: Information Technology and Capital Goods for the period January 2009 till April 2016 and have studied the relationships of these two time series with the time series of DJIA index, NIFTY index and the US Dollar to Indian Rupee exchange rate. We establish by graphical and statistical tests that while the IT sector of India has a strong association with DJIA index and the Dollar to Rupee exchange rate, the Indian CG sector exhibits a strong association with the NIFTY index. We contend that these observations corroborate our hypotheses that the Indian IT sector is strongly coupled with the world economy whereas the CG sector of India reflects internal economic growth of India. We also present several models of regression between the time series which exhibit strong association among them. The effectiveness of these models have been demonstrated by very low values of their forecasting errors.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

We present TraDE, a self-attention-based architecture for auto-regressive density estimation with continuous and discrete valued data. Our model is trained using a penalized maximum likelihood objective, which ensures that samples from the density estimate resemble the training data distribution. The use of self-attention means that the model need not retain conditional sufficient statistics during the auto-regressive process beyond what is needed for each covariate. On standard tabular and image data benchmarks, TraDE produces significantly better density estimates than existing approaches such as normalizing flow estimators and recurrent auto-regressive models. However log-likelihood on held-out data only partially reflects how useful these estimates are in real-world applications. In order to systematically evaluate density estimators, we present a suite of tasks such as regression using generated samples, out-of-distribution detection, and robustness to noise in the training data and demonstrate that TraDE works well in these scenarios.

With the rapid development and evolution of sophisticated algorithms for statistical analysis of time series data, the research community has started spending considerable effort in technical analysis of such data. Forecasting is also an area which has witnessed a paradigm shift in its approach. In this work, we have used the time series of the index values of the Auto sector in India during January 2010 to December 2015 for a deeper understanding of the behavior of its three constituent components, e.g., the Trend, the Seasonal component, and the Random component. Based on this structural analysis, we have also designed three approaches for forecasting and also computed their accuracy in prediction using suitably chosen training and test data sets. The results clearly demonstrate the accuracy of our decomposition results and efficiency of our forecasting techniques, even in presence of a dominant Random component in the time series.

We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both temporal and contemporaneous causal relations. One may ask if temporal and contemporaneous relations should be treated differently. The presented algorithm gradually refines a causal graph by learning long-term temporal relations before short-term ones, where contemporaneous relations are learned last. This ordering of causal relations to be learnt leads to a reduction in the required number of statistical tests. We validate this reduction empirically and demonstrate that it leads to higher accuracy for synthetic data and more plausible causal graphs for real-world data compared to state-of-the-art algorithms.

In many real-world settings, agents must learn from an offline dataset gathered by some prior behavior policy. Such a setting naturally leads to distribution shift between the behavior policy and the target policy being trained - requiring policy conservatism to avoid instability and overestimation bias. Autoregressive world models offer a different solution to this by generating synthetic, on-policy experience. However, in practice, model rollouts must be severely truncated to avoid compounding error. As an alternative, we propose policy-guided diffusion. Our method uses diffusion models to generate entire trajectories under the behavior distribution, applying guidance from the target policy to move synthetic experience further on-policy. We show that policy-guided diffusion models a regularized form of the target distribution that balances action likelihood under both the target and behavior policies, leading to plausible trajectories with high target policy probability, while retaining a lower dynamics error than an offline world model baseline. Using synthetic experience from policy-guided diffusion as a drop-in substitute for real data, we demonstrate significant improvements in performance across a range of standard offline reinforcement learning algorithms and environments. Our approach provides an effective alternative to autoregressive offline world models, opening the door to the controllable generation of synthetic training data.

The recent surge of interest in comprehensive multimodal models has necessitated the unification of diverse modalities. However, the unification suffers from disparate methodologies. Continuous visual generation necessitates the full-sequence diffusion-based approach, despite its divergence from the autoregressive modeling in the text domain. We posit that autoregressive modeling, i.e., predicting the future based on past deterministic experience, remains crucial in developing both a visual generation model and a potential unified multimodal model. In this paper, we explore an interpolation between the autoregressive modeling and full-parameters diffusion to model visual information. At its core, we present ACDiT, an Autoregressive blockwise Conditional Diffusion Transformer, where the block size of diffusion, i.e., the size of autoregressive units, can be flexibly adjusted to interpolate between token-wise autoregression and full-sequence diffusion. ACDiT is easy to implement, as simple as creating a Skip-Causal Attention Mask (SCAM) during training. During inference, the process iterates between diffusion denoising and autoregressive decoding that can make full use of KV-Cache. We verify the effectiveness of ACDiT on image and video generation tasks. We also demonstrate that benefitted from autoregressive modeling, ACDiT can be seamlessly used in visual understanding tasks despite being trained on the diffusion objective. The analysis of the trade-off between autoregressive modeling and diffusion demonstrates the potential of ACDiT to be used in long-horizon visual generation tasks. These strengths make it promising as the backbone of future unified models.

We introduce AutoGluon-TimeSeries - an open-source AutoML library for probabilistic time series forecasting. Focused on ease of use and robustness, AutoGluon-TimeSeries enables users to generate accurate point and quantile forecasts with just 3 lines of Python code. Built on the design philosophy of AutoGluon, AutoGluon-TimeSeries leverages ensembles of diverse forecasting models to deliver high accuracy within a short training time. AutoGluon-TimeSeries combines both conventional statistical models, machine-learning based forecasting approaches, and ensembling techniques. In our evaluation on 29 benchmark datasets, AutoGluon-TimeSeries demonstrates strong empirical performance, outperforming a range of forecasting methods in terms of both point and quantile forecast accuracy, and often even improving upon the best-in-hindsight combination of prior methods.

Analysis and prediction of stock market time series data has attracted considerable interest from the research community over the last decade. Rapid development and evolution of sophisticated algorithms for statistical analysis of time series data, and availability of high-performance hardware has made it possible to process and analyze high volume stock market time series data effectively, in real-time. Among many other important characteristics and behavior of such data, forecasting is an area which has witnessed considerable focus. In this work, we have used time series of the index values of the Auto sector in India during January 2010 to December 2015 for a deeper understanding of the behavior of its three constituent components, e.g., the trend, the seasonal component, and the random component. Based on this structural analysis, we have also designed five approaches for forecasting and also computed their accuracy in prediction using suitably chosen training and test data sets. Extensive results are presented to demonstrate the effectiveness of our proposed decomposition approaches of time series and the efficiency of our forecasting techniques, even in presence of a random component and a sharply changing trend component in the time-series.

Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis have also been made along the way but are less visible to the community due to the predominant research on sequence modeling in this domain. However, the discrepancy between continuous time series and the discrete token space of LLMs, and the challenges in explicitly modeling the correlations of variates in multivariate time series have shifted some research attentions to the equally successful Large Vision Models (LVMs) and Vision Language Models (VLMs). To fill the blank in the existing literature, this survey discusses the advantages of vision models over LLMs in time series analysis. It provides a comprehensive and in-depth overview of the existing methods, with dual views of detailed taxonomy that answer the key research questions including how to encode time series as images and how to model the imaged time series for various tasks. Additionally, we address the challenges in the pre- and post-processing steps involved in this framework and outline future directions to further advance time series analysis with vision models.

We introduce AiM, an autoregressive (AR) image generative model based on Mamba architecture. AiM employs Mamba, a novel state-space model characterized by its exceptional performance for long-sequence modeling with linear time complexity, to supplant the commonly utilized Transformers in AR image generation models, aiming to achieve both superior generation quality and enhanced inference speed. Unlike existing methods that adapt Mamba to handle two-dimensional signals via multi-directional scan, AiM directly utilizes the next-token prediction paradigm for autoregressive image generation. This approach circumvents the need for extensive modifications to enable Mamba to learn 2D spatial representations. By implementing straightforward yet strategically targeted modifications for visual generative tasks, we preserve Mamba's core structure, fully exploiting its efficient long-sequence modeling capabilities and scalability. We provide AiM models in various scales, with parameter counts ranging from 148M to 1.3B. On the ImageNet1K 256*256 benchmark, our best AiM model achieves a FID of 2.21, surpassing all existing AR models of comparable parameter counts and demonstrating significant competitiveness against diffusion models, with 2 to 10 times faster inference speed. Code is available at https://github.com/hp-l33/AiM

This work challenges the residual prediction paradigm in visual autoregressive modeling and presents FlexVAR, a new Flexible Visual AutoRegressive image generation paradigm. FlexVAR facilitates autoregressive learning with ground-truth prediction, enabling each step to independently produce plausible images. This simple, intuitive approach swiftly learns visual distributions and makes the generation process more flexible and adaptable. Trained solely on low-resolution images (leq 256px), FlexVAR can: (1) Generate images of various resolutions and aspect ratios, even exceeding the resolution of the training images. (2) Support various image-to-image tasks, including image refinement, in/out-painting, and image expansion. (3) Adapt to various autoregressive steps, allowing for faster inference with fewer steps or enhancing image quality with more steps. Our 1.0B model outperforms its VAR counterpart on the ImageNet 256times256 benchmark. Moreover, when zero-shot transfer the image generation process with 13 steps, the performance further improves to 2.08 FID, outperforming state-of-the-art autoregressive models AiM/VAR by 0.25/0.28 FID and popular diffusion models LDM/DiT by 1.52/0.19 FID, respectively. When transferring our 1.0B model to the ImageNet 512times512 benchmark in a zero-shot manner, FlexVAR achieves competitive results compared to the VAR 2.3B model, which is a fully supervised model trained at 512times512 resolution.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Recent advances in autoregressive (AR) models with continuous tokens for image generation show promising results by eliminating the need for discrete tokenization. However, these models face efficiency challenges due to their sequential token generation nature and reliance on computationally intensive diffusion-based sampling. We present ECAR (Efficient Continuous Auto-Regressive Image Generation via Multistage Modeling), an approach that addresses these limitations through two intertwined innovations: (1) a stage-wise continuous token generation strategy that reduces computational complexity and provides progressively refined token maps as hierarchical conditions, and (2) a multistage flow-based distribution modeling method that transforms only partial-denoised distributions at each stage comparing to complete denoising in normal diffusion models. Holistically, ECAR operates by generating tokens at increasing resolutions while simultaneously denoising the image at each stage. This design not only reduces token-to-image transformation cost by a factor of the stage number but also enables parallel processing at the token level. Our approach not only enhances computational efficiency but also aligns naturally with image generation principles by operating in continuous token space and following a hierarchical generation process from coarse to fine details. Experimental results demonstrate that ECAR achieves comparable image quality to DiT Peebles & Xie [2023] while requiring 10times FLOPs reduction and 5times speedup to generate a 256times256 image.

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper, we propose TimeDiff, a non-autoregressive diffusion model that achieves high-quality time series prediction with the introduction of two novel conditioning mechanisms: future mixup and autoregressive initialization. Similar to teacher forcing, future mixup allows parts of the ground-truth future predictions for conditioning, while autoregressive initialization helps better initialize the model with basic time series patterns such as short-term trends. Extensive experiments are performed on nine real-world datasets. Results show that TimeDiff consistently outperforms existing time series diffusion models, and also achieves the best overall performance across a variety of the existing strong baselines (including transformers and FiLM).

We present Symphony, an E(3)-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for molecules utilize rotationally invariant features to respect the 3D symmetries of molecules. In contrast, Symphony uses message-passing with higher-degree E(3)-equivariant features. This allows a novel representation of probability distributions via spherical harmonic signals to efficiently model the 3D geometry of molecules. We show that Symphony is able to accurately generate small molecules from the QM9 dataset, outperforming existing autoregressive models and approaching the performance of diffusion models.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

Prediction of stock prices plays a significant role in aiding the decision-making of investors. Considering its importance, a growing literature has emerged trying to forecast stock prices with improved accuracy. In this study, we introduce an innovative approach for forecasting stock prices with greater accuracy. We incorporate external economic environment-related information along with stock prices. In our novel approach, we improve the performance of stock price prediction by taking into account variations due to future expected macroeconomic policy changes as investors adjust their current behavior ahead of time based on expected future macroeconomic policy changes. Furthermore, we incorporate macroeconomic variables along with historical stock prices to make predictions. Results from this strongly support the inclusion of future economic policy changes along with current macroeconomic information. We confirm the supremacy of our method over the conventional approach using several tree-based machine-learning algorithms. Results are strongly conclusive across various machine learning models. Our preferred model outperforms the conventional approach with an RMSE value of 1.61 compared to an RMSE value of 1.75 from the conventional approach.

We introduce Causal Diffusion as the autoregressive (AR) counterpart of Diffusion models. It is a next-token(s) forecasting framework that is friendly to both discrete and continuous modalities and compatible with existing next-token prediction models like LLaMA and GPT. While recent works attempt to combine diffusion with AR models, we show that introducing sequential factorization to a diffusion model can substantially improve its performance and enables a smooth transition between AR and diffusion generation modes. Hence, we propose CausalFusion - a decoder-only transformer that dual-factorizes data across sequential tokens and diffusion noise levels, leading to state-of-the-art results on the ImageNet generation benchmark while also enjoying the AR advantage of generating an arbitrary number of tokens for in-context reasoning. We further demonstrate CausalFusion's multimodal capabilities through a joint image generation and captioning model, and showcase CausalFusion's ability for zero-shot in-context image manipulations. We hope that this work could provide the community with a fresh perspective on training multimodal models over discrete and continuous data.

Causal discovery, i.e., inferring underlying cause-effect relationships from observations of a scene or system, is an inherent mechanism in human cognition, but has been shown to be highly challenging to automate. The majority of approaches in the literature aiming for this task consider constrained scenarios with fully observed variables or data from stationary time-series. In this work we aim for causal discovery in a more general class of scenarios, scenes with non-stationary behavior over time. For our purposes we here regard a scene as a composition objects interacting with each other over time. Non-stationarity is modeled as stationarity conditioned on an underlying variable, a state, which can be of varying dimension, more or less hidden given observations of the scene, and also depend more or less directly on these observations. We propose a probabilistic deep learning approach called State-Dependent Causal Inference (SDCI) for causal discovery in such conditionally stationary time-series data. Results in two different synthetic scenarios show that this method is able to recover the underlying causal dependencies with high accuracy even in cases with hidden states.

Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block's probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN. Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules.

This paper proposes to model chaos in the ATM cash withdrawal time series of a big Indian bank and forecast the withdrawals using deep learning methods. It also considers the importance of day-of-the-week and includes it as a dummy exogenous variable. We first modelled the chaos present in the withdrawal time series by reconstructing the state space of each series using the lag, and embedding dimension found using an auto-correlation function and Cao's method. This process converts the uni-variate time series into multi variate time series. The "day-of-the-week" is converted into seven features with the help of one-hot encoding. Then these seven features are augmented to the multivariate time series. For forecasting the future cash withdrawals, using algorithms namely ARIMA, random forest (RF), support vector regressor (SVR), multi-layer perceptron (MLP), group method of data handling (GMDH), general regression neural network (GRNN), long short term memory neural network and 1-dimensional convolutional neural network. We considered a daily cash withdrawals data set from an Indian commercial bank. After modelling chaos and adding exogenous features to the data set, we observed improvements in the forecasting for all models. Even though the random forest (RF) yielded better Symmetric Mean Absolute Percentage Error (SMAPE) value, deep learning algorithms, namely LSTM and 1D CNN, showed similar performance compared to RF, based on t-test.

Autoregressive models excel in modeling sequential dependencies by enforcing causal constraints, yet they struggle to capture complex bidirectional patterns due to their unidirectional nature. In contrast, mask-based models leverage bidirectional context, enabling richer dependency modeling. However, they often assume token independence during prediction, which undermines the modeling of sequential dependencies. Additionally, the corruption of sequences through masking or absorption can introduce unnatural distortions, complicating the learning process. To address these issues, we propose Bidirectional Autoregressive Diffusion (BAD), a novel approach that unifies the strengths of autoregressive and mask-based generative models. BAD utilizes a permutation-based corruption technique that preserves the natural sequence structure while enforcing causal dependencies through randomized ordering, enabling the effective capture of both sequential and bidirectional relationships. Comprehensive experiments show that BAD outperforms autoregressive and mask-based models in text-to-motion generation, suggesting a novel pre-training strategy for sequence modeling. The codebase for BAD is available on https://github.com/RohollahHS/BAD.

Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical drawbacks. Firstly, these methods often rely on a single dataset for training, limiting the model's generalizability due to the restricted scale of the training data. Secondly, the one-step generation schema is widely followed, which necessitates a customized forecasting head and overlooks the temporal dependencies in the output series, and also leads to increased training costs under different horizon length settings. To address these issues, we propose a novel generative pretrained hierarchical transformer architecture for forecasting, named GPHT. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset for pretraining our model, comprising various datasets from diverse data scenarios. This approach significantly expands the scale of training data, allowing our model to uncover commonalities in time series data and facilitating improved transfer to specific datasets. On the other hand, GPHT employs an auto-regressive forecasting approach under the channel-independent assumption, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling a single model to forecast at arbitrary horizon settings. We conduct sufficient experiments on eight datasets with mainstream self-supervised pretraining models and supervised models. The results demonstrated that GPHT surpasses the baseline models across various fine-tuning and zero/few-shot learning settings in the traditional long-term forecasting task, providing support for verifying the feasibility of pretrained time series large models.

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

The integration of Vector Quantised Variational AutoEncoder (VQ-VAE) with autoregressive models as generation part has yielded high-quality results on image generation. However, the autoregressive models will strictly follow the progressive scanning order during the sampling phase. This leads the existing VQ series models to hardly escape the trap of lacking global information. Denoising Diffusion Probabilistic Models (DDPM) in the continuous domain have shown a capability to capture the global context, while generating high-quality images. In the discrete state space, some works have demonstrated the potential to perform text generation and low resolution image generation. We show that with the help of a content-rich discrete visual codebook from VQ-VAE, the discrete diffusion model can also generate high fidelity images with global context, which compensates for the deficiency of the classical autoregressive model along pixel space. Meanwhile, the integration of the discrete VAE with the diffusion model resolves the drawback of conventional autoregressive models being oversized, and the diffusion model which demands excessive time in the sampling process when generating images. It is found that the quality of the generated images is heavily dependent on the discrete visual codebook. Extensive experiments demonstrate that the proposed Vector Quantised Discrete Diffusion Model (VQ-DDM) is able to achieve comparable performance to top-tier methods with low complexity. It also demonstrates outstanding advantages over other vectors quantised with autoregressive models in terms of image inpainting tasks without additional training.

We introduce Hybrid Autoregressive Transformer (HART), an autoregressive (AR) visual generation model capable of directly generating 1024x1024 images, rivaling diffusion models in image generation quality. Existing AR models face limitations due to the poor image reconstruction quality of their discrete tokenizers and the prohibitive training costs associated with generating 1024px images. To address these challenges, we present the hybrid tokenizer, which decomposes the continuous latents from the autoencoder into two components: discrete tokens representing the big picture and continuous tokens representing the residual components that cannot be represented by the discrete tokens. The discrete component is modeled by a scalable-resolution discrete AR model, while the continuous component is learned with a lightweight residual diffusion module with only 37M parameters. Compared with the discrete-only VAR tokenizer, our hybrid approach improves reconstruction FID from 2.11 to 0.30 on MJHQ-30K, leading to a 31% generation FID improvement from 7.85 to 5.38. HART also outperforms state-of-the-art diffusion models in both FID and CLIP score, with 4.5-7.7x higher throughput and 6.9-13.4x lower MACs. Our code is open sourced at https://github.com/mit-han-lab/hart.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Time series is a collection of data instances that are ordered according to a time stamp. Stock prices, temperature, etc are examples of time series data in real life. Time series data are used for forecasting sales, predicting trends. Visualization is the process of visually representing data or the relationship between features of a data either in a two-dimensional plot or a three-dimensional plot. Visualizing the time series data constitutes an important part of the process for working with a time series dataset. Visualizing the data not only helps in the modelling process but it can also be used to identify trends and features that cause those trends. In this work, we take a real-life time series dataset and analyse how the target feature relates to other features of the dataset through visualization. From the work that has been carried out, we present an effective method of visualization for time series data which will be much useful for machine learning modelling with such datasets.

Causal Inference plays an significant role in explaining the decisions taken by statistical models and artificial intelligence models. Of late, this field started attracting the attention of researchers and practitioners alike. This paper presents a comprehensive survey of 37 papers published during 1992-2023 and concerning the application of causal inference to banking, finance, and insurance. The papers are categorized according to the following families of domains: (i) Banking, (ii) Finance and its subdomains such as corporate finance, governance finance including financial risk and financial policy, financial economics, and Behavioral finance, and (iii) Insurance. Further, the paper covers the primary ingredients of causal inference namely, statistical methods such as Bayesian Causal Network, Granger Causality and jargon used thereof such as counterfactuals. The review also recommends some important directions for future research. In conclusion, we observed that the application of causal inference in the banking and insurance sectors is still in its infancy, and thus more research is possible to turn it into a viable method.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.

In the realm of time series forecasting (TSF), it is imperative for models to adeptly discern and distill hidden patterns within historical time series data to forecast future states. Transformer-based models exhibit formidable efficacy in TSF, primarily attributed to their advantage in apprehending these patterns. However, the quadratic complexity of the Transformer leads to low computational efficiency and high costs, which somewhat hinders the deployment of the TSF model in real-world scenarios. Recently, Mamba, a selective state space model, has gained traction due to its ability to process dependencies in sequences while maintaining near-linear complexity. For TSF tasks, these characteristics enable Mamba to comprehend hidden patterns as the Transformer and reduce computational overhead compared to the Transformer. Therefore, we propose a Mamba-based model named Simple-Mamba (S-Mamba) for TSF. Specifically, we tokenize the time points of each variate autonomously via a linear layer. A bidirectional Mamba layer is utilized to extract inter-variate correlations and a Feed-Forward Network is set to learn temporal dependencies. Finally, the generation of forecast outcomes through a linear mapping layer. Experiments on thirteen public datasets prove that S-Mamba maintains low computational overhead and achieves leading performance. Furthermore, we conduct extensive experiments to explore Mamba's potential in TSF tasks. Our code is available at https://github.com/wzhwzhwzh0921/S-D-Mamba.

Representation learning seeks to expose certain aspects of observed data in a learned representation that's amenable to downstream tasks like classification. For instance, a good representation for 2D images might be one that describes only global structure and discards information about detailed texture. In this paper, we present a simple but principled method to learn such global representations by combining Variational Autoencoder (VAE) with neural autoregressive models such as RNN, MADE and PixelRNN/CNN. Our proposed VAE model allows us to have control over what the global latent code can learn and , by designing the architecture accordingly, we can force the global latent code to discard irrelevant information such as texture in 2D images, and hence the VAE only "autoencodes" data in a lossy fashion. In addition, by leveraging autoregressive models as both prior distribution p(z) and decoding distribution p(x|z), we can greatly improve generative modeling performance of VAEs, achieving new state-of-the-art results on MNIST, OMNIGLOT and Caltech-101 Silhouettes density estimation tasks.

Volatility clustering is a crucial property that has a substantial impact on stock market patterns. Nonetheless, developing robust models for accurately predicting future stock price volatility is a difficult research topic. For predicting the volatility of three equities listed on India's national stock market (NSE), we propose multiple volatility models depending on the generalized autoregressive conditional heteroscedasticity (GARCH), Glosten-Jagannathan-GARCH (GJR-GARCH), Exponential general autoregressive conditional heteroskedastic (EGARCH), and LSTM framework. Sector-wise stocks have been chosen in our study. The sectors which have been considered are banking, information technology (IT), and pharma. yahoo finance has been used to obtain stock price data from Jan 2017 to Dec 2021. Among the pulled-out records, the data from Jan 2017 to Dec 2020 have been taken for training, and data from 2021 have been chosen for testing our models. The performance of predicting the volatility of stocks of three sectors has been evaluated by implementing three different types of GARCH models as well as by the LSTM model are compared. It has been observed the LSTM performed better in predicting volatility in pharma over banking and IT sectors. In tandem, it was also observed that E-GARCH performed better in the case of the banking sector and for IT and pharma, GJR-GARCH performed better.

Continuous-valued Autoregressive (AR) image generation models have demonstrated notable superiority over their discrete-token counterparts, showcasing considerable reconstruction quality and higher generation fidelity. However, the computational demands of the autoregressive framework result in significant inference overhead. While speculative decoding has proven effective in accelerating Large Language Models (LLMs), their adaptation to continuous-valued visual autoregressive models remains unexplored. This work generalizes the speculative decoding algorithm from discrete tokens to continuous space. By analyzing the intrinsic properties of output distribution, we establish a tailored acceptance criterion for the diffusion distributions prevalent in such models. To overcome the inconsistency that occurred in speculative decoding output distributions, we introduce denoising trajectory alignment and token pre-filling methods. Additionally, we identify the hard-to-sample distribution in the rejection phase. To mitigate this issue, we propose a meticulous acceptance-rejection sampling method with a proper upper bound, thereby circumventing complex integration. Experimental results show that our continuous speculative decoding achieves a remarkable 2.33times speed-up on off-the-shelf models while maintaining the output distribution. Codes will be available at https://github.com/MarkXCloud/CSpD

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D J_1-J_2 Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for scientific simulations of quantum many-body physics and quantum technology.

Time series forecasting has been a widely explored task of great importance in many applications. However, it is common that real-world time series data are recorded in a short time period, which results in a big gap between the deep model and the limited and noisy time series. In this work, we propose to address the time series forecasting problem with generative modeling and propose a bidirectional variational auto-encoder (BVAE) equipped with diffusion, denoise, and disentanglement, namely D3VAE. Specifically, a coupled diffusion probabilistic model is proposed to augment the time series data without increasing the aleatoric uncertainty and implement a more tractable inference process with BVAE. To ensure the generated series move toward the true target, we further propose to adapt and integrate the multiscale denoising score matching into the diffusion process for time series forecasting. In addition, to enhance the interpretability and stability of the prediction, we treat the latent variable in a multivariate manner and disentangle them on top of minimizing total correlation. Extensive experiments on synthetic and real-world data show that D3VAE outperforms competitive algorithms with remarkable margins. Our implementation is available at https://github.com/PaddlePaddle/PaddleSpatial/tree/main/research/D3VAE.

Volatility clustering is an important characteristic that has a significant effect on the behavior of stock markets. However, designing robust models for accurate prediction of future volatilities of stock prices is a very challenging research problem. We present several volatility models based on generalized autoregressive conditional heteroscedasticity (GARCH) framework for modeling the volatility of ten stocks listed in the national stock exchange (NSE) of India. The stocks are selected from the auto sector and the banking sector of the Indian economy, and they have a significant impact on the sectoral index of their respective sectors in the NSE. The historical stock price records from Jan 1, 2010, to Apr 30, 2021, are scraped from the Yahoo Finance website using the DataReader API of the Pandas module in the Python programming language. The GARCH modules are built and fine-tuned on the training data and then tested on the out-of-sample data to evaluate the performance of the models. The analysis of the results shows that asymmetric GARCH models yield more accurate forecasts on the future volatility of stocks.

Accurately forecasting patient arrivals at Urgent Care Clinics (UCCs) and Emergency Departments (EDs) is important for effective resourcing and patient care. However, correctly estimating patient flows is not straightforward since it depends on many drivers. The predictability of patient arrivals has recently been further complicated by the COVID-19 pandemic conditions and the resulting lockdowns. This study investigates how a suite of novel quasi-real-time variables like Google search terms, pedestrian traffic, the prevailing incidence levels of influenza, as well as the COVID-19 Alert Level indicators can both generally improve the forecasting models of patient flows and effectively adapt the models to the unfolding disruptions of pandemic conditions. This research also uniquely contributes to the body of work in this domain by employing tools from the eXplainable AI field to investigate more deeply the internal mechanics of the models than has previously been done. The Voting ensemble-based method combining machine learning and statistical techniques was the most reliable in our experiments. Our study showed that the prevailing COVID-19 Alert Level feature together with Google search terms and pedestrian traffic were effective at producing generalisable forecasts. The implications of this study are that proxy variables can effectively augment standard autoregressive features to ensure accurate forecasting of patient flows. The experiments showed that the proposed features are potentially effective model inputs for preserving forecast accuracies in the event of future pandemic outbreaks.

Interpretable time series prediction is crucial for safety-critical areas such as healthcare and autonomous driving. Most existing methods focus on interpreting predictions by assigning important scores to segments of time series. In this paper, we take a different and more challenging route and aim at developing a self-interpretable model, dubbed Counterfactual Time Series (CounTS), which generates counterfactual and actionable explanations for time series predictions. Specifically, we formalize the problem of time series counterfactual explanations, establish associated evaluation protocols, and propose a variational Bayesian deep learning model equipped with counterfactual inference capability of time series abduction, action, and prediction. Compared with state-of-the-art baselines, our self-interpretable model can generate better counterfactual explanations while maintaining comparable prediction accuracy.

Time series forecasting plays a crucial role in decision-making across various domains, but it presents significant challenges. Recent studies have explored image-driven approaches using computer vision models to address these challenges, often employing lineplots as the visual representation of time series data. In this paper, we propose a novel approach that uses time-frequency spectrograms as the visual representation of time series data. We introduce the use of a vision transformer for multimodal learning, showcasing the advantages of our approach across diverse datasets from different domains. To evaluate its effectiveness, we compare our method against statistical baselines (EMA and ARIMA), a state-of-the-art deep learning-based approach (DeepAR), other visual representations of time series data (lineplot images), and an ablation study on using only the time series as input. Our experiments demonstrate the benefits of utilizing spectrograms as a visual representation for time series data, along with the advantages of employing a vision transformer for simultaneous learning in both the time and frequency domains.

Diffusion models have recently been shown to be relevant for high-quality speech generation. Most work has been focused on generating spectrograms, and as such, they further require a subsequent model to convert the spectrogram to a waveform (i.e., a vocoder). This work proposes a diffusion probabilistic end-to-end model for generating a raw speech waveform. The proposed model is autoregressive, generating overlapping frames sequentially, where each frame is conditioned on a portion of the previously generated one. Hence, our model can effectively synthesize an unlimited speech duration while preserving high-fidelity synthesis and temporal coherence. We implemented the proposed model for unconditional and conditional speech generation, where the latter can be driven by an input sequence of phonemes, amplitudes, and pitch values. Working on the waveform directly has some empirical advantages. Specifically, it allows the creation of local acoustic behaviors, like vocal fry, which makes the overall waveform sounds more natural. Furthermore, the proposed diffusion model is stochastic and not deterministic; therefore, each inference generates a slightly different waveform variation, enabling abundance of valid realizations. Experiments show that the proposed model generates speech with superior quality compared with other state-of-the-art neural speech generation systems.

Financial markets have a vital role in the development of modern society. They allow the deployment of economic resources. Changes in stock prices reflect changes in the market. In this study, we focus on predicting stock prices by deep learning model. This is a challenge task, because there is much noise and uncertainty in information that is related to stock prices. So this work uses sparse autoencoders with one-dimension (1-D) residual convolutional networks which is a deep learning model, to de-noise the data. Long-short term memory (LSTM) is then used to predict the stock price. The prices, indices and macroeconomic variables in past are the features used to predict the next day's price. Experiment results show that 1-D residual convolutional networks can de-noise data and extract deep features better than a model that combines wavelet transforms (WT) and stacked autoencoders (SAEs). In addition, we compare the performances of model with two different forecast targets of stock price: absolute stock price and price rate of change. The results show that predicting stock price through price rate of change is better than predicting absolute prices directly.

Diffusion models have become the dominant approach for visual generation. They are trained by denoising a Markovian process that gradually adds noise to the input. We argue that the Markovian property limits the models ability to fully utilize the generation trajectory, leading to inefficiencies during training and inference. In this paper, we propose DART, a transformer-based model that unifies autoregressive (AR) and diffusion within a non-Markovian framework. DART iteratively denoises image patches spatially and spectrally using an AR model with the same architecture as standard language models. DART does not rely on image quantization, enabling more effective image modeling while maintaining flexibility. Furthermore, DART seamlessly trains with both text and image data in a unified model. Our approach demonstrates competitive performance on class-conditioned and text-to-image generation tasks, offering a scalable, efficient alternative to traditional diffusion models. Through this unified framework, DART sets a new benchmark for scalable, high-quality image synthesis.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

Large Transformer networks are increasingly used in settings where low inference latency can improve the end-user experience and enable new applications. However, autoregressive inference is resource intensive and requires parallelism for efficiency. Parallelism introduces collective communication that is both expensive and represents a phase when hardware resources are underutilized. Towards mitigating this, Kraken is an evolution of the standard Transformer architecture that is designed to complement existing tensor parallelism schemes for efficient inference on multi-device systems. By introducing a fixed degree of intra-layer model parallelism, the architecture allows collective operations to be overlapped with compute, decreasing latency and increasing hardware utilization. When trained on OpenWebText, Kraken models reach a similar perplexity as standard Transformers while also preserving their language modeling capabilities when evaluated on the SuperGLUE benchmark. Importantly, when tested on multi-GPU systems using TensorRT-LLM engines, Kraken speeds up Time To First Token by a mean of 35.6% across a range of model sizes, context lengths, and degrees of tensor parallelism.

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

The paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

Observational studies require adjustment for confounding factors that are correlated with both the treatment and outcome. In the setting where the observed variables are tabular quantities such as average income in a neighborhood, tools have been developed for addressing such confounding. However, in many parts of the developing world, features about local communities may be scarce. In this context, satellite imagery can play an important role, serving as a proxy for the confounding variables otherwise unobserved. In this paper, we study confounder adjustment in this non-tabular setting, where patterns or objects found in satellite images contribute to the confounder bias. Using the evaluation of anti-poverty aid programs in Africa as our running example, we formalize the challenge of performing causal adjustment with such unstructured data -- what conditions are sufficient to identify causal effects, how to perform estimation, and how to quantify the ways in which certain aspects of the unstructured image object are most predictive of the treatment decision. Via simulation, we also explore the sensitivity of satellite image-based observational inference to image resolution and to misspecification of the image-associated confounder. Finally, we apply these tools in estimating the effect of anti-poverty interventions in African communities from satellite imagery.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (AUEL), Random Dropping (RD) training strategy, and Multi-kernel Local Smoothing (MKLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

The industry is rich in cases when we are required to make forecasting for large amounts of time series at once. However, we might be in a situation where we can not afford to train a separate model for each of them. Such issue in time series modeling remains without due attention. The remedy for this setting is the establishment of a foundation model. Such a model is expected to work in zero-shot and few-shot regimes. However, what should we take as a training dataset for such kind of model? Witnessing the benefits from the enrichment of NLP datasets with artificially-generated data, we might want to adopt their experience for time series. In contrast to natural language, the process of generation of synthetic time series data is even more favorable because it provides full control of series patterns, time horizons, and number of samples. In this work, we consider the essential question if it is advantageous to train a foundation model on synthetic data or it is better to utilize only a limited number of real-life examples. Our experiments are conducted only for regular time series and speak in favor of leveraging solely the real time series. Moreover, the choice of the proper source dataset strongly influences the performance during inference. When provided access even to a limited quantity of short time series data, employing it within a supervised framework yields more favorable results than training on a larger volume of synthetic data. The code for our experiments is publicly available on Github https://github.com/sb-ai-lab/synthesize_or_not.

Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and applicability issues. An alternative is to use fully latent temporal models which untie frame synthesis and temporal dynamics. However, no such model for stochastic video prediction has been proposed in the literature yet, due to design and training difficulties. In this paper, we overcome these difficulties by introducing a novel stochastic temporal model whose dynamics are governed in a latent space by a residual update rule. This first-order scheme is motivated by discretization schemes of differential equations. It naturally models video dynamics as it allows our simpler, more interpretable, latent model to outperform prior state-of-the-art methods on challenging datasets.

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

Transaction data from digital payment systems can be used to study economic processes at such a detail that was not possible previously. Here, we analyse the data from Sarafu token network, a community inclusion currency in Kenya. During the COVID-19 emergency, the Sarafu was disbursed as part of a humanitarian aid project. In this work, the transactions are analysed using network science. A topological categorisation is defined to identify cyclic and acyclic components. Furthermore, temporal aspects of circulation taking place within these components are considered. The significant presence of different types of strongly connected components as compared to randomized null models shows the importance of cycles in this economic network. Especially, indicating their key role in currency recirculation. In some acyclic components, the most significant triad suggests the presence of a group of users collecting currency from accounts active only once, hinting at a misuse of the system. In some other acyclic components, small isolated groups of users were active only once, suggesting the presence of users only interested in trying out the system. The methods used in this paper can answer specific questions related to user activities, currency design, and assessment of monetary interventions. Our methodology provides a general quantitative tool for analysing the behaviour of users in a currency network.

We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we propose a learning paradigm that directly establishes causation between events in the course of time. We present two key lemmas to compute causal contributions and frame them as reinforcement learning problems. Our approach offers formal and computational tools for uncovering and quantifying causal relationships in diffusion processes, subsuming various important settings such as discrete-time Markov decision processes. Finally, in fairly intricate experiments and through sheer learning, our framework reveals and quantifies causal links, which otherwise seem inexplicable.

Recognizing that traditional forecasting models often rely solely on historical demand, this work investigates the potential of data-driven techniques to automatically select and integrate market indicators for improving customer demand predictions. By adopting an exploratory methodology, we integrate macroeconomic time series, such as national GDP growth, from the Eurostat database into Neural Prophet and SARIMAX forecasting models. Suitable time series are automatically identified through different state-of-the-art feature selection methods and applied to sales data from our industrial partner. It could be shown that forecasts can be significantly enhanced by incorporating external information. Notably, the potential of feature selection methods stands out, especially due to their capability for automation without expert knowledge and manual selection effort. In particular, the Forward Feature Selection technique consistently yielded superior forecasting accuracy for both SARIMAX and Neural Prophet across different company sales datasets. In the comparative analysis of the errors of the selected forecasting models, namely Neural Prophet and SARIMAX, it is observed that neither model demonstrates a significant superiority over the other.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

In the field of quantitative trading, it is common practice to transform raw historical stock data into indicative signals for the market trend. Such signals are called alpha factors. Alphas in formula forms are more interpretable and thus favored by practitioners concerned with risk. In practice, a set of formulaic alphas is often used together for better modeling precision, so we need to find synergistic formulaic alpha sets that work well together. However, most traditional alpha generators mine alphas one by one separately, overlooking the fact that the alphas would be combined later. In this paper, we propose a new alpha-mining framework that prioritizes mining a synergistic set of alphas, i.e., it directly uses the performance of the downstream combination model to optimize the alpha generator. Our framework also leverages the strong exploratory capabilities of reinforcement learning~(RL) to better explore the vast search space of formulaic alphas. The contribution to the combination models' performance is assigned to be the return used in the RL process, driving the alpha generator to find better alphas that improve upon the current set. Experimental evaluations on real-world stock market data demonstrate both the effectiveness and the efficiency of our framework for stock trend forecasting. The investment simulation results show that our framework is able to achieve higher returns compared to previous approaches.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model -- not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many large language models in deployment. However, autoregressive models rely on myopic temperature scaling that greedily optimizes the next token. To address this, we propose Long Horizon Temperature Scaling (LHTS), a novel approach for sampling from temperature-scaled joint distributions. LHTS is compatible with all likelihood-based models, and optimizes for the long-horizon likelihood of samples. We derive a temperature-dependent LHTS objective, and show that fine-tuning a model on a range of temperatures produces a single model capable of generation with a controllable long-horizon temperature parameter. We experiment with LHTS on image diffusion models and character/language autoregressive models, demonstrating advantages over myopic temperature scaling in likelihood and sample quality, and showing improvements in accuracy on a multiple choice analogy task by 10%.

Institutional investors have been increasing the allocation of the illiquid alternative assets such as private equity funds in their portfolios, yet there exists a very limited literature on cash flow forecasting of illiquid alternative assets. The net cash flow of private equity funds typically follow a J-curve pattern, however the timing and the size of the contributions and distributions depend on the investment opportunities. In this paper, we develop a benchmark model and present two novel approaches (direct vs. indirect) to predict the cash flows of private equity funds. We introduce a sliding window approach to apply on our cash flow data because different vintage year funds contain different lengths of cash flow information. We then pass the data to an LSTM/ GRU model to predict the future cash flows either directly or indirectly (based on the benchmark model). We further integrate macroeconomic indicators into our data, which allows us to consider the impact of market environment on cash flows and to apply stress testing. Our results indicate that the direct model is easier to implement compared to the benchmark model and the indirect model, but still the predicted cash flows align better with the actual cash flows. We also show that macroeconomic variables improve the performance of the direct model whereas the impact is not obvious on the indirect model.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

[This paper was initially published in PHME conference in 2016, selected for further publication in International Journal of Prognostics and Health Management.] This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM) for fault detection and prognostics of equipments based on sensors' data. It is a particular dynamic Bayesian network that allows to represent the dynamics of a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR) process. The Markov chain assumes that the system is switching back and forth between internal states while the AR process ensures a temporal coherence on sensor measurements. A sound learning procedure of standard ARHMM based on maximum likelihood allows to iteratively estimate all parameters simultaneously. This paper suggests a modification of the learning procedure considering that one may have prior knowledge about the structure which becomes partially hidden. The integration of the prior is based on the Theory of Weighted Distributions which is compatible with the Expectation-Maximization algorithm in the sense that the convergence properties are still satisfied. We show how to apply this model to estimate the remaining useful life based on health indicators. The autoregressive parameters can indeed be used for prediction while the latent structure can be used to get information about the degradation level. The interest of the proposed method for prognostics and health assessment is demonstrated on CMAPSS datasets.

Temporally dense single-person "small data" have become widely available thanks to mobile apps and wearable sensors. Many caregivers and self-trackers want to use these data to help a specific person change their behavior to achieve desired health outcomes. Ideally, this involves discerning possible causes from correlations using that person's own observational time series data. In this paper, we estimate within-individual average treatment effects of physical activity on sleep duration, and vice-versa. We introduce the model twin randomization (MoTR; "motor") method for analyzing an individual's intensive longitudinal data. Formally, MoTR is an application of the g-formula (i.e., standardization, back-door adjustment) under serial interference. It estimates stable recurring effects, as is done in n-of-1 trials and single case experimental designs. We compare our approach to standard methods (with possible confounding) to show how to use causal inference to make better personalized recommendations for health behavior change, and analyze 222 days of Fitbit sleep and steps data for one of the authors.

Portfolio optimization has been an area that has attracted considerable attention from the financial research community. Designing a profitable portfolio is a challenging task involving precise forecasting of future stock returns and risks. This chapter presents a comparative study of three portfolio design approaches, the mean-variance portfolio (MVP), hierarchical risk parity (HRP)-based portfolio, and autoencoder-based portfolio. These three approaches to portfolio design are applied to the historical prices of stocks chosen from ten thematic sectors listed on the National Stock Exchange (NSE) of India. The portfolios are designed using the stock price data from January 1, 2018, to December 31, 2021, and their performances are tested on the out-of-sample data from January 1, 2022, to December 31, 2022. Extensive results are analyzed on the performance of the portfolios. It is observed that the performance of the MVP portfolio is the best on the out-of-sample data for the risk-adjusted returns. However, the autoencoder portfolios outperformed their counterparts on annual returns.

In this work we propose for the first time a transformer-based framework for unsupervised representation learning of multivariate time series. Pre-trained models can be potentially used for downstream tasks such as regression and classification, forecasting and missing value imputation. By evaluating our models on several benchmark datasets for multivariate time series regression and classification, we show that not only does our modeling approach represent the most successful method employing unsupervised learning of multivariate time series presented to date, but also that it exceeds the current state-of-the-art performance of supervised methods; it does so even when the number of training samples is very limited, while offering computational efficiency. Finally, we demonstrate that unsupervised pre-training of our transformer models offers a substantial performance benefit over fully supervised learning, even without leveraging additional unlabeled data, i.e., by reusing the same data samples through the unsupervised objective.

Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules. Analogous to fractals in mathematics, our method constructs a new type of generative model by recursively invoking atomic generative modules, resulting in self-similar fractal architectures that we call fractal generative models. As a running example, we instantiate our fractal framework using autoregressive models as the atomic generative modules and examine it on the challenging task of pixel-by-pixel image generation, demonstrating strong performance in both likelihood estimation and generation quality. We hope this work could open a new paradigm in generative modeling and provide a fertile ground for future research. Code is available at https://github.com/LTH14/fractalgen.

Over the last few years, machine learning based methods have been applied to extract information from news flow in the financial domain. However, this information has mostly been in the form of the financial sentiments contained in the news headlines, primarily for the stock prices. In our current work, we propose that various other dimensions of information can be extracted from news headlines, which will be of interest to investors, policy-makers and other practitioners. We propose a framework that extracts information such as past movements and expected directionality in prices, asset comparison and other general information that the news is referring to. We apply this framework to the commodity "Gold" and train the machine learning models using a dataset of 11,412 human-annotated news headlines (released with this study), collected from the period 2000-2019. We experiment to validate the causal effect of news flow on gold prices and observe that the information produced from our framework significantly impacts the future gold price.

In recent years, microservices have gained widespread adoption in IT operations due to their scalability, maintenance, and flexibility. However, it becomes challenging for site reliability engineers (SREs) to pinpoint the root cause due to the complex relationships in microservices when facing system malfunctions. Previous research employed structured learning methods (e.g., PC-algorithm) to establish causal relationships and derive root causes from causal graphs. Nevertheless, they ignored the temporal order of time series data and failed to leverage the rich information inherent in the temporal relationships. For instance, in cases where there is a sudden spike in CPU utilization, it can lead to an increase in latency for other microservices. However, in this scenario, the anomaly in CPU utilization occurs before the latency increase, rather than simultaneously. As a result, the PC-algorithm fails to capture such characteristics. To address these challenges, we propose RUN, a novel approach for root cause analysis using neural Granger causal discovery with contrastive learning. RUN enhances the backbone encoder by integrating contextual information from time series, and leverages a time series forecasting model to conduct neural Granger causal discovery. In addition, RUN incorporates Pagerank with a personalization vector to efficiently recommend the top-k root causes. Extensive experiments conducted on the synthetic and real-world microservice-based datasets demonstrate that RUN noticeably outperforms the state-of-the-art root cause analysis methods. Moreover, we provide an analysis scenario for the sock-shop case to showcase the practicality and efficacy of RUN in microservice-based applications. Our code is publicly available at https://github.com/zmlin1998/RUN.

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

Generating time series data using Generative Adversarial Networks (GANs) presents several prevalent challenges, such as slow convergence, information loss in embedding spaces, instability, and performance variability depending on the series length. To tackle these obstacles, we introduce a robust framework aimed at addressing and mitigating these issues effectively. This advanced framework integrates the benefits of an Autoencoder-generated embedding space with the adversarial training dynamics of GANs. This framework benefits from a time series-based loss function and oversight from a supervisory network, both of which capture the stepwise conditional distributions of the data effectively. The generator functions within the latent space, while the discriminator offers essential feedback based on the feature space. Moreover, we introduce an early generation algorithm and an improved neural network architecture to enhance stability and ensure effective generalization across both short and long time series. Through joint training, our framework consistently outperforms existing benchmarks, generating high-quality time series data across a range of real and synthetic datasets with diverse characteristics.

Multivariate time series forecasting tasks are usually conducted in a channel-dependent (CD) way since it can incorporate more variable-relevant information. However, it may also involve a lot of irrelevant variables, and this even leads to worse performance than the channel-independent (CI) strategy. This paper combines the strengths of both strategies and proposes the Deep Graph Clustering Transformer (DGCformer) for multivariate time series forecasting. Specifically, it first groups these relevant variables by a graph convolutional network integrated with an autoencoder, and a former-latter masked self-attention mechanism is then considered with the CD strategy being applied to each group of variables while the CI one for different groups. Extensive experimental results on eight datasets demonstrate the superiority of our method against state-of-the-art models, and our code will be publicly available upon acceptance.

Vaccine supply chain optimization can benefit from hierarchical time series forecasting, when grouping the vaccines by type or location. However, forecasts of different hierarchy levels become incoherent when higher levels do not match the sum of the lower levels forecasts, which can be addressed by reconciliation methods. In this paper, we tackle the vaccine sale forecasting problem by modeling sales data from GSK between 2010 and 2021 as a hierarchical time series. After forecasting future values with several ARIMA models, we systematically compare the performance of various reconciliation methods, using statistical tests. We also compare the performance of the forecast before and after COVID. The results highlight Minimum Trace and Weighted Least Squares with Structural scaling as the best performing methods, which provided a coherent forecast while reducing the forecast error of the baseline ARIMA.

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.

This paper analyzes how expectations of Transformative AI (TAI) affect current economic behavior by introducing a novel mechanism where automation redirects labor income from workers to those controlling AI systems, with the share of automated labor controlled by each household depending on their wealth at the time of invention. Using a modified neoclassical growth model calibrated to contemporary AI timeline forecasts, I find that even moderate assumptions about wealth-based allocation of AI labor generate substantial increases in pre-TAI interest rates. Under baseline scenarios with proportional wealth-based allocation, one-year interest rates rise to 10-16% compared to approximately 3% without strategic competition. The model reveals a notable divergence between interest rates and capital rental rates, as households accept lower productive returns in exchange for the strategic value of wealth accumulation. These findings suggest that evolving beliefs about TAI could create significant upward pressure on interest rates well before any technological breakthrough occurs, with important implications for monetary policy and financial stability.

For autoregressive (AR) modeling of high-resolution images, vector quantization (VQ) represents an image as a sequence of discrete codes. A short sequence length is important for an AR model to reduce its computational costs to consider long-range interactions of codes. However, we postulate that previous VQ cannot shorten the code sequence and generate high-fidelity images together in terms of the rate-distortion trade-off. In this study, we propose the two-stage framework, which consists of Residual-Quantized VAE (RQ-VAE) and RQ-Transformer, to effectively generate high-resolution images. Given a fixed codebook size, RQ-VAE can precisely approximate a feature map of an image and represent the image as a stacked map of discrete codes. Then, RQ-Transformer learns to predict the quantized feature vector at the next position by predicting the next stack of codes. Thanks to the precise approximation of RQ-VAE, we can represent a 256times256 image as 8times8 resolution of the feature map, and RQ-Transformer can efficiently reduce the computational costs. Consequently, our framework outperforms the existing AR models on various benchmarks of unconditional and conditional image generation. Our approach also has a significantly faster sampling speed than previous AR models to generate high-quality images.

One of the challenging research problems in the domain of time series analysis and forecasting is making efficient and robust prediction of stock market prices. With rapid development and evolution of sophisticated algorithms and with the availability of extremely fast computing platforms, it has now become possible to effectively extract, store, process and analyze high volume stock market time series data. Complex algorithms for forecasting are now available for speedy execution over parallel architecture leading to fairly accurate results. In this paper, we have used time series data of the two sectors of the Indian economy: Consumer Durables sector and the Small Cap sector for the period January 2010 to December 2015 and proposed a decomposition approach for better understanding of the behavior of each of the time series. Our contention is that various sectors reveal different time series patterns and understanding them is essential for portfolio formation. Further, based on this structural analysis, we have also proposed several robust forecasting techniques and analyzed their accuracy in prediction using suitably chosen training and test data sets. Extensive results are presented to demonstrate the effectiveness of our propositions.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

Prediction of future movement of stock prices has always been a challenging task for the researchers. While the advocates of the efficient market hypothesis (EMH) believe that it is impossible to design any predictive framework that can accurately predict the movement of stock prices, there are seminal work in the literature that have clearly demonstrated that the seemingly random movement patterns in the time series of a stock price can be predicted with a high level of accuracy. Design of such predictive models requires choice of appropriate variables, right transformation methods of the variables, and tuning of the parameters of the models. In this work, we present a very robust and accurate framework of stock price prediction that consists of an agglomeration of statistical, machine learning and deep learning models. We use the daily stock price data, collected at five minutes interval of time, of a very well known company that is listed in the National Stock Exchange (NSE) of India. The granular data is aggregated into three slots in a day, and the aggregated data is used for building and training the forecasting models. We contend that the agglomerative approach of model building that uses a combination of statistical, machine learning, and deep learning approaches, can very effectively learn from the volatile and random movement patterns in a stock price data. We build eight classification and eight regression models based on statistical and machine learning approaches. In addition to these models, a deep learning regression model using a long-and-short-term memory (LSTM) network is also built. Extensive results have been presented on the performance of these models, and the results are critically analyzed.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3times sampling speedup over existing diffusion models.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utilized these benchmarking archives. These algorithms are designed for these specific problems, but may not be useful for tasks such as predicting the heart rate of a person using photoplethysmogram (PPG) and accelerometer data. We refer to this problem as Time Series Extrinsic Regression (TSER), where we are interested in a more general methodology of predicting a single continuous value, from univariate or multivariate time series. This prediction can be from the same time series or not directly related to the predictor time series and does not necessarily need to be a future value or depend heavily on recent values. To the best of our knowledge, research into TSER has received much less attention in the time series research community and there are no models developed for general time series extrinsic regression problems. Most models are developed for a specific problem. Therefore, we aim to motivate and support the research into TSER by introducing the first TSER benchmarking archive. This archive contains 19 datasets from different domains, with varying number of dimensions, unequal length dimensions, and missing values. In this paper, we introduce the datasets in this archive and did an initial benchmark on existing models.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events. We also conduct a range of ablation studies to investigate the effectiveness of each component of our proposed methods.

Artificial Neural Networks (ANN) which are a branch of artificial intelligence, have shown their high value in lots of applications and are used as a suitable forecasting method. Therefore, this study aims at forecasting imports in OECD member selected countries and Iran for 20 seasons from 2021 to 2025 by means of ANN. Data related to the imports of such countries collected over 50 years from 1970 to 2019 from valid resources including World Bank, WTO, IFM,the data turned into seasonal data to increase the number of collected data for better performance and high accuracy of the network by using Diz formula that there were totally 200 data related to imports. This study has used LSTM to analyse data in Pycharm. 75% of data considered as training data and 25% considered as test data and the results of the analysis were forecasted with 99% accuracy which revealed the validity and reliability of the output. Since the imports is consumption function and since the consumption is influenced during Covid-19 Pandemic, so it is time-consuming to correct and improve it to be influential on the imports, thus the imports in the years after Covid-19 Pandemic has had a fluctuating trend.

We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discuss how they achieve competitive performance in modeling both binary and real-valued observations. We also present how deep NADE models can be trained to be agnostic to the ordering of input dimensions used by the autoregressive product rule decomposition. Finally, we also show how to exploit the topological structure of pixels in images using a deep convolutional architecture for NADE.

We investigate the performance of a state-of-the art (SoTA) architecture T5 (available on the SuperGLUE) and compare with it 3 other previous SoTA architectures across 5 different tasks from 2 relatively diverse datasets. The datasets are diverse in terms of the number and types of tasks they have. To improve performance, we augment the training data by using an autoregressive model. We achieve near-SoTA results on a couple of the tasks - macro F1 scores of 81.66% for task A of the OLID 2019 dataset and 82.54% for task A of the hate speech and offensive content (HASOC) 2021 dataset, where SoTA are 82.9% and 83.05%, respectively. We perform error analysis and explain why one of the models (Bi-LSTM) makes the predictions it does by using a publicly available algorithm: Integrated Gradient (IG). This is because explainable artificial intelligence (XAI) is essential for earning the trust of users. The main contributions of this work are the implementation method of T5, which is discussed; the data augmentation using a new conversational AI model checkpoint, which brought performance improvements; and the revelation on the shortcomings of HASOC 2021 dataset. It reveals the difficulties of poor data annotation by using a small set of examples where the T5 model made the correct predictions, even when the ground truth of the test set were incorrect (in our opinion). We also provide our model checkpoints on the HuggingFace hub1 to foster transparency.

In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately 10k parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: https://github.com/VEWOXIC/FITS

The UCR Time Series Archive - introduced in 2002, has become an important resource in the time series data mining community, with at least one thousand published papers making use of at least one data set from the archive. The original incarnation of the archive had sixteen data sets but since that time, it has gone through periodic expansions. The last expansion took place in the summer of 2015 when the archive grew from 45 to 85 data sets. This paper introduces and will focus on the new data expansion from 85 to 128 data sets. Beyond expanding this valuable resource, this paper offers pragmatic advice to anyone who may wish to evaluate a new algorithm on the archive. Finally, this paper makes a novel and yet actionable claim: of the hundreds of papers that show an improvement over the standard baseline (1-nearest neighbor classification), a large fraction may be mis-attributing the reasons for their improvement. Moreover, they may have been able to achieve the same improvement with a much simpler modification, requiring just a single line of code.

This paper introduces a novel approach to financial risk analysis that does not rely on traditional price and market data, instead using market news to model assets as distributions over a metric space of risk factors. By representing asset returns as integrals over the scalar field of these risk factors, we derive the covariance structure between asset returns. Utilizing encoder-only language models to embed this news data, we explore the relationships between asset return distributions through the concept of Energy Distance, establishing connections between distributional differences and excess returns co-movements. This data-agnostic approach provides new insights into portfolio diversification, risk management, and the construction of hedging strategies. Our findings have significant implications for both theoretical finance and practical risk management, offering a more robust framework for modelling complex financial systems without depending on conventional market data.

Transformers have been actively studied for time-series forecasting in recent years. While often showing promising results in various scenarios, traditional Transformers are not designed to fully exploit the characteristics of time-series data and thus suffer some fundamental limitations, e.g., they generally lack of decomposition capability and interpretability, and are neither effective nor efficient for long-term forecasting. In this paper, we propose ETSFormer, a novel time-series Transformer architecture, which exploits the principle of exponential smoothing in improving Transformers for time-series forecasting. In particular, inspired by the classical exponential smoothing methods in time-series forecasting, we propose the novel exponential smoothing attention (ESA) and frequency attention (FA) to replace the self-attention mechanism in vanilla Transformers, thus improving both accuracy and efficiency. Based on these, we redesign the Transformer architecture with modular decomposition blocks such that it can learn to decompose the time-series data into interpretable time-series components such as level, growth and seasonality. Extensive experiments on various time-series benchmarks validate the efficacy and advantages of the proposed method. Code is available at https://github.com/salesforce/ETSformer.

In robotic visuomotor policy learning, diffusion-based models have achieved significant success in improving the accuracy of action trajectory generation compared to traditional autoregressive models. However, they suffer from inefficiency due to multiple denoising steps and limited flexibility from complex constraints. In this paper, we introduce Coarse-to-Fine AutoRegressive Policy (CARP), a novel paradigm for visuomotor policy learning that redefines the autoregressive action generation process as a coarse-to-fine, next-scale approach. CARP decouples action generation into two stages: first, an action autoencoder learns multi-scale representations of the entire action sequence; then, a GPT-style transformer refines the sequence prediction through a coarse-to-fine autoregressive process. This straightforward and intuitive approach produces highly accurate and smooth actions, matching or even surpassing the performance of diffusion-based policies while maintaining efficiency on par with autoregressive policies. We conduct extensive evaluations across diverse settings, including single-task and multi-task scenarios on state-based and image-based simulation benchmarks, as well as real-world tasks. CARP achieves competitive success rates, with up to a 10% improvement, and delivers 10x faster inference compared to state-of-the-art policies, establishing a high-performance, efficient, and flexible paradigm for action generation in robotic tasks.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.

The present work investigates two properties of level crossings of a stationary Gaussian process X(t) with autocorrelation function R_X(tau). We show firstly that if R_X(tau) admits finite second and fourth derivatives at the origin, the length of up-excursions above a large negative level -gamma is asymptotically exponential as -gamma to -infty. Secondly, assuming that R_X(tau) admits a finite second derivative at the origin and some defined properties, we derive the mean number of crossings as well as the length of successive excursions above two subsequent large levels. The asymptotic results are shown to be effective even for moderate values of crossing level. An application of the developed results is proposed to derive the probability of successive excursions above adjacent levels during a time window.

International trade policies have recently garnered attention for limiting cross-border exchange of essential goods (e.g. steel, aluminum, soybeans, and beef). Since trade critically affects employment and wages, predicting future patterns of trade is a high-priority for policy makers around the world. While traditional economic models aim to be reliable predictors, we consider the possibility that Machine Learning (ML) techniques allow for better predictions to inform policy decisions. Open-government data provide the fuel to power the algorithms that can explain and forecast trade flows to inform policies. Data collected in this article describe international trade transactions and commonly associated economic factors. Machine learning (ML) models deployed include: ARIMA, GBoosting, XGBoosting, and LightGBM for predicting future trade patterns, and K-Means clustering of countries according to economic factors. Unlike short-term and subjective (straight-line) projections and medium-term (aggre-gated) projections, ML methods provide a range of data-driven and interpretable projections for individual commodities. Models, their results, and policies are introduced and evaluated for prediction quality.

Reinforcement learning has been applied in operation research and has shown promise in solving large combinatorial optimization problems. However, existing works focus on developing neural network architectures for certain problems. These works lack the flexibility to incorporate recent advances in reinforcement learning, as well as the flexibility of customizing model architectures for operation research problems. In this work, we analyze the end-to-end autoregressive models for vehicle routing problems and show that these models can benefit from the recent advances in reinforcement learning with a careful re-implementation of the model architecture. In particular, we re-implemented the Attention Model and trained it with Proximal Policy Optimization (PPO) in CleanRL, showing at least 8 times speed up in training time. We hereby introduce RLOR, a flexible framework for Deep Reinforcement Learning for Operation Research. We believe that a flexible framework is key to developing deep reinforcement learning models for operation research problems. The code of our work is publicly available at https://github.com/cpwan/RLOR.

A pair-trading strategy is an approach that utilizes the fluctuations between prices of a pair of stocks in a short-term time frame, while in the long-term the pair may exhibit a strong association and co-movement pattern. When the prices of the stocks exhibit significant divergence, the shares of the stock that gains in price are sold (a short strategy) while the shares of the other stock whose price falls are bought (a long strategy). This paper presents a cointegration-based approach that identifies stocks listed in the five sectors of the National Stock Exchange (NSE) of India for designing efficient pair-trading portfolios. Based on the stock prices from Jan 1, 2018, to Dec 31, 2020, the cointegrated stocks are identified and the pairs are formed. The pair-trading portfolios are evaluated on their annual returns for the year 2021. The results show that the pairs of stocks from the auto and the realty sectors, in general, yielded the highest returns among the five sectors studied in the work. However, two among the five pairs from the information technology (IT) sector are found to have yielded negative returns.

Automated Vehicles (AVs) promise significant advances in transportation. Critical to these improvements is understanding AVs' longitudinal behavior, relying heavily on real-world trajectory data. Existing open-source trajectory datasets of AV, however, often fall short in refinement, reliability, and completeness, hindering effective performance metrics analysis and model development. This study addresses these challenges by creating a Unified Longitudinal TRAjectory dataset for AVs (Ultra-AV) to analyze their microscopic longitudinal driving behaviors. This dataset compiles data from 13 distinct sources, encompassing various AV types, test sites, and experiment scenarios. We established a three-step data processing: 1. extraction of longitudinal trajectory data, 2. general data cleaning, and 3. data-specific cleaning to obtain the longitudinal trajectory data and car-following trajectory data. The validity of the processed data is affirmed through performance evaluations across safety, mobility, stability, and sustainability, along with an analysis of the relationships between variables in car-following models. Our work not only furnishes researchers with standardized data and metrics for longitudinal AV behavior studies but also sets guidelines for data collection and model development.

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.

A multivariate time series refers to observations of two or more variables taken from a device or a system simultaneously over time. There is an increasing need to monitor multivariate time series and detect anomalies in real time to ensure proper system operation and good service quality. It is also highly desirable to have a lightweight anomaly detection system that considers correlations between different variables, adapts to changes in the pattern of the multivariate time series, offers immediate responses, and provides supportive information regarding detection results based on unsupervised learning and online model training. In the past decade, many multivariate time series anomaly detection approaches have been introduced. However, they are unable to offer all the above-mentioned features. In this paper, we propose RoLA, a real-time online lightweight anomaly detection system for multivariate time series based on a divide-and-conquer strategy, parallel processing, and the majority rule. RoLA employs multiple lightweight anomaly detectors to monitor multivariate time series in parallel, determine the correlations between variables dynamically on the fly, and then jointly detect anomalies based on the majority rule in real time. To demonstrate the performance of RoLA, we conducted an experiment based on a public dataset provided by the FerryBox of the One Ocean Expedition. The results show that RoLA provides satisfactory detection accuracy and lightweight performance.

Designing efficient and robust algorithms for accurate prediction of stock market prices is one of the most exciting challenges in the field of time series analysis and forecasting. With the exponential rate of development and evolution of sophisticated algorithms and with the availability of fast computing platforms, it has now become possible to effectively and efficiently extract, store, process and analyze high volume of stock market data with diversity in its contents. Availability of complex algorithms which can execute very fast on parallel architecture over the cloud has made it possible to achieve higher accuracy in forecasting results while reducing the time required for computation. In this paper, we use the time series data of the healthcare sector of India for the period January 2010 till December 2016. We first demonstrate a decomposition approach of the time series and then illustrate how the decomposition results provide us with useful insights into the behavior and properties exhibited by the time series. Further, based on the structural analysis of the time series, we propose six different methods of forecasting for predicting the time series index of the healthcare sector. Extensive results are provided on the performance of the forecasting methods to demonstrate their effectiveness.

This paper introduces WaveGrad, a conditional model for waveform generation which estimates gradients of the data density. The model is built on prior work on score matching and diffusion probabilistic models. It starts from a Gaussian white noise signal and iteratively refines the signal via a gradient-based sampler conditioned on the mel-spectrogram. WaveGrad offers a natural way to trade inference speed for sample quality by adjusting the number of refinement steps, and bridges the gap between non-autoregressive and autoregressive models in terms of audio quality. We find that it can generate high fidelity audio samples using as few as six iterations. Experiments reveal WaveGrad to generate high fidelity audio, outperforming adversarial non-autoregressive baselines and matching a strong likelihood-based autoregressive baseline using fewer sequential operations. Audio samples are available at https://wavegrad.github.io/.

Can meta-learning discover generic ways of processing time series (TS) from a diverse dataset so as to greatly improve generalization on new TS coming from different datasets? This work provides positive evidence to this using a broad meta-learning framework which we show subsumes many existing meta-learning algorithms. Our theoretical analysis suggests that residual connections act as a meta-learning adaptation mechanism, generating a subset of task-specific parameters based on a given TS input, thus gradually expanding the expressive power of the architecture on-the-fly. The same mechanism is shown via linearization analysis to have the interpretation of a sequential update of the final linear layer. Our empirical results on a wide range of data emphasize the importance of the identified meta-learning mechanisms for successful zero-shot univariate forecasting, suggesting that it is viable to train a neural network on a source TS dataset and deploy it on a different target TS dataset without retraining, resulting in performance that is at least as good as that of state-of-practice univariate forecasting models.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

Building predictive models for robust and accurate prediction of stock prices and stock price movement is a challenging research problem to solve. The well-known efficient market hypothesis believes in the impossibility of accurate prediction of future stock prices in an efficient stock market as the stock prices are assumed to be purely stochastic. However, numerous works proposed by researchers have demonstrated that it is possible to predict future stock prices with a high level of precision using sophisticated algorithms, model architectures, and the selection of appropriate variables in the models. This chapter proposes a collection of predictive regression models built on deep learning architecture for robust and precise prediction of the future prices of a stock listed in the diversified sectors in the National Stock Exchange (NSE) of India. The Metastock tool is used to download the historical stock prices over a period of two years (2013- 2014) at 5 minutes intervals. While the records for the first year are used to train the models, the testing is carried out using the remaining records. The design approaches of all the models and their performance results are presented in detail. The models are also compared based on their execution time and accuracy of prediction.

With most technical fields, there exists a delay between fundamental academic research and practical industrial uptake. Whilst some sciences have robust and well-established processes for commercialisation, such as the pharmaceutical practice of regimented drug trials, other fields face transitory periods in which fundamental academic advancements diffuse gradually into the space of commerce and industry. For the still relatively young field of Automated/Autonomous Machine Learning (AutoML/AutonoML), that transitory period is under way, spurred on by a burgeoning interest from broader society. Yet, to date, little research has been undertaken to assess the current state of this dissemination and its uptake. Thus, this review makes two primary contributions to knowledge around this topic. Firstly, it provides the most up-to-date and comprehensive survey of existing AutoML tools, both open-source and commercial. Secondly, it motivates and outlines a framework for assessing whether an AutoML solution designed for real-world application is 'performant'; this framework extends beyond the limitations of typical academic criteria, considering a variety of stakeholder needs and the human-computer interactions required to service them. Thus, additionally supported by an extensive assessment and comparison of academic and commercial case-studies, this review evaluates mainstream engagement with AutoML in the early 2020s, identifying obstacles and opportunities for accelerating future uptake.

Oil production forecasting is an important step in controlling the cost-effect and monitoring the functioning of petroleum reservoirs. As a result, oil production forecasting makes it easier for reservoir engineers to develop feasible projects, which helps to avoid risky investments and achieve long-term growth. As a result, reliable petroleum reservoir forecasting is critical for controlling and managing the effective cost of oil reservoirs. Oil production is influenced by reservoir qualities such as porosity, permeability, compressibility, fluid saturation, and other well operational parameters. Three-time series algorithms i.e., Seasonal Naive method, Exponential Smoothening and ARIMA to forecast the Distillate Fuel Oil Refinery and Propane Blender net production for the next two years.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Generating realistic time series data is important for many engineering and scientific applications. Existing work tackles this problem using generative adversarial networks (GANs). However, GANs are often unstable during training, and they can suffer from mode collapse. While variational autoencoders (VAEs) are known to be more robust to these issues, they are (surprisingly) less often considered for time series generation. In this work, we introduce Koopman VAE (KVAE), a new generative framework that is based on a novel design for the model prior, and that can be optimized for either regular and irregular training data. Inspired by Koopman theory, we represent the latent conditional prior dynamics using a linear map. Our approach enhances generative modeling with two desired features: (i) incorporating domain knowledge can be achieved by leverageing spectral tools that prescribe constraints on the eigenvalues of the linear map; and (ii) studying the qualitative behavior and stablity of the system can be performed using tools from dynamical systems theory. Our results show that KVAE outperforms state-of-the-art GAN and VAE methods across several challenging synthetic and real-world time series generation benchmarks. Whether trained on regular or irregular data, KVAE generates time series that improve both discriminative and predictive metrics. We also present visual evidence suggesting that KVAE learns probability density functions that better approximate empirical ground truth distributions.

With the increasing volume of high-frequency data in the information age, both challenges and opportunities arise in the prediction of stock volatility. On one hand, the outcome of prediction using tradition method combining stock technical and macroeconomic indicators still leaves room for improvement; on the other hand, macroeconomic indicators and peoples' search record on those search engines affecting their interested topics will intuitively have an impact on the stock volatility. For the convenience of assessment of the influence of these indicators, macroeconomic indicators and stock technical indicators are then grouped into objective factors, while Baidu search indices implying people's interested topics are defined as subjective factors. To align different frequency data, we introduce GARCH-MIDAS model. After mixing all the above data, we then feed them into Transformer model as part of the training data. Our experiments show that this model outperforms the baselines in terms of mean square error. The adaption of both types of data under Transformer model significantly reduces the mean square error from 1.00 to 0.86.

The utilization of long contexts poses a big challenge for large language models due to their limited context window length. Although the context window can be extended through fine-tuning, it will result in a considerable cost at both training and inference time, and exert an unfavorable impact to the LLM's original capabilities. In this work, we propose Activation Beacon, which condenses LLM's raw activations into more compact forms such that it can perceive a much longer context with a limited context window. Activation Beacon is introduced as a plug-and-play module for the LLM. It fully preserves the LLM's original capability on short contexts while extending the new capability on processing longer contexts. Besides, it works with short sliding windows to process the long context, which achieves a competitive memory and time efficiency in both training and inference. Activation Beacon is learned by the auto-regression task conditioned on a mixture of beacons with diversified condensing ratios. Thanks to such a treatment, it can be efficiently trained purely with short-sequence data in just 10K steps, which consumes less than 9 hours on a single 8xA800 GPU machine. The experimental studies show that Activation Beacon is able to extend Llama-2-7B's context length by times100 times (from 4K to 400K), meanwhile achieving a superior result on both long-context generation and understanding tasks. Our model and code will be available at the BGE repository.

We present an approach to pose object recognition as next token prediction. The idea is to apply a language decoder that auto-regressively predicts the text tokens from image embeddings to form labels. To ground this prediction process in auto-regression, we customize a non-causal attention mask for the decoder, incorporating two key features: modeling tokens from different labels to be independent, and treating image tokens as a prefix. This masking mechanism inspires an efficient method - one-shot sampling - to simultaneously sample tokens of multiple labels in parallel and rank generated labels by their probabilities during inference. To further enhance the efficiency, we propose a simple strategy to construct a compact decoder by simply discarding the intermediate blocks of a pretrained language model. This approach yields a decoder that matches the full model's performance while being notably more efficient. The code is available at https://github.com/kaiyuyue/nxtp

Recently, large language models (LLMs) have demonstrated superior capabilities in understanding and zero-shot learning on textual data, promising significant advances for many text-related domains. In the graph domain, various real-world scenarios also involve textual data, where tasks and node features can be described by text. These text-attributed graphs (TAGs) have broad applications in social media, recommendation systems, etc. Thus, this paper explores how to utilize LLMs to model TAGs. Previous methods for TAG modeling are based on million-scale LMs. When scaled up to billion-scale LLMs, they face huge challenges in computational costs. Additionally, they also ignore the zero-shot inference capabilities of LLMs. Therefore, we propose GraphAdapter, which uses a graph neural network (GNN) as an efficient adapter in collaboration with LLMs to tackle TAGs. In terms of efficiency, the GNN adapter introduces only a few trainable parameters and can be trained with low computation costs. The entire framework is trained using auto-regression on node text (next token prediction). Once trained, GraphAdapter can be seamlessly fine-tuned with task-specific prompts for various downstream tasks. Through extensive experiments across multiple real-world TAGs, GraphAdapter based on Llama 2 gains an average improvement of approximately 5\% in terms of node classification. Furthermore, GraphAdapter can also adapt to other language models, including RoBERTa, GPT-2. The promising results demonstrate that GNNs can serve as effective adapters for LLMs in TAG modeling.

We introduce NeuralProphet, a successor to Facebook Prophet, which set an industry standard for explainable, scalable, and user-friendly forecasting frameworks. With the proliferation of time series data, explainable forecasting remains a challenging task for business and operational decision making. Hybrid solutions are needed to bridge the gap between interpretable classical methods and scalable deep learning models. We view Prophet as a precursor to such a solution. However, Prophet lacks local context, which is essential for forecasting the near-term future and is challenging to extend due to its Stan backend. NeuralProphet is a hybrid forecasting framework based on PyTorch and trained with standard deep learning methods, making it easy for developers to extend the framework. Local context is introduced with auto-regression and covariate modules, which can be configured as classical linear regression or as Neural Networks. Otherwise, NeuralProphet retains the design philosophy of Prophet and provides the same basic model components. Our results demonstrate that NeuralProphet produces interpretable forecast components of equivalent or superior quality to Prophet on a set of generated time series. NeuralProphet outperforms Prophet on a diverse collection of real-world datasets. For short to medium-term forecasts, NeuralProphet improves forecast accuracy by 55 to 92 percent.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

The Russian Financial Statements Database (RFSD) is an open, harmonized collection of annual unconsolidated financial statements of the universe of Russian firms in 2011-2023. It is the first open data set with information on every active firm in the country, including non-filing firms. With 56.6 million geolocated firm-year observations gathered from two official sources, the RFSD features multiple end-user quality-of-life improvements such as data imputation, statement articulation, harmonization across data providers and formats, and data enrichment. Extensive internal and external validation shows that most statements articulate well while their aggregates display higher correlation with the regional GDP than the previous gridded GDP data products. We also examine the direction and magnitude of the reporting bias by comparing the universe of firms that are required to file with the actual filers. The RFSD can be used in various economic applications as diverse as calibration of micro-founded models, estimation of markups and productivity, or assessing industry organization and market power.

We introduce the concept of Automated Causal Discovery (AutoCD), defined as any system that aims to fully automate the application of causal discovery and causal reasoning methods. AutoCD's goal is to deliver all causal information that an expert human analyst would and answer a user's causal queries. We describe the architecture of such a platform, and illustrate its performance on synthetic data sets. As a case study, we apply it on temporal telecommunication data. The system is general and can be applied to a plethora of causal discovery problems.

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

While supervised learning has enabled great progress in many applications, unsupervised learning has not seen such widespread adoption, and remains an important and challenging endeavor for artificial intelligence. In this work, we propose a universal unsupervised learning approach to extract useful representations from high-dimensional data, which we call Contrastive Predictive Coding. The key insight of our model is to learn such representations by predicting the future in latent space by using powerful autoregressive models. We use a probabilistic contrastive loss which induces the latent space to capture information that is maximally useful to predict future samples. It also makes the model tractable by using negative sampling. While most prior work has focused on evaluating representations for a particular modality, we demonstrate that our approach is able to learn useful representations achieving strong performance on four distinct domains: speech, images, text and reinforcement learning in 3D environments.

Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep time-index models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias. In this paper, we propose DeepTime, a meta-optimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

Designing robust frameworks for precise prediction of future prices of stocks has always been considered a very challenging research problem. The advocates of the classical efficient market hypothesis affirm that it is impossible to accurately predict the future prices in an efficiently operating market due to the stochastic nature of the stock price variables. However, numerous propositions exist in the literature with varying degrees of sophistication and complexity that illustrate how algorithms and models can be designed for making efficient, accurate, and robust predictions of stock prices. We present a gamut of ten deep learning models of regression for precise and robust prediction of the future prices of the stock of a critical company in the auto sector of India. Using a very granular stock price collected at 5 minutes intervals, we train the models based on the records from 31st Dec, 2012 to 27th Dec, 2013. The testing of the models is done using records from 30th Dec, 2013 to 9th Jan 2015. We explain the design principles of the models and analyze the results of their performance based on accuracy in forecasting and speed of execution.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval. Empirically, RADD is up to 3.5 times faster while achieving similar performance with the strongest baseline. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.