autoregressive models

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

Powerful priors allow us to perform inference with insufficient information. In this paper, we propose an autoregressive prior for 3D shapes to solve multimodal 3D tasks such as shape completion, reconstruction, and generation. We model the distribution over 3D shapes as a non-sequential autoregressive distribution over a discretized, low-dimensional, symbolic grid-like latent representation of 3D shapes. This enables us to represent distributions over 3D shapes conditioned on information from an arbitrary set of spatially anchored query locations and thus perform shape completion in such arbitrary settings (e.g., generating a complete chair given only a view of the back leg). We also show that the learned autoregressive prior can be leveraged for conditional tasks such as single-view reconstruction and language-based generation. This is achieved by learning task-specific naive conditionals which can be approximated by light-weight models trained on minimal paired data. We validate the effectiveness of the proposed method using both quantitative and qualitative evaluation and show that the proposed method outperforms the specialized state-of-the-art methods trained for individual tasks. The project page with code and video visualizations can be found at this https URL.

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we narrow this performance gap by leveraging a key insight: Uniform-state diffusion processes naturally emerge from an underlying Gaussian diffusion. Our method, Duo, transfers powerful techniques from Gaussian diffusion to improve both training and sampling. First, we introduce a curriculum learning strategy guided by the Gaussian process, doubling training speed by reducing variance. Models trained with curriculum learning surpass autoregressive models in zero-shot perplexity on 3 of 7 benchmarks. Second, we present Discrete Consistency Distillation, which adapts consistency distillation from the continuous to the discrete setting. This algorithm unlocks few-step generation in diffusion language models by accelerating sampling by two orders of magnitude. We provide the code and model checkpoints on the project page: https://s-sahoo.com/duo

We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation process. Distinct to the classical recurrent VAEs, our CR-VAE uses a multi-head decoder, in which the p-th head is responsible for generating the p-th dimension of x (i.e., x^p). By imposing a sparsity-inducing penalty on the weights (of the decoder) and encouraging specific sets of weights to be zero, our CR-VAE learns a sparse adjacency matrix that encodes causal relations between all pairs of variables. Thanks to this causal matrix, our decoder strictly obeys the underlying principles of Granger causality, thereby making the data generating process transparent. We develop a two-stage approach to train the overall objective. Empirically, we evaluate the behavior of our model in synthetic data and two real-world human brain datasets involving, respectively, the electroencephalography (EEG) signals and the functional magnetic resonance imaging (fMRI) data. Our model consistently outperforms state-of-the-art time series generative models both qualitatively and quantitatively. Moreover, it also discovers a faithful causal graph with similar or improved accuracy over existing Granger causality-based causal inference methods. Code of CR-VAE is publicly available at https://github.com/hongmingli1995/CR-VAE.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on continuous-valued time series without discrete tokenization. Conditioned on arbitrary-length time series, our models are pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving more flexibility in representation learning than using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with one trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse via TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which achieve unprecedented model capacity and generalization performance. In addition to excellent scalability, Sundial achieves state-of-the-art results on both point and probabilistic forecasting benchmarks with a just-in-time inference speed, i.e., making zero-shot predictions within a few milliseconds. We believe that Sundial's pioneering generative forecasting capability can improve model reliability in real-world decision-making. Code is available at: https://github.com/thuml/Sundial.

A good generative model for time-series data should preserve temporal dynamics, in the sense that new sequences respect the original relationships between variables across time. Existing methods that bring generative adversarial networks (GANs) into the sequential setting do not adequately attend to the temporal correlations unique to time-series data. At the same time, supervised models for sequence prediction—which allow finer control over network dynamics—are inherently deterministic. We propose a novel framework for generating realistic time-series data that combines the flexibility of the unsupervised paradigm with the control afforded by supervised training. Through a learned embedding space jointly optimized with both supervised and adversarial objectives, we encourage the network to adhere to the dynamics of the training data during sampling. Empirically, we evaluate the ability of our method to generate realistic samples using a variety of real and synthetic time-series datasets. Qualitatively and quantitatively, we find that the proposed framework consistently and significantly outperforms state-of-the-art benchmarks with respect to measures of similarity and predictive ability.

We present the Pathways Autoregressive Text-to-Image (Parti) model, which generates high-fidelity photorealistic images and supports content-rich synthesis involving complex compositions and world knowledge. Parti treats text-to-image generation as a sequence-to-sequence modeling problem, akin to machine translation, with sequences of image tokens as the target outputs rather than text tokens in another language. This strategy can naturally tap into the rich body of prior work on large language models, which have seen continued advances in capabilities and performance through scaling data and model sizes. Our approach is simple: First, Parti uses a Transformer-based image tokenizer, ViT-VQGAN, to encode images as sequences of discrete tokens. Second, we achieve consistent quality improvements by scaling the encoder-decoder Transformer model up to 20B parameters, with a new state-of-the-art zero-shot FID score of 7.23 and finetuned FID score of 3.22 on MS-COCO. Our detailed analysis on Localized Narratives as well as PartiPrompts (P2), a new holistic benchmark of over 1600 English prompts, demonstrate the effectiveness of Parti across a wide variety of categories and difficulty aspects. We also explore and highlight limitations of our models in order to define and exemplify key areas of focus for further improvements. See this https URL for high-resolution images.

Recent models for learned image compression are based on autoencoders, learning approximately invertible mappings from pixels to a quantized latent representation. These are combined with an entropy model, a prior on the latent representation that can be used with standard arithmetic coding algorithms to yield a compressed bitstream. Recently, hierarchical entropy models have been introduced as a way to exploit more structure in the latents than simple fully factorized priors, improving compression performance while maintaining end-to-end optimization. Inspired by the success of autoregressive priors in probabilistic generative models, we examine autoregressive, hierarchical, as well as combined priors as alternatives, weighing their costs and benefits in the context of image compression. While it is well known that autoregressive models come with a significant computational penalty, we find that in terms of compression performance, autoregressive and hierarchical priors are complementary and, together, exploit the probabilistic structure in the latents better than all previous learned models. The combined model yields state-of-the-art rate--distortion performance, providing a 15.8% average reduction in file size over the previous state-of-the-art method based on deep learning, which corresponds to a 59.8% size reduction over JPEG, more than 35% reduction compared to WebP and JPEG2000, and bitstreams 8.4% smaller than BPG, the current state-of-the-art image codec. To the best of our knowledge, our model is the first learning-based method to outperform BPG on both PSNR and MS-SSIM distortion metrics.

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.

Knowledge distillation is commonly used for compressing neural networks to reduce their inference cost and memory footprint. However, current distillation methods for auto-regressive models, such as generative language models (LMs), suffer from two key issues: (1) distribution mismatch between output sequences during training and the sequences generated by the student during its deployment, and (2) model under-specification, where the student model may not be expressive enough to fit the teacher's distribution. To address these issues, we propose Generalized Knowledge Distillation (GKD). GKD mitigates distribution mismatch by sampling output sequences from the student during training. Furthermore, GKD handles model under-specification by optimizing alternative divergences, such as reverse KL, that focus on generating samples from the student that are likely under the teacher's distribution. We demonstrate that GKD outperforms commonly-used approaches for distilling LLMs on summarization, machine translation, and arithmetic reasoning tasks.