Daily Papers

Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series Dense Encoder (TiDE), for long-term time-series forecasting that enjoys the simplicity and speed of linear models while also being able to handle covariates and non-linear dependencies. Theoretically, we prove that the simplest linear analogue of our model can achieve near optimal error rate for linear dynamical systems (LDS) under some assumptions. Empirically, we show that our method can match or outperform prior approaches on popular long-term time-series forecasting benchmarks while being 5-10x faster than the best Transformer based model.

The stock market is a fundamental component of financial systems, reflecting economic health, providing investment opportunities, and influencing global dynamics. Accurate stock market predictions can lead to significant gains and promote better investment decisions. However, predicting stock market trends is challenging due to their non-linear and stochastic nature. This study investigates the efficacy of advanced deep learning models for short-term trend forecasting using daily and hourly closing prices from the S&P 500 index and the Brazilian ETF EWZ. The models explored include Temporal Convolutional Networks (TCN), Neural Basis Expansion Analysis for Time Series Forecasting (N-BEATS), Temporal Fusion Transformers (TFT), Neural Hierarchical Interpolation for Time Series Forecasting (N-HiTS), and Time-series Dense Encoder (TiDE). Furthermore, we introduce the Extended Long Short-Term Memory for Time Series (xLSTM-TS) model, an xLSTM adaptation optimised for time series prediction. Wavelet denoising techniques were applied to smooth the signal and reduce minor fluctuations, providing cleaner data as input for all approaches. Denoising significantly improved performance in predicting stock price direction. Among the models tested, xLSTM-TS consistently outperformed others. For example, it achieved a test accuracy of 72.82% and an F1 score of 73.16% on the EWZ daily dataset. By leveraging advanced deep learning models and effective data preprocessing techniques, this research provides valuable insights into the application of machine learning for market movement forecasting, highlighting both the potential and the challenges involved.

Transformer-based models have significantly advanced time series forecasting, with patch-based input strategies offering efficiency and improved long-horizon modeling. Yet, existing approaches rely on temporally-agnostic patch construction, where arbitrary starting positions and fixed lengths fracture temporal coherence by splitting natural transitions across boundaries. This naive segmentation often disrupts short-term dependencies and weakens representation learning. In response, we propose EntroPE (Entropy-Guided Dynamic Patch Encoder), a novel, temporally informed framework that dynamically detects transition points via conditional entropy and dynamically places patch boundaries. This preserves temporal structure while retaining the computational benefits of patching. EntroPE consists of two key modules, namely an Entropy-based Dynamic Patcher (EDP) that applies information-theoretic criteria to locate natural temporal shifts and determine patch boundaries, and an Adaptive Patch Encoder (APE) that employs pooling and cross-attention to capture intra-patch dependencies and produce fixed-size latent representations. These embeddings are then processed by a global transformer to model inter-patch dynamics. Experiments across long-term forecasting benchmarks demonstrate that EntroPE improves both accuracy and efficiency, establishing entropy-guided dynamic patching as a promising new paradigm for time series modeling. Code is available at: https://github.com/Sachithx/EntroPE.

Pre-trained Transformer language models (LM) have become go-to text representation encoders. Prior research fine-tunes deep LMs to encode text sequences such as sentences and passages into single dense vector representations for efficient text comparison and retrieval. However, dense encoders require a lot of data and sophisticated techniques to effectively train and suffer in low data situations. This paper finds a key reason is that standard LMs' internal attention structure is not ready-to-use for dense encoders, which needs to aggregate text information into the dense representation. We propose to pre-train towards dense encoder with a novel Transformer architecture, Condenser, where LM prediction CONditions on DENSE Representation. Our experiments show Condenser improves over standard LM by large margins on various text retrieval and similarity tasks.

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

This paper presents TS2Vec, a universal framework for learning representations of time series in an arbitrary semantic level. Unlike existing methods, TS2Vec performs contrastive learning in a hierarchical way over augmented context views, which enables a robust contextual representation for each timestamp. Furthermore, to obtain the representation of an arbitrary sub-sequence in the time series, we can apply a simple aggregation over the representations of corresponding timestamps. We conduct extensive experiments on time series classification tasks to evaluate the quality of time series representations. As a result, TS2Vec achieves significant improvement over existing SOTAs of unsupervised time series representation on 125 UCR datasets and 29 UEA datasets. The learned timestamp-level representations also achieve superior results in time series forecasting and anomaly detection tasks. A linear regression trained on top of the learned representations outperforms previous SOTAs of time series forecasting. Furthermore, we present a simple way to apply the learned representations for unsupervised anomaly detection, which establishes SOTA results in the literature. The source code is publicly available at https://github.com/yuezhihan/ts2vec.

Modern techniques like contrastive learning have been effectively used in many areas, including computer vision, natural language processing, and graph-structured data. Creating positive examples that assist the model in learning robust and discriminative representations is a crucial stage in contrastive learning approaches. Usually, preset human intuition directs the selection of relevant data augmentations. Due to patterns that are easily recognized by humans, this rule of thumb works well in the vision and language domains. However, it is impractical to visually inspect the temporal structures in time series. The diversity of time series augmentations at both the dataset and instance levels makes it difficult to choose meaningful augmentations on the fly. In this study, we address this gap by analyzing time series data augmentation using information theory and summarizing the most commonly adopted augmentations in a unified format. We then propose a contrastive learning framework with parametric augmentation, AutoTCL, which can be adaptively employed to support time series representation learning. The proposed approach is encoder-agnostic, allowing it to be seamlessly integrated with different backbone encoders. Experiments on univariate forecasting tasks demonstrate the highly competitive results of our method, with an average 6.5\% reduction in MSE and 4.7\% in MAE over the leading baselines. In classification tasks, AutoTCL achieves a 1.2% increase in average accuracy.

Recent advancements in language modeling have shown promising results when applied to time series data. In particular, fine-tuning pre-trained large language models (LLMs) for time series classification tasks has achieved state-of-the-art (SOTA) performance on standard benchmarks. However, these LLM-based models have a significant drawback due to the large model size, with the number of trainable parameters in the millions. In this paper, we propose an alternative approach to leveraging the success of language modeling in the time series domain. Instead of fine-tuning LLMs, we utilize a language embedding model to embed time series and then pair the embeddings with a simple classification head composed of convolutional neural networks (CNN) and multilayer perceptron (MLP). We conducted extensive experiments on well-established time series classification benchmark datasets. We demonstrated LETS-C not only outperforms the current SOTA in classification accuracy but also offers a lightweight solution, using only 14.5% of the trainable parameters on average compared to the SOTA model. Our findings suggest that leveraging language encoders to embed time series data, combined with a simple yet effective classification head, offers a promising direction for achieving high-performance time series classification while maintaining a lightweight model architecture.

Time-series representation learning is a fundamental task for time-series analysis. While significant progress has been made to achieve accurate representations for downstream applications, the learned representations often lack interpretability and do not expose semantic meanings. Different from previous efforts on the entangled feature space, we aim to extract the semantic-rich temporal correlations in the latent interpretable factorized representation of the data. Motivated by the success of disentangled representation learning in computer vision, we study the possibility of learning semantic-rich time-series representations, which remains unexplored due to three main challenges: 1) sequential data structure introduces complex temporal correlations and makes the latent representations hard to interpret, 2) sequential models suffer from KL vanishing problem, and 3) interpretable semantic concepts for time-series often rely on multiple factors instead of individuals. To bridge the gap, we propose Disentangle Time Series (DTS), a novel disentanglement enhancement framework for sequential data. Specifically, to generate hierarchical semantic concepts as the interpretable and disentangled representation of time-series, DTS introduces multi-level disentanglement strategies by covering both individual latent factors and group semantic segments. We further theoretically show how to alleviate the KL vanishing problem: DTS introduces a mutual information maximization term, while preserving a heavier penalty on the total correlation and the dimension-wise KL to keep the disentanglement property. Experimental results on various real-world benchmark datasets demonstrate that the representations learned by DTS achieve superior performance in downstream applications, with high interpretability of semantic concepts.

Multivariate time-series data in numerous real-world applications (e.g., healthcare and industry) are informative but challenging due to the lack of labels and high dimensionality. Recent studies in self-supervised learning have shown their potential in learning rich representations without relying on labels, yet they fall short in learning disentangled embeddings and addressing issues of inductive bias (e.g., transformation-invariance). To tackle these challenges, we propose TimeDRL, a generic multivariate time-series representation learning framework with disentangled dual-level embeddings. TimeDRL is characterized by three novel features: (i) disentangled derivation of timestamp-level and instance-level embeddings from patched time-series data using a [CLS] token strategy; (ii) utilization of timestamp-predictive and instance-contrastive tasks for disentangled representation learning, with the former optimizing timestamp-level embeddings with predictive loss, and the latter optimizing instance-level embeddings with contrastive loss; and (iii) avoidance of augmentation methods to eliminate inductive biases, such as transformation-invariance from cropping and masking. Comprehensive experiments on 6 time-series forecasting datasets and 5 time-series classification datasets have shown that TimeDRL consistently surpasses existing representation learning approaches, achieving an average improvement of forecasting by 58.02% in MSE and classification by 1.48% in accuracy. Furthermore, extensive ablation studies confirmed the relative contribution of each component in TimeDRL's architecture, and semi-supervised learning evaluations demonstrated its effectiveness in real-world scenarios, even with limited labeled data. The code is available at https://github.com/blacksnail789521/TimeDRL.

Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical contributions that are tailored to the numerical properties of time-series data and allow the model to scale to large datasets, e.g., millions of temporal sequences. We adopt the Transformer architecture by first partitioning the input into non-overlapping windows. Each window is then characterized by its normalized shape and two scalar values denoting the mean and standard deviation within each window. To embed scalar values that may possess arbitrary numerical scales to high-dimensional vectors, we propose a numerically multi-scaled embedding module enumerating all possible scales for the scalar values. The model undergoes pretraining using the proposed numerically multi-scaled embedding with a simple contrastive objective on a large-scale dataset containing over a million sequences. We study its transfer performance on a number of univariate and multivariate classification benchmarks. Our method exhibits remarkable improvement against previous representation learning approaches and establishes the new state of the art, even compared with domain-specific non-learning-based methods.

The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by network architecture instead of learned from data. In this work, we propose the dense transformer networks, which can learn the shapes and sizes of patches from data. The dense transformer networks employ an encoder-decoder architecture, and a pair of dense transformer modules are inserted into each of the encoder and decoder paths. The novelty of this work is that we provide technical solutions for learning the shapes and sizes of patches from data and efficiently restoring the spatial correspondence required for dense prediction. The proposed dense transformer modules are differentiable, thus the entire network can be trained. We apply the proposed networks on natural and biological image segmentation tasks and show superior performance is achieved in comparison to baseline methods.

Time series, characterized by a sequence of data points organized in a discrete-time order, are ubiquitous in real-world scenarios. Unlike other data modalities, time series present unique challenges due to their intricate and dynamic nature, including the entanglement of nonlinear patterns and time-variant trends. Analyzing such data is of great significance in practical applications and has been extensively studied for centuries. Recent years have witnessed remarkable breakthroughs in the time series community, with techniques shifting from traditional statistical methods to contemporary deep learning models. In this paper, we delve into the design of deep time series models across various analysis tasks and review the existing literature from two perspectives: basic modules and model architectures. Further, we develop and release Time Series Library (TSLib) as a fair benchmark of deep time series models for diverse analysis tasks. TSLib implements 30 prominent models, covers 30 datasets from different domains, and supports five prevalent analysis tasks. Based on TSLib, we thoroughly evaluate 13 advanced deep time series models across diverse tasks. Empirical results indicate that models with specific structures are well-suited for distinct analytical tasks, providing insights for research and adoption of deep time series models. Code and datasets are available at https://github.com/thuml/Time-Series-Library.

Generative modeling of time series is a central challenge in time series analysis, particularly under data-scarce conditions. Despite recent advances in generative modeling, a comprehensive understanding of how state-of-the-art generative models perform under limited supervision remains lacking. In this work, we conduct the first large-scale study evaluating leading generative models in data-scarce settings, revealing a substantial performance gap between full-data and data-scarce regimes. To close this gap, we propose a unified diffusion-based generative framework that can synthesize high-fidelity time series across diverse domains using just a few examples. Our model is pre-trained on a large, heterogeneous collection of time series datasets, enabling it to learn generalizable temporal representations. It further incorporates architectural innovations such as dynamic convolutional layers for flexible channel adaptation and dataset token conditioning for domain-aware generation. Without requiring abundant supervision, our unified model achieves state-of-the-art performance in few-shot settings-outperforming domain-specific baselines across a wide range of subset sizes. Remarkably, it also surpasses all baselines even when tested on full datasets benchmarks, highlighting the strength of pre-training and cross-domain generalization. We hope this work encourages the community to revisit few-shot generative modeling as a key problem in time series research and pursue unified solutions that scale efficiently across domains. Code is available at https://github.com/azencot-group/ImagenFew.

Masked time series modeling has recently gained much attention as a self-supervised representation learning strategy for time series. Inspired by masked image modeling in computer vision, recent works first patchify and partially mask out time series, and then train Transformers to capture the dependencies between patches by predicting masked patches from unmasked patches. However, we argue that capturing such patch dependencies might not be an optimal strategy for time series representation learning; rather, learning to embed patches independently results in better time series representations. Specifically, we propose to use 1) the simple patch reconstruction task, which autoencode each patch without looking at other patches, and 2) the simple patch-wise MLP that embeds each patch independently. In addition, we introduce complementary contrastive learning to hierarchically capture adjacent time series information efficiently. Our proposed method improves time series forecasting and classification performance compared to state-of-the-art Transformer-based models, while it is more efficient in terms of the number of parameters and training/inference time. Code is available at this repository: https://github.com/seunghan96/pits.

Contrastive learning has shown to be effective to learn representations from time series in a self-supervised way. However, contrasting similar time series instances or values from adjacent timestamps within a time series leads to ignore their inherent correlations, which results in deteriorating the quality of learned representations. To address this issue, we propose SoftCLT, a simple yet effective soft contrastive learning strategy for time series. This is achieved by introducing instance-wise and temporal contrastive loss with soft assignments ranging from zero to one. Specifically, we define soft assignments for 1) instance-wise contrastive loss by the distance between time series on the data space, and 2) temporal contrastive loss by the difference of timestamps. SoftCLT is a plug-and-play method for time series contrastive learning that improves the quality of learned representations without bells and whistles. In experiments, we demonstrate that SoftCLT consistently improves the performance in various downstream tasks including classification, semi-supervised learning, transfer learning, and anomaly detection, showing state-of-the-art performance. Code is available at this repository: https://github.com/seunghan96/softclt.

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

Multi-modal large language models (MLLMs) have enabled numerous advances in understanding and reasoning in domains like vision, but we have not yet seen this broad success for time-series. Although prior works on time-series MLLMs have shown promising performance in time-series forecasting, very few works show how an LLM could be used for time-series reasoning in natural language. We propose a novel multi-modal time-series LLM approach that learns generalizable information across various domains with powerful zero-shot performance. First, we train a lightweight time-series encoder on top of an LLM to directly extract time-series information. Then, we fine-tune our model with chain-of-thought augmented time-series tasks to encourage the model to generate reasoning paths. We show that our model learns a latent representation that reflects specific time-series features (e.g. slope, frequency), as well as outperforming GPT-4o on a set of zero-shot reasoning tasks on a variety of domains.

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

In this paper, we investigate the distillation of time series reasoning capabilities into small, instruction-tuned language models as a step toward building interpretable time series foundation models. Leveraging a synthetic dataset of mean-reverting time series with systematically varied trends and noise levels, we generate natural language annotations using a large multimodal model and use these to supervise the fine-tuning of compact Qwen models. We introduce evaluation metrics that assess the quality of the distilled reasoning - focusing on trend direction, noise intensity, and extremum localization - and show that the post-trained models acquire meaningful interpretive capabilities. Our results highlight the feasibility of compressing time series understanding into lightweight, language-capable models suitable for on-device or privacy-sensitive deployment. This work contributes a concrete foundation toward developing small, interpretable models that explain temporal patterns in natural language.

Spatially dense self-supervised learning is a rapidly growing problem domain with promising applications for unsupervised segmentation and pretraining for dense downstream tasks. Despite the abundance of temporal data in the form of videos, this information-rich source has been largely overlooked. Our paper aims to address this gap by proposing a novel approach that incorporates temporal consistency in dense self-supervised learning. While methods designed solely for images face difficulties in achieving even the same performance on videos, our method improves not only the representation quality for videos-but also images. Our approach, which we call time-tuning, starts from image-pretrained models and fine-tunes them with a novel self-supervised temporal-alignment clustering loss on unlabeled videos. This effectively facilitates the transfer of high-level information from videos to image representations. Time-tuning improves the state-of-the-art by 8-10% for unsupervised semantic segmentation on videos and matches it for images. We believe this method paves the way for further self-supervised scaling by leveraging the abundant availability of videos. The implementation can be found here : https://github.com/SMSD75/Timetuning

Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or quasi-periodic dynamics that are often not adequately captured by existing deep learning-based solutions. This results in an incomplete representation of the underlying dynamic behaviors of interest. To address this gap, we propose an unsupervised method called Floss that automatically regularizes learned representations in the frequency domain. The Floss method first automatically detects major periodicities from the time series. It then employs periodic shift and spectral density similarity measures to learn meaningful representations with periodic consistency. In addition, Floss can be easily incorporated into both supervised, semi-supervised, and unsupervised learning frameworks. We conduct extensive experiments on common time series classification, forecasting, and anomaly detection tasks to demonstrate the effectiveness of Floss. We incorporate Floss into several representative deep learning solutions to justify our design choices and demonstrate that it is capable of automatically discovering periodic dynamics and improving state-of-the-art deep learning models.

Fast and scalable alignment of time series is a fundamental challenge in many domains. The standard solution, Dynamic Time Warping (DTW), struggles with poor scalability and sensitivity to noise. We introduce TimePoint, a self-supervised method that dramatically accelerates DTW-based alignment while typically improving alignment accuracy by learning keypoints and descriptors from synthetic data. Inspired by 2D keypoint detection but carefully adapted to the unique challenges of 1D signals, TimePoint leverages efficient 1D diffeomorphisms, which effectively model nonlinear time warping, to generate realistic training data. This approach, along with fully convolutional and wavelet convolutional architectures, enables the extraction of informative keypoints and descriptors. Applying DTW to these sparse representations yield major speedups and typically higher alignment accuracy than standard DTW applied to the full signals. TimePoint demonstrates strong generalization to real-world time series when trained solely on synthetic data, and further improves with fine-tuning on real data. Extensive experiments demonstrate that TimePoint consistently achieves faster and more accurate alignments than standard DTW, making it a scalable solution for time-series analysis. Our code is available at https://github.com/BGU-CS-VIL/TimePoint

Time series analysis is of immense importance in extensive applications, such as weather forecasting, anomaly detection, and action recognition. This paper focuses on temporal variation modeling, which is the common key problem of extensive analysis tasks. Previous methods attempt to accomplish this directly from the 1D time series, which is extremely challenging due to the intricate temporal patterns. Based on the observation of multi-periodicity in time series, we ravel out the complex temporal variations into the multiple intraperiod- and interperiod-variations. To tackle the limitations of 1D time series in representation capability, we extend the analysis of temporal variations into the 2D space by transforming the 1D time series into a set of 2D tensors based on multiple periods. This transformation can embed the intraperiod- and interperiod-variations into the columns and rows of the 2D tensors respectively, making the 2D-variations to be easily modeled by 2D kernels. Technically, we propose the TimesNet with TimesBlock as a task-general backbone for time series analysis. TimesBlock can discover the multi-periodicity adaptively and extract the complex temporal variations from transformed 2D tensors by a parameter-efficient inception block. Our proposed TimesNet achieves consistent state-of-the-art in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection. Code is available at this repository: https://github.com/thuml/TimesNet.

The advent of data-driven weather forecasting models, which learn from hundreds of terabytes (TB) of reanalysis data, has significantly advanced forecasting capabilities. However, the substantial costs associated with data storage and transmission present a major challenge for data providers and users, affecting resource-constrained researchers and limiting their accessibility to participate in AI-based meteorological research. To mitigate this issue, we introduce an efficient neural codec, the Variational Autoencoder Transformer (VAEformer), for extreme compression of climate data to significantly reduce data storage cost, making AI-based meteorological research portable to researchers. Our approach diverges from recent complex neural codecs by utilizing a low-complexity Auto-Encoder transformer. This encoder produces a quantized latent representation through variance inference, which reparameterizes the latent space as a Gaussian distribution. This method improves the estimation of distributions for cross-entropy coding. Extensive experiments demonstrate that our VAEformer outperforms existing state-of-the-art compression methods in the context of climate data. By applying our VAEformer, we compressed the most popular ERA5 climate dataset (226 TB) into a new dataset, CRA5 (0.7 TB). This translates to a compression ratio of over 300 while retaining the dataset's utility for accurate scientific analysis. Further, downstream experiments show that global weather forecasting models trained on the compact CRA5 dataset achieve forecasting accuracy comparable to the model trained on the original dataset. Code, the CRA5 dataset, and the pre-trained model are available at https://github.com/taohan10200/CRA5.

We present TimeFound, an encoder-decoder transformer-based time series foundation model for out-of-the-box zero-shot forecasting. To handle time series data from various domains, TimeFound employs a multi-resolution patching strategy to capture complex temporal patterns at multiple scales. We pre-train our model with two sizes (200M and 710M parameters) on a large time-series corpus comprising both real-world and synthetic datasets. Over a collection of unseen datasets across diverse domains and forecasting horizons, our empirical evaluations suggest that TimeFound can achieve superior or competitive zero-shot forecasting performance, compared to state-of-the-art time series foundation models.

This paper presents our latest investigation on Densely Connected Convolutional Networks (DenseNets) for acoustic modelling (AM) in automatic speech recognition. DenseN-ets are very deep, compact convolutional neural networks, which have demonstrated incredible improvements over the state-of-the-art results on several data sets in computer vision. Our experimental results show that DenseNet can be used for AM significantly outperforming other neural-based models such as DNNs, CNNs, VGGs. Furthermore, results on Wall Street Journal revealed that with only a half of the training data DenseNet was able to outperform other models trained with the full data set by a large margin.

The transformer architecture by Vaswani et al. (2017) is now ubiquitous across application domains, from natural language processing to speech processing and image understanding. We propose DenseFormer, a simple modification to the standard architecture that improves the perplexity of the model without increasing its size -- adding a few thousand parameters for large-scale models in the 100B parameters range. Our approach relies on an additional averaging step after each transformer block, which computes a weighted average of current and past representations -- we refer to this operation as Depth-Weighted-Average (DWA). The learned DWA weights exhibit coherent patterns of information flow, revealing the strong and structured reuse of activations from distant layers. Experiments demonstrate that DenseFormer is more data efficient, reaching the same perplexity of much deeper transformer models, and that for the same perplexity, these new models outperform transformer baselines in terms of memory efficiency and inference time.

Self-supervised learning has seen great success recently in unsupervised representation learning, enabling breakthroughs in natural language and image processing. However, these methods often rely on autoregressive and masked modeling, which aim to reproduce masked information in the input, which can be vulnerable to the presence of noise or confounding variables. To address this problem, Joint-Embedding Predictive Architectures (JEPA) has been introduced with the aim to perform self-supervised learning in the latent space. To leverage these advancements in the domain of time series, we introduce Time Series JEPA (TS-JEPA), an architecture specifically adapted for time series representation learning. We validate TS-JEPA on both classification and forecasting, showing that it can match or surpass current state-of-the-art baselines on different standard datasets. Notably, our approach demonstrates a strong performance balance across diverse tasks, indicating its potential as a robust foundation for learning general representations. Thus, this work lays the groundwork for developing future time series foundation models based on Joint Embedding.

Language models have achieved remarkable success in various natural language processing tasks. However, their application to time series data, a crucial component in many domains, remains limited. This paper proposes LiPCoT (Linear Predictive Coding based Tokenizer for time series), a novel tokenizer that encodes time series data into a sequence of tokens, enabling self-supervised learning of time series using existing Language model architectures such as BERT. Unlike traditional time series tokenizers that rely heavily on CNN encoder for time series feature generation, LiPCoT employs stochastic modeling through linear predictive coding to create a latent space for time series providing a compact yet rich representation of the inherent stochastic nature of the data. Furthermore, LiPCoT is computationally efficient and can effectively handle time series data with varying sampling rates and lengths, overcoming common limitations of existing time series tokenizers. In this proof-of-concept work, we present the effectiveness of LiPCoT in classifying Parkinson's disease (PD) using an EEG dataset from 46 participants. In particular, we utilize LiPCoT to encode EEG data into a small vocabulary of tokens and then use BERT for self-supervised learning and the downstream task of PD classification. We benchmark our approach against several state-of-the-art CNN-based deep learning architectures for PD detection. Our results reveal that BERT models utilizing self-supervised learning outperformed the best-performing existing method by 7.1% in precision, 2.3% in recall, 5.5% in accuracy, 4% in AUC, and 5% in F1-score highlighting the potential for self-supervised learning even on small datasets. Our work will inform future foundational models for time series, particularly for self-supervised learning.

Large Language Models (LLMs) have been extensively applied in time series analysis. Yet, their utility in the few-shot classification (i.e., a crucial training scenario due to the limited training data available in industrial applications) concerning multivariate time series data remains underexplored. We aim to leverage the extensive pre-trained knowledge in LLMs to overcome the data scarcity problem within multivariate time series. Specifically, we propose LLMFew, an LLM-enhanced framework to investigate the feasibility and capacity of LLMs for few-shot multivariate time series classification. This model introduces a Patch-wise Temporal Convolution Encoder (PTCEnc) to align time series data with the textual embedding input of LLMs. We further fine-tune the pre-trained LLM decoder with Low-rank Adaptations (LoRA) to enhance its feature representation learning ability in time series data. Experimental results show that our model outperformed state-of-the-art baselines by a large margin, achieving 125.2% and 50.2% improvement in classification accuracy on Handwriting and EthanolConcentration datasets, respectively. Moreover, our experimental results demonstrate that LLM-based methods perform well across a variety of datasets in few-shot MTSC, delivering reliable results compared to traditional models. This success paves the way for their deployment in industrial environments where data are limited.

We propose a simple but strong baseline for time series classification from scratch with deep neural networks. Our proposed baseline models are pure end-to-end without any heavy preprocessing on the raw data or feature crafting. The proposed Fully Convolutional Network (FCN) achieves premium performance to other state-of-the-art approaches and our exploration of the very deep neural networks with the ResNet structure is also competitive. The global average pooling in our convolutional model enables the exploitation of the Class Activation Map (CAM) to find out the contributing region in the raw data for the specific labels. Our models provides a simple choice for the real world application and a good starting point for the future research. An overall analysis is provided to discuss the generalization capability of our models, learned features, network structures and the classification semantics.

In time series editing, we aim to modify some properties of a given time series without altering others. For example, when analyzing a hospital patient's blood pressure, we may add a sudden early drop and observe how it impacts their future while preserving other conditions. Existing diffusion-based editors rely on rigid, predefined attribute vectors as conditions and produce all-or-nothing edits through sampling. This attribute- and sampling-based approach limits flexibility in condition format and lacks customizable control over editing strength. To overcome these limitations, we introduce Instruction-based Time Series Editing, where users specify intended edits using natural language. This allows users to express a wider range of edits in a more accessible format. We then introduce InstructTime, the first instruction-based time series editor. InstructTime takes in time series and instructions, embeds them into a shared multi-modal representation space, then decodes their embeddings to generate edited time series. By learning a structured multi-modal representation space, we can easily interpolate between embeddings to achieve varying degrees of edit. To handle local and global edits together, we propose multi-resolution encoders. In our experiments, we use synthetic and real datasets and find that InstructTime is a state-of-the-art time series editor: InstructTime achieves high-quality edits with controllable strength, can generalize to unseen instructions, and can be easily adapted to unseen conditions through few-shot learning.

Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we embrace this observation and introduce the Dense Convolutional Network (DenseNet), which connects each layer to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections - one between each layer and its subsequent layer - our network has L(L+1)/2 direct connections. For each layer, the feature-maps of all preceding layers are used as inputs, and its own feature-maps are used as inputs into all subsequent layers. DenseNets have several compelling advantages: they alleviate the vanishing-gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters. We evaluate our proposed architecture on four highly competitive object recognition benchmark tasks (CIFAR-10, CIFAR-100, SVHN, and ImageNet). DenseNets obtain significant improvements over the state-of-the-art on most of them, whilst requiring less computation to achieve high performance. Code and pre-trained models are available at https://github.com/liuzhuang13/DenseNet .

Self-supervised learning has garnered increasing attention in time series analysis for benefiting various downstream tasks and reducing reliance on labeled data. Despite its effectiveness, existing methods often struggle to comprehensively capture both long-term dynamic evolution and subtle local patterns in a unified manner. In this work, we propose TimeDART, a novel self-supervised time series pre-training framework that unifies two powerful generative paradigms to learn more transferable representations. Specifically, we first employ a causal Transformer encoder, accompanied by a patch-based embedding strategy, to model the evolving trends from left to right. Building on this global modeling, we further introduce a denoising diffusion process to capture fine-grained local patterns through forward diffusion and reverse denoising. Finally, we optimize the model in an autoregressive manner. As a result, TimeDART effectively accounts for both global and local sequence features in a coherent way. We conduct extensive experiments on public datasets for time series forecasting and classification. The experimental results demonstrate that TimeDART consistently outperforms previous compared methods, validating the effectiveness of our approach. Our code is available at https://github.com/Melmaphother/TimeDART.

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

Time series data is fundamental to decision-making in many crucial domains including healthcare, finance, and environmental science. However, analyzing this data often requires incorporating unstructured contextual information, answering domain-specific questions, and generating natural language explanations -- capabilities that traditional time series models lack due to their inability to process text. While Large Language Models (LLMs) excel at contextual reasoning and knowledge integration, they struggle with numerical time series due to inefficient text-based representations and limited exposure to temporal data during pretraining. We address this gap by augmenting an LLM with specialized time series perception through a patch-based encoder-decoder architecture. We train this Time Series-augmented LLM (TsLLM) on a large corpus of over 2 million interleaved time series and text examples spanning diverse analysis tasks: forecasting with contextual information, time series question-answering, pattern explanation, classification with natural language outputs, and report generation. This training enables TsLLM to leverage both its language understanding and newly acquired temporal reasoning capabilities. While not designed to surpass specialized models on traditional benchmarks, TsLLM demonstrates strong performance on tasks requiring the integration of time series analysis with natural language -- capabilities that existing approaches cannot provide. Our work establishes a new paradigm for time series analysis that bridges numerical computation and natural language understanding, democratizing access to sophisticated temporal reasoning through natural language interaction.

Dense retrieval requires high-quality text sequence embeddings to support effective search in the representation space. Autoencoder-based language models are appealing in dense retrieval as they train the encoder to output high-quality embedding that can reconstruct the input texts. However, in this paper, we provide theoretical analyses and show empirically that an autoencoder language model with a low reconstruction loss may not provide good sequence representations because the decoder may take shortcuts by exploiting language patterns. To address this, we propose a new self-learning method that pre-trains the autoencoder using a weak decoder, with restricted capacity and attention flexibility to push the encoder to provide better text representations. Our experiments on web search, news recommendation, and open domain question answering show that our pre-trained model significantly boosts the effectiveness and few-shot ability of dense retrieval models. Our code is available at https://github.com/microsoft/SEED-Encoder/.

The task of recognising Handwritten Mathematical Expressions (HMER) is crucial in the fields of digital education and scholarly research. However, it is difficult to accurately determine the length and complex spatial relationships among symbols in handwritten mathematical expressions. In this study, we present a novel encoder-decoder architecture (DenseBAM-GI) for HMER, where the encoder has a Bottleneck Attention Module (BAM) to improve feature representation and the decoder has a Gated Input-GRU (GI-GRU) unit with an extra gate to make decoding long and complex expressions easier. The proposed model is an efficient and lightweight architecture with performance equivalent to state-of-the-art models in terms of Expression Recognition Rate (exprate). It also performs better in terms of top 1, 2, and 3 error accuracy across the CROHME 2014, 2016, and 2019 datasets. DenseBAM-GI achieves the best exprate among all models on the CROHME 2019 dataset. Importantly, these successes are accomplished with a drop in the complexity of the calculation and a reduction in the need for GPU memory.

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.

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.

The widespread adoption of scalable mobile sensing has led to large amounts of time series data for real-world applications. A fundamental application is multivariate time series forecasting (MTSF), which aims to predict future time series values based on historical observations. Existing MTSF methods suffer from limited parameterization and small-scale training data. Recently, Large language models (LLMs) have been introduced in time series, which achieve promising forecasting performance but incur heavy computational costs. To solve these challenges, we propose TimeCMA, an LLM-empowered framework for time series forecasting with cross-modality alignment. We design a dual-modality encoding module with two branches, where the time series encoding branch extracts relatively low-quality yet pure embeddings of time series through an inverted Transformer. In addition, the LLM-empowered encoding branch wraps the same time series as prompts to obtain high-quality yet entangled prompt embeddings via a Pre-trained LLM. Then, we design a cross-modality alignment module to retrieve high-quality and pure time series embeddings from the prompt embeddings. Moreover, we develop a time series forecasting module to decode the aligned embeddings while capturing dependencies among multiple variables for forecasting. Notably, we tailor the prompt to encode sufficient temporal information into a last token and design the last token embedding storage to reduce computational costs. Extensive experiments on real data offer insight into the accuracy and efficiency of the proposed framework.

The past decade has witnessed significant advances in time series modeling with deep learning. While achieving state-of-the-art results, the best-performing architectures vary highly across applications and domains. Meanwhile, for natural language processing, the Generative Pre-trained Transformer (GPT) has demonstrated impressive performance via training one general-purpose model across various textual datasets. It is intriguing to explore whether GPT-type architectures can be effective for time series, capturing the intrinsic dynamic attributes and leading to significant accuracy improvements. In this paper, we propose a novel framework, TEMPO, that can effectively learn time series representations. We focus on utilizing two essential inductive biases of the time series task for pre-trained models: (i) decomposition of the complex interaction between trend, seasonal and residual components; and (ii) introducing the selection-based prompts to facilitate distribution adaptation in non-stationary time series. TEMPO expands the capability for dynamically modeling real-world temporal phenomena from data within diverse domains. Our experiments demonstrate the superior performance of TEMPO over state-of-the-art methods on a number of time series benchmark datasets. This performance gain is observed not only in standard supervised learning settings but also in scenarios involving previously unseen datasets as well as in scenarios with multi-modal inputs. This compelling finding highlights TEMPO's potential to constitute a foundational model-building framework.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence without increasing the computational effort for inference.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet

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.

Self-supervised learning (SSL) has recently achieved impressive performance on various time series tasks. The most prominent advantage of SSL is that it reduces the dependence on labeled data. Based on the pre-training and fine-tuning strategy, even a small amount of labeled data can achieve high performance. Compared with many published self-supervised surveys on computer vision and natural language processing, a comprehensive survey for time series SSL is still missing. To fill this gap, we review current state-of-the-art SSL methods for time series data in this article. To this end, we first comprehensively review existing surveys related to SSL and time series, and then provide a new taxonomy of existing time series SSL methods by summarizing them from three perspectives: generative-based, contrastive-based, and adversarial-based. These methods are further divided into ten subcategories with detailed reviews and discussions about their key intuitions, main frameworks, advantages and disadvantages. To facilitate the experiments and validation of time series SSL methods, we also summarize datasets commonly used in time series forecasting, classification, anomaly detection, and clustering tasks. Finally, we present the future directions of SSL for time series analysis.

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.

Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, model weights, and data will be released.

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.

SDForger is a flexible and efficient framework for generating high-quality multivariate time series using LLMs. Leveraging a compact data representation, SDForger provides synthetic time series generation from a few samples and low-computation fine-tuning of any autoregressive LLM. Specifically, the framework transforms univariate and multivariate signals into tabular embeddings, which are then encoded into text and used to fine-tune the LLM. At inference, new textual embeddings are sampled and decoded into synthetic time series that retain the original data's statistical properties and temporal dynamics. Across a diverse range of datasets, SDForger outperforms existing generative models in many scenarios, both in similarity-based evaluations and downstream forecasting tasks. By enabling textual conditioning in the generation process, SDForger paves the way for multimodal modeling and the streamlined integration of time series with textual information. SDForger source code will be open-sourced soon.

Deep neural networks, including transformers and convolutional neural networks, have significantly improved multivariate time series classification (MTSC). However, these methods often rely on supervised learning, which does not fully account for the sparsity and locality of patterns in time series data (e.g., diseases-related anomalous points in ECG). To address this challenge, we formally reformulate MTSC as a weakly supervised problem, introducing a novel multiple-instance learning (MIL) framework for better localization of patterns of interest and modeling time dependencies within time series. Our novel approach, TimeMIL, formulates the temporal correlation and ordering within a time-aware MIL pooling, leveraging a tokenized transformer with a specialized learnable wavelet positional token. The proposed method surpassed 26 recent state-of-the-art methods, underscoring the effectiveness of the weakly supervised TimeMIL in MTSC. The code will be available at https://github.com/xiwenc1/TimeMIL.

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 time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

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.

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.

Multivariate Time Series forecasting has been an increasingly popular topic in various applications and scenarios. Recently, contrastive learning and Transformer-based models have achieved good performance in many long-term series forecasting tasks. However, there are still several issues in existing methods. First, the training paradigm of contrastive learning and downstream prediction tasks are inconsistent, leading to inaccurate prediction results. Second, existing Transformer-based models which resort to similar patterns in historical time series data for predicting future values generally induce severe distribution shift problems, and do not fully leverage the sequence information compared to self-supervised methods. To address these issues, we propose a novel framework named Ti-MAE, in which the input time series are assumed to follow an integrate distribution. In detail, Ti-MAE randomly masks out embedded time series data and learns an autoencoder to reconstruct them at the point-level. Ti-MAE adopts mask modeling (rather than contrastive learning) as the auxiliary task and bridges the connection between existing representation learning and generative Transformer-based methods, reducing the difference between upstream and downstream forecasting tasks while maintaining the utilization of original time series data. Experiments on several public real-world datasets demonstrate that our framework of masked autoencoding could learn strong representations directly from the raw data, yielding better performance in time series forecasting and classification tasks.

Multivariate time series classification is a crucial task in data mining, attracting growing research interest due to its broad applications. While many existing methods focus on discovering discriminative patterns in time series, real-world data does not always present such patterns, and sometimes raw numerical values can also serve as discriminative features. Additionally, the recent success of Transformer models has inspired many studies. However, when applying to time series classification, the self-attention mechanisms in Transformer models could introduce classification-irrelevant features, thereby compromising accuracy. To address these challenges, we propose a novel method, VSFormer, that incorporates both discriminative patterns (shape) and numerical information (value). In addition, we extract class-specific prior information derived from supervised information to enrich the positional encoding and provide classification-oriented self-attention learning, thereby enhancing its effectiveness. Extensive experiments on all 30 UEA archived datasets demonstrate the superior performance of our method compared to SOTA models. Through ablation studies, we demonstrate the effectiveness of the improved encoding layer and the proposed self-attention mechanism. Finally, We provide a case study on a real-world time series dataset without discriminative patterns to interpret our model.

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.

The rise of time-series pre-trained models has advanced temporal representation learning, but current state-of-the-art models are often large-scale, requiring substantial compute. We introduce TSPulse, ultra-compact time-series pre-trained models with only 1M parameters, specialized to perform strongly across classification, anomaly detection, imputation, and retrieval tasks. TSPulse introduces innovations at both the architecture and task levels. At the architecture level, it employs a dual-space masked reconstruction, learning from both time and frequency domains to capture complementary signals. This is further enhanced by a dual-embedding disentanglement, generating both detailed embeddings for fine-grained analysis and high-level semantic embeddings for broader task understanding. Notably, TSPulse's semantic embeddings are robust to shifts in time, magnitude, and noise, which is important for robust retrieval. At the task level, TSPulse incorporates TSLens, a fine-tuning component enabling task-specific feature attention. It also introduces a multi-head triangulation technique that correlates deviations from multiple prediction heads, enhancing anomaly detection by fusing complementary model outputs. Additionally, a hybrid mask pretraining is proposed to improves zero-shot imputation by reducing pre-training bias. These architecture and task innovations collectively contribute to TSPulse's significant performance gains: 5-16% on the UEA classification benchmarks, +20% on the TSB-AD anomaly detection leaderboard, +50% in zero-shot imputation, and +25% in time-series retrieval. Remarkably, these results are achieved with just 1M parameters, making TSPulse 10-100X smaller than existing pre-trained models. Its efficiency enables GPU-free inference and rapid pre-training, setting a new standard for efficient time-series pre-trained models. Models will be open-sourced soon.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.

Learning to classify time series with limited data is a practical yet challenging problem. Current methods are primarily based on hand-designed feature extraction rules or domain-specific data augmentation. Motivated by the advances in deep speech processing models and the fact that voice data are univariate temporal signals, in this paper, we propose Voice2Series (V2S), a novel end-to-end approach that reprograms acoustic models for time series classification, through input transformation learning and output label mapping. Leveraging the representation learning power of a large-scale pre-trained speech processing model, on 30 different time series tasks we show that V2S performs competitive results on 19 time series classification tasks. We further provide a theoretical justification of V2S by proving its population risk is upper bounded by the source risk and a Wasserstein distance accounting for feature alignment via reprogramming. Our results offer new and effective means to time series classification.

Time-series data are critical in diverse applications, such as industrial monitoring, medical diagnostics, and climate research. However, effectively integrating these high-dimensional temporal signals with natural language for dynamic, interactive tasks remains a significant challenge. To address this, we introduce the Time-Series Question Answering (Time-Series QA) task and release EngineMT-QA, the first large-scale, multi-task, temporal-textual QA dataset designed to capture complex interactions between time-series signals and natural language. Building on this resource, we propose the Instruct Time Transformer (ITFormer), a novel framework that bridges time-series encoders with frozen large language models (LLMs). ITFormer effectively extracts, aligns, and fuses temporal and textual features, achieving a strong improvement in QA accuracy over strong baselines with fewer than 1\% additional trainable parameters. By combining computational efficiency with robust cross-modal modeling, our work establishes a adaptable paradigm for integrating temporal data with natural language, paving the way for new research and applications in multi-modal AI. More details about the project, including datasets and code, are available at: https://pandalin98.github.io/itformer_site/

We present DenseAV, a novel dual encoder grounding architecture that learns high-resolution, semantically meaningful, and audio-visually aligned features solely through watching videos. We show that DenseAV can discover the ``meaning'' of words and the ``location'' of sounds without explicit localization supervision. Furthermore, it automatically discovers and distinguishes between these two types of associations without supervision. We show that DenseAV's localization abilities arise from a new multi-head feature aggregation operator that directly compares dense image and audio representations for contrastive learning. In contrast, many other systems that learn ``global'' audio and video representations cannot localize words and sound. Finally, we contribute two new datasets to improve the evaluation of AV representations through speech and sound prompted semantic segmentation. On these and other datasets we show DenseAV dramatically outperforms the prior art on speech and sound prompted semantic segmentation. DenseAV outperforms the previous state-of-the-art, ImageBind, on cross-modal retrieval using fewer than half of the parameters. Project Page: https://aka.ms/denseav{https://aka.ms/denseav}

Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many existing methods focus on a single type of feature such as shape or frequency. Building on the recent success of convolutional neural networks for time series classification, we show that simple linear classifiers using random convolutional kernels achieve state-of-the-art accuracy with a fraction of the computational expense of existing methods.

The scientific reasoning ability of large language models (LLMs) has recently attracted significant attention. Time series, as a fundamental modality in scientific data, presents unique challenges that are often overlooked in current multimodal LLMs, which either encode numerical sequences as text or convert them into images. Such approaches may be insufficient for comprehensive scientific time series understanding and generation. Existing unified time series models typically specialise in either forecasting or analysis, and their effectiveness on non-periodic, heterogeneous scientific signals remains unclear. To address these gaps, we introduce SciTS, a benchmark spanning 12 scientific domains and 43 tasks, with over 50k+ instances, both univariate and multivariate signals ranging from 10^0 to 10^7 in length and up to 10~MHz in frequency. We benchmark 17 models, including text-only LLMs, multimodal LLMs, and unified time series models, and find that general-purpose LLMs exhibit stronger generalisability than specialised time series models, while representing time series as text or images limits their performance due to excessively long sequences and loss of numerical precision, respectively. We then introduce TimeOmni, a framework that equips LLMs with the ability to understand and generate time series while remaining compatible with general-purpose LLM training. This work fills a gap in both dedicated benchmarks and modelling frameworks for scientific time series, paving the way for LLMs to understand and generate complex temporal scientific data.

Pre-trained encoders are widely employed in dense prediction tasks for their capability to effectively extract visual features from images. The decoder subsequently processes these features to generate pixel-level predictions. However, due to structural differences and variations in input data, only encoders benefit from pre-learned representations from vision benchmarks such as image classification and self-supervised learning, while decoders are typically trained from scratch. In this paper, we introduce timesNet, which facilitates a "pre-trained encoder times pre-trained decoder" collaboration through three innovative designs. timesNet enables the direct utilization of pre-trained models within the decoder, integrating pre-learned representations into the decoding process to enhance performance in dense prediction tasks. By simply coupling the pre-trained encoder and pre-trained decoder, timesNet distinguishes itself as a highly promising approach. Remarkably, it achieves this without relying on decoding-specific structures or task-specific algorithms. Despite its streamlined design, timesNet outperforms advanced methods in tasks such as monocular depth estimation and semantic segmentation, achieving state-of-the-art performance particularly in monocular depth estimation. and semantic segmentation, achieving state-of-the-art results, especially in monocular depth estimation. embedding algorithms. Despite its streamlined design, timesNet outperforms advanced methods in tasks such as monocular depth estimation and semantic segmentation, achieving state-of-the-art performance particularly in monocular depth estimation.

Wind power is attracting increasing attention around the world due to its renewable, pollution-free, and other advantages. However, safely and stably integrating the high permeability intermittent power energy into electric power systems remains challenging. Accurate wind power forecasting (WPF) can effectively reduce power fluctuations in power system operations. Existing methods are mainly designed for short-term predictions and lack effective spatial-temporal feature augmentation. In this work, we propose a novel end-to-end wind power forecasting model named Hierarchical Spatial-Temporal Transformer Network (HSTTN) to address the long-term WPF problems. Specifically, we construct an hourglass-shaped encoder-decoder framework with skip-connections to jointly model representations aggregated in hierarchical temporal scales, which benefits long-term forecasting. Based on this framework, we capture the inter-scale long-range temporal dependencies and global spatial correlations with two parallel Transformer skeletons and strengthen the intra-scale connections with downsampling and upsampling operations. Moreover, the complementary information from spatial and temporal features is fused and propagated in each other via Contextual Fusion Blocks (CFBs) to promote the prediction further. Extensive experimental results on two large-scale real-world datasets demonstrate the superior performance of our HSTTN over existing solutions.

In recent years, there has been increasing interest in developing foundation models for time series data that can generalize across diverse downstream tasks. While numerous forecasting-oriented foundation models have been introduced, there is a notable scarcity of models tailored for time series classification. To address this gap, we present Mantis, a new open-source foundation model for time series classification based on the Vision Transformer (ViT) architecture that has been pre-trained using a contrastive learning approach. Our experimental results show that Mantis outperforms existing foundation models both when the backbone is frozen and when fine-tuned, while achieving the lowest calibration error. In addition, we propose several adapters to handle the multivariate setting, reducing memory requirements and modeling channel interdependence.

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/.

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.

This paper revives Densely Connected Convolutional Networks (DenseNets) and reveals the underrated effectiveness over predominant ResNet-style architectures. We believe DenseNets' potential was overlooked due to untouched training methods and traditional design elements not fully revealing their capabilities. Our pilot study shows dense connections through concatenation are strong, demonstrating that DenseNets can be revitalized to compete with modern architectures. We methodically refine suboptimal components - architectural adjustments, block redesign, and improved training recipes towards widening DenseNets and boosting memory efficiency while keeping concatenation shortcuts. Our models, employing simple architectural elements, ultimately surpass Swin Transformer, ConvNeXt, and DeiT-III - key architectures in the residual learning lineage. Furthermore, our models exhibit near state-of-the-art performance on ImageNet-1K, competing with the very recent models and downstream tasks, ADE20k semantic segmentation, and COCO object detection/instance segmentation. Finally, we provide empirical analyses that uncover the merits of the concatenation over additive shortcuts, steering a renewed preference towards DenseNet-style designs. Our code is available at https://github.com/naver-ai/rdnet.

The performance of transformers for time-series forecasting has improved significantly. Recent architectures learn complex temporal patterns by segmenting a time-series into patches and using the patches as tokens. The patch size controls the ability of transformers to learn the temporal patterns at different frequencies: shorter patches are effective for learning localized, high-frequency patterns, whereas mining long-term seasonalities and trends requires longer patches. Inspired by this observation, we propose a novel framework, Multi-resolution Time-Series Transformer (MTST), which consists of a multi-branch architecture for simultaneous modeling of diverse temporal patterns at different resolutions. In contrast to many existing time-series transformers, we employ relative positional encoding, which is better suited for extracting periodic components at different scales. Extensive experiments on several real-world datasets demonstrate the effectiveness of MTST in comparison to state-of-the-art forecasting techniques.

We build upon time-series classification by leveraging the capabilities of Vision Language Models (VLMs). We find that VLMs produce competitive results after two or less epochs of fine-tuning. We develop a novel approach that incorporates graphical data representations as images in conjunction with numerical data. This approach is rooted in the hypothesis that graphical representations can provide additional contextual information that numerical data alone may not capture. Additionally, providing a graphical representation can circumvent issues such as limited context length faced by LLMs. To further advance this work, we implemented a scalable end-to-end pipeline for training on different scenarios, allowing us to isolate the most effective strategies for transferring learning capabilities from LLMs to Time Series Classification (TSC) tasks. Our approach works with univariate and multivariate time-series data. In addition, we conduct extensive and practical experiments to show how this approach works for time-series classification and generative labels.

Denoising diffusion probabilistic models (DDPMs) are becoming the leading paradigm for generative models. It has recently shown breakthroughs in audio synthesis, time series imputation and forecasting. In this paper, we propose Diffusion-TS, a novel diffusion-based framework that generates multivariate time series samples of high quality by using an encoder-decoder transformer with disentangled temporal representations, in which the decomposition technique guides Diffusion-TS to capture the semantic meaning of time series while transformers mine detailed sequential information from the noisy model input. Different from existing diffusion-based approaches, we train the model to directly reconstruct the sample instead of the noise in each diffusion step, combining a Fourier-based loss term. Diffusion-TS is expected to generate time series satisfying both interpretablity and realness. In addition, it is shown that the proposed Diffusion-TS can be easily extended to conditional generation tasks, such as forecasting and imputation, without any model changes. This also motivates us to further explore the performance of Diffusion-TS under irregular settings. Finally, through qualitative and quantitative experiments, results show that Diffusion-TS achieves the state-of-the-art results on various realistic analyses of time series.

We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.

Time series anomaly detection forms a very crucial area in several domains but poses substantial challenges. Due to time series data possessing seasonality, trends, noise, and evolving patterns (concept drift), it becomes very difficult to set a general notion of what constitutes normal behavior. Anomalies themselves could be varied, ranging from a single outlier to contextual or collective anomalies, and are normally very rare; hence, the dataset is largely imbalanced. Additional layers of complexities arise due to the problems of increased dimensionality of modern time series, real-time detection criteria, setting up appropriate detection thresholds, and arriving at results that are interpretable. To embrace these multifaceted challenges, very strong, flexible, and interpretable approaches are required. This paper presents THEMIS, a new framework for time series anomaly detection that exploits pretrained knowledge from foundation models. THEMIS extracts embeddings from the encoder of the Chronos time series foundation model and applies outlier detection techniques like Local Outlier Factor and Spectral Decomposition on the self-similarity matrix, to spot anomalies in the data. Our experiments show that this modular method achieves SOTA results on the MSL dataset and performs quite competitively on the SMAP and SWAT^* datasets. Notably, THEMIS exceeds models trained specifically for anomaly detection, presenting hyperparameter robustness and interpretability by default. This paper advocates for pretrained representations from foundation models for performing efficient and adaptable anomaly detection for time series data.

Time series forecasting is a long-standing and highly challenging research topic. Recently, driven by the rise of large language models (LLMs), research has increasingly shifted from purely time series methods toward harnessing textual modalities to enhance forecasting performance. However, the vast discrepancy between text and temporal data often leads current multimodal architectures to over-emphasise one modality while neglecting the other, resulting in information loss that harms forecasting performance. To address this modality imbalance, we introduce BALM-TSF (Balanced Multimodal Alignment for LLM-Based Time Series Forecasting), a lightweight time series forecasting framework that maintains balance between the two modalities. Specifically, raw time series are processed by the time series encoder, while descriptive statistics of raw time series are fed to an LLM with learnable prompt, producing compact textual embeddings. To ensure balanced cross-modal context alignment of time series and textual embeddings, a simple yet effective scaling strategy combined with a contrastive objective then maps these textual embeddings into the latent space of the time series embeddings. Finally, the aligned textual semantic embeddings and time series embeddings are together integrated for forecasting. Extensive experiments on standard benchmarks show that, with minimal trainable parameters, BALM-TSF achieves state-of-the-art performance in both long-term and few-shot forecasting, confirming its ability to harness complementary information from text and time series. Code is available at https://github.com/ShiqiaoZhou/BALM-TSF.

We introduce the Cisco Time Series Model, a univariate zero-shot forecaster. This time series foundation model is the result of a general architectural innovation to a time series model enabling it to accept multiresolution input, applied to a popular decoder-only time series model (TimesFM). The resulting multiresolution decoder-only model is trained on over 300B unique data points, with more than half coming from the observability domain. Quantitative and qualitative evaluations demonstrate that the resulting model achieves superior performance on observability datasets while retaining very similar performance on a standard general-purpose forecasting benchmark (GIFT-Eval), and suggest that the multiresolution structure enables the model to make more accurate predictions on long context input.

Time series analysis is crucial in diverse scenarios. Beyond forecasting, considerable real-world tasks are categorized into classification, imputation, and anomaly detection, underscoring different capabilities termed time series understanding in this paper. While GPT-style models have been positioned as foundation models for time series forecasting, the BERT-style architecture, which has made significant advances in natural language understanding, has not been fully unlocked for time series understanding, possibly attributed to the undesirable dropout of essential elements of BERT. In this paper, inspired by the shared multi-granularity structure between multivariate time series and multisentence documents, we design TimesBERT to learn generic representations of time series including temporal patterns and variate-centric characteristics. In addition to a natural adaptation of masked modeling, we propose a parallel task of functional token prediction to embody vital multi-granularity structures. Our model is pre-trained on 260 billion time points across diverse domains. Leveraging multi-granularity representations, TimesBERT achieves state-of-the-art performance across four typical downstream understanding tasks, outperforming task-specific models and language pre-trained backbones, positioning it as a versatile foundation model for time series understanding.

One of the primary objectives of satellite remote sensing is to capture the complex dynamics of the Earth environment, which encompasses tasks such as reconstructing continuous cloud-free time series images, detecting land cover changes, and forecasting future surface evolution. However, existing methods typically require specialized models tailored to different tasks, lacking unified modeling of spatiotemporal features across multiple time series tasks. In this paper, we propose a Unified Time Series Generative Model (UniTS), a general framework applicable to various time series tasks, including time series reconstruction, time series cloud removal, time series semantic change detection, and time series forecasting. Based on the flow matching generative paradigm, UniTS constructs a deterministic evolution path from noise to targets under the guidance of task-specific conditions, achieving unified modeling of spatiotemporal representations for multiple tasks. The UniTS architecture consists of a diffusion transformer with spatio-temporal blocks, where we design an Adaptive Condition Injector (ACor) to enhance the model's conditional perception of multimodal inputs, enabling high-quality controllable generation. Additionally, we design a Spatiotemporal-aware Modulator (STM) to improve the ability of spatio-temporal blocks to capture complex spatiotemporal dependencies. Furthermore, we construct two high-quality multimodal time series datasets, TS-S12 and TS-S12CR, filling the gap of benchmark datasets for time series cloud removal and forecasting tasks. Extensive experiments demonstrate that UniTS exhibits exceptional generative and cognitive capabilities in both low-level and high-level time series tasks. It significantly outperforms existing methods, particularly when facing challenges such as severe cloud contamination, modality absence, and forecasting phenological variations.

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.

We propose a novel approach for time-scale modification of audio signals. Unlike traditional methods that rely on the framing technique or the short-time Fourier transform to preserve the frequency during temporal stretching, our neural network model encodes the raw audio into a high-level latent representation, dubbed Neuralgram, where each vector represents 1024 audio sample points. Due to a sufficient compression ratio, we are able to apply arbitrary spatial interpolation of the Neuralgram to perform temporal stretching. Finally, a learned neural decoder synthesizes the time-scaled audio samples based on the stretched Neuralgram representation. Both the encoder and decoder are trained with latent regression losses and adversarial losses in order to obtain high-fidelity audio samples. Despite its simplicity, our method has comparable performance compared to the existing baselines and opens a new possibility in research into modern time-scale modification. Audio samples can be found at https://tsmnet-mmasia23.github.io

Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, including quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a ProbSparse self-attention mechanism, which achieves O(L log L) in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.

Video autoencoders compress videos into compact latent representations for efficient reconstruction, playing a vital role in enhancing the quality and efficiency of video generation. However, existing video autoencoders often entangle spatial and temporal information, limiting their ability to capture temporal consistency and leading to suboptimal performance. To address this, we propose Autoregressive Video Autoencoder (ARVAE), which compresses and reconstructs each frame conditioned on its predecessor in an autoregressive manner, allowing flexible processing of videos with arbitrary lengths. ARVAE introduces a temporal-spatial decoupled representation that combines downsampled flow field for temporal coherence with spatial relative compensation for newly emerged content, achieving high compression efficiency without information loss. Specifically, the encoder compresses the current and previous frames into the temporal motion and spatial supplement, while the decoder reconstructs the original frame from the latent representations given the preceding frame. A multi-stage training strategy is employed to progressively optimize the model. Extensive experiments demonstrate that ARVAE achieves superior reconstruction quality with extremely lightweight models and small-scale training data. Moreover, evaluations on video generation tasks highlight its strong potential for downstream applications.

Deep implicit functions have been found to be an effective tool for efficiently encoding all manner of natural signals. Their attractiveness stems from their ability to compactly represent signals with little to no off-line training data. Instead, they leverage the implicit bias of deep networks to decouple hidden redundancies within the signal. In this paper, we explore the hypothesis that additional compression can be achieved by leveraging the redundancies that exist between layers. We propose to use a novel run-time decoder-only hypernetwork - that uses no offline training data - to better model this cross-layer parameter redundancy. Previous applications of hyper-networks with deep implicit functions have applied feed-forward encoder/decoder frameworks that rely on large offline datasets that do not generalize beyond the signals they were trained on. We instead present a strategy for the initialization of run-time deep implicit functions for single-instance signals through a Decoder-Only randomly projected Hypernetwork (D'OH). By directly changing the dimension of a latent code to approximate a target implicit neural architecture, we provide a natural way to vary the memory footprint of neural representations without the costly need for neural architecture search on a space of alternative low-rate structures.

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.

Visualizing multiple time series presents fundamental tradeoffs between scalability and visual clarity. Time series capture the behavior of many large-scale real-world processes, from stock market trends to urban activities. Users often gain insights by visualizing them as line charts, juxtaposing or superposing multiple time series to compare them and identify trends and patterns. However, existing representations struggle with scalability: when covering long time spans, leading to visual clutter from too many small multiples or overlapping lines. We propose TiVy, a new algorithm that summarizes time series using sequential patterns. It transforms the series into a set of symbolic sequences based on subsequence visual similarity using Dynamic Time Warping (DTW), then constructs a disjoint grouping of similar subsequences based on the frequent sequential patterns. The grouping result, a visual summary of time series, provides uncluttered superposition with fewer small multiples. Unlike common clustering techniques, TiVy extracts similar subsequences (of varying lengths) aligned in time. We also present an interactive time series visualization that renders large-scale time series in real-time. Our experimental evaluation shows that our algorithm (1) extracts clear and accurate patterns when visualizing time series data, (2) achieves a significant speed-up (1000X) compared to a straightforward DTW clustering. We also demonstrate the efficiency of our approach to explore hidden structures in massive time series data in two usage scenarios.

Time series data is essential in various applications, including climate modeling, healthcare monitoring, and financial analytics. Understanding the contextual information associated with real-world time series data is often essential for accurate and reliable event predictions. In this paper, we introduce TimeCAP, a time-series processing framework that creatively employs Large Language Models (LLMs) as contextualizers of time series data, extending their typical usage as predictors. TimeCAP incorporates two independent LLM agents: one generates a textual summary capturing the context of the time series, while the other uses this enriched summary to make more informed predictions. In addition, TimeCAP employs a multi-modal encoder that synergizes with the LLM agents, enhancing predictive performance through mutual augmentation of inputs with in-context examples. Experimental results on real-world datasets demonstrate that TimeCAP outperforms state-of-the-art methods for time series event prediction, including those utilizing LLMs as predictors, achieving an average improvement of 28.75% in F1 score.

This paper introduces WeatherFormer, a transformer encoder-based model designed to learn robust weather features from minimal observations. It addresses the challenge of modeling complex weather dynamics from small datasets, a bottleneck for many prediction tasks in agriculture, epidemiology, and climate science. WeatherFormer was pretrained on a large pretraining dataset comprised of 39 years of satellite measurements across the Americas. With a novel pretraining task and fine-tuning, WeatherFormer achieves state-of-the-art performance in county-level soybean yield prediction and influenza forecasting. Technical innovations include a unique spatiotemporal encoding that captures geographical, annual, and seasonal variations, adapting the transformer architecture to continuous weather data, and a pretraining strategy to learn representations that are robust to missing weather features. This paper for the first time demonstrates the effectiveness of pretraining large transformer encoder models for weather-dependent applications across multiple domains.

We present a state-of-the-art end-to-end Automatic Speech Recognition (ASR) model. We learn to listen and write characters with a joint Connectionist Temporal Classification (CTC) and attention-based encoder-decoder network. The encoder is a deep Convolutional Neural Network (CNN) based on the VGG network. The CTC network sits on top of the encoder and is jointly trained with the attention-based decoder. During the beam search process, we combine the CTC predictions, the attention-based decoder predictions and a separately trained LSTM language model. We achieve a 5-10\% error reduction compared to prior systems on spontaneous Japanese and Chinese speech, and our end-to-end model beats out traditional hybrid ASR systems.

Predicting and reasoning about the future lie at the heart of many time-series questions. For example, goal-conditioned reinforcement learning can be viewed as learning representations to predict which states are likely to be visited in the future. While prior methods have used contrastive predictive coding to model time series data, learning representations that encode long-term dependencies usually requires large amounts of data. In this paper, we introduce a temporal difference version of contrastive predictive coding that stitches together pieces of different time series data to decrease the amount of data required to learn predictions of future events. We apply this representation learning method to derive an off-policy algorithm for goal-conditioned RL. Experiments demonstrate that, compared with prior RL methods, ours achieves 2 times median improvement in success rates and can better cope with stochastic environments. In tabular settings, we show that our method is about 20 times more sample efficient than the successor representation and 1500 times more sample efficient than the standard (Monte Carlo) version of contrastive predictive coding.

Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. There exist significant challenges in LTSF due to its complex temporal dependencies and high computational demands. Although Transformer-based models offer high forecasting accuracy, they are often too compute-intensive to be deployed on devices with hardware constraints. On the other hand, the linear models aim to reduce the computational overhead by employing either decomposition methods in the time domain or compact representations in the frequency domain. In this paper, we propose MixLinear, an ultra-lightweight multivariate time series forecasting model specifically designed for resource-constrained devices. MixLinear effectively captures both temporal and frequency domain features by modeling intra-segment and inter-segment variations in the time domain and extracting frequency variations from a low-dimensional latent space in the frequency domain. By reducing the parameter scale of a downsampled n-length input/output one-layer linear model from O(n^2) to O(n), MixLinear achieves efficient computation without sacrificing accuracy. Extensive evaluations with four benchmark datasets show that MixLinear attains forecasting performance comparable to, or surpassing, state-of-the-art models with significantly fewer parameters (0.1K), which makes it well-suited for deployment on devices with limited computational capacity.

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.

Dense retrieval (DR) has shown promising results in information retrieval. In essence, DR requires high-quality text representations to support effective search in the representation space. Recent studies have shown that pre-trained autoencoder-based language models with a weak decoder can provide high-quality text representations, boosting the effectiveness and few-shot ability of DR models. However, even a weak autoregressive decoder has the bypass effect on the encoder. More importantly, the discriminative ability of learned representations may be limited since each token is treated equally important in decoding the input texts. To address the above problems, in this paper, we propose a contrastive pre-training approach to learn a discriminative autoencoder with a lightweight multi-layer perception (MLP) decoder. The basic idea is to generate word distributions of input text in a non-autoregressive fashion and pull the word distributions of two masked versions of one text close while pushing away from others. We theoretically show that our contrastive strategy can suppress the common words and highlight the representative words in decoding, leading to discriminative representations. Empirical results show that our method can significantly outperform the state-of-the-art autoencoder-based language models and other pre-trained models for dense retrieval.

Sequence and channel mixers, the core mechanism in sequence models, have become the de facto standard in time series analysis (TSA). However, recent studies have questioned the necessity of complex sequence mixers, such as attention mechanisms, demonstrating that simpler architectures can achieve comparable or even superior performance. This suggests that the benefits attributed to complex sequencemixers might instead emerge from other architectural or optimization factors. Based on this observation, we pose a central question: Are common sequence mixers necessary for time-series analysis? Therefore, we propose JustDense, an empirical study that systematically replaces sequence mixers in various well-established TSA models with dense layers. Grounded in the MatrixMixer framework, JustDense treats any sequence mixer as a mixing matrix and replaces it with a dense layer. This substitution isolates the mixing operation, enabling a clear theoretical foundation for understanding its role. Therefore, we conducted extensive experiments on 29 benchmarks covering five representative TSA tasks using seven state-of-the-art TSA models to address our research question. The results show that replacing sequence mixers with dense layers yields comparable or even superior performance. In the cases where dedicated sequence mixers still offer benefits, JustDense challenges the assumption that "deeper and more complex architectures are inherently better" in TSA.

Time series classification is a fundamental task in healthcare and industry, yet the development of time series foundation models (TSFMs) remains limited by the scarcity of publicly available time series datasets. In this work, we propose Time Vision Transformer (TiViT), a framework that converts time series into images to leverage the representational power of frozen Vision Transformers (ViTs) pretrained on large-scale image datasets. First, we theoretically motivate our approach by analyzing the 2D patching of ViTs for time series, showing that it can increase the number of label-relevant tokens and reduce the sample complexity. Second, we empirically demonstrate that TiViT achieves state-of-the-art performance on standard time series classification benchmarks by utilizing the hidden representations of large OpenCLIP models. We explore the structure of TiViT representations and find that intermediate layers with high intrinsic dimension are the most effective for time series classification. Finally, we assess the alignment between TiViT and TSFM representation spaces and identify a strong complementarity, with further performance gains achieved by combining their features. Our findings reveal a new direction for reusing vision representations in a non-visual domain. Code is available at https://github.com/ExplainableML/TiViT.

Real-world multivariate time series can exhibit intricate multi-scale structures, including global trends, local periodicities, and non-stationary regimes, which makes long-horizon forecasting challenging. Although sparse Mixture-of-Experts (MoE) approaches improve scalability and specialization, they typically rely on homogeneous MLP experts that poorly capture the diverse temporal dynamics of time series data. We address these limitations with MoHETS, an encoder-only Transformer that integrates sparse Mixture-of-Heterogeneous-Experts (MoHE) layers. MoHE routes temporal patches to a small subset of expert networks, combining a shared depthwise-convolution expert for sequence-level continuity with routed Fourier-based experts for patch-level periodic structures. MoHETS further improves robustness to non-stationary dynamics by incorporating exogenous information via cross-attention over covariate patch embeddings. Finally, we replace parameter-heavy linear projection heads with a lightweight convolutional patch decoder, improving parameter efficiency, reducing training instability, and allowing a single model to generalize across arbitrary forecast horizons. We validate across seven multivariate benchmarks and multiple horizons, with MoHETS consistently achieving state-of-the-art performance, reducing the average MSE by 12% compared to strong recent baselines, demonstrating effective heterogeneous specialization for long-term forecasting.

We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.

Foundation models (FMs) have transformed natural language processing, but their success has not yet translated to time series forecasting. Existing time series foundation models (TSFMs), often based on transformer variants, struggle with generalization across varying context and target lengths, lack adaptability to different sampling rates, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that addresses these challenges through two key innovations: a state space model (SSM) based encoder and a functional basis decoder. This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons. In contrast to other state-of-the-art TSFMs, which require training data across all possible sampling rates to memorize patterns at each scale, FlowState inherently adapts its internal dynamics to the input scale, enabling smaller models, reduced data requirements, and improved efficiency. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being the smallest model, FlowState outperforms all other models and is state-of-the-art for the GIFT-ZS and the Chronos-ZS benchmarks. Ablation studies confirm the effectiveness of its components, and we demonstrate its unique ability to adapt online to varying input sampling rates.

We introduce a state-of-the-art real-time, high-fidelity, audio codec leveraging neural networks. It consists in a streaming encoder-decoder architecture with quantized latent space trained in an end-to-end fashion. We simplify and speed-up the training by using a single multiscale spectrogram adversary that efficiently reduces artifacts and produce high-quality samples. We introduce a novel loss balancer mechanism to stabilize training: the weight of a loss now defines the fraction of the overall gradient it should represent, thus decoupling the choice of this hyper-parameter from the typical scale of the loss. Finally, we study how lightweight Transformer models can be used to further compress the obtained representation by up to 40%, while staying faster than real time. We provide a detailed description of the key design choices of the proposed model including: training objective, architectural changes and a study of various perceptual loss functions. We present an extensive subjective evaluation (MUSHRA tests) together with an ablation study for a range of bandwidths and audio domains, including speech, noisy-reverberant speech, and music. Our approach is superior to the baselines methods across all evaluated settings, considering both 24 kHz monophonic and 48 kHz stereophonic audio. Code and models are available at github.com/facebookresearch/encodec.

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on heterogeneous datasets strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without considerable loss in accuracy.

In this paper, we propose an efficient and accurate streaming speech recognition model based on the FastConformer architecture. We adapted the FastConformer architecture for streaming applications through: (1) constraining both the look-ahead and past contexts in the encoder, and (2) introducing an activation caching mechanism to enable the non-autoregressive encoder to operate autoregressively during inference. The proposed model is thoughtfully designed in a way to eliminate the accuracy disparity between the train and inference time which is common for many streaming models. Furthermore, our proposed encoder works with various decoder configurations including Connectionist Temporal Classification (CTC) and RNN-Transducer (RNNT) decoders. Additionally, we introduced a hybrid CTC/RNNT architecture which utilizes a shared encoder with both a CTC and RNNT decoder to boost the accuracy and save computation. We evaluate the proposed model on LibriSpeech dataset and a multi-domain large scale dataset and demonstrate that it can achieve better accuracy with lower latency and inference time compared to a conventional buffered streaming model baseline. We also showed that training a model with multiple latencies can achieve better accuracy than single latency models while it enables us to support multiple latencies with a single model. Our experiments also showed the hybrid architecture would not only speedup the convergence of the CTC decoder but also improves the accuracy of streaming models compared to single decoder models.

Despite the eminent successes of deep neural networks, many architectures are often hard to transfer to irregularly-sampled and asynchronous time series that commonly occur in real-world datasets, especially in healthcare applications. This paper proposes a novel approach for classifying irregularly-sampled time series with unaligned measurements, focusing on high scalability and data efficiency. Our method SeFT (Set Functions for Time Series) is based on recent advances in differentiable set function learning, extremely parallelizable with a beneficial memory footprint, thus scaling well to large datasets of long time series and online monitoring scenarios. Furthermore, our approach permits quantifying per-observation contributions to the classification outcome. We extensively compare our method with existing algorithms on multiple healthcare time series datasets and demonstrate that it performs competitively whilst significantly reducing runtime.

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.

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.

Timeseries analytics is of great importance in many real-world applications. Recently, the Transformer model, popular in natural language processing, has been leveraged to learn high quality feature embeddings from timeseries, core to the performance of various timeseries analytics tasks. However, the quadratic time and space complexities limit Transformers' scalability, especially for long timeseries. To address these issues, we develop a timeseries analytics tool, RITA, which uses a novel attention mechanism, named group attention, to address this scalability issue. Group attention dynamically clusters the objects based on their similarity into a small number of groups and approximately computes the attention at the coarse group granularity. It thus significantly reduces the time and space complexity, yet provides a theoretical guarantee on the quality of the computed attention. The dynamic scheduler of RITA continuously adapts the number of groups and the batch size in the training process, ensuring group attention always uses the fewest groups needed to meet the approximation quality requirement. Extensive experiments on various timeseries datasets and analytics tasks demonstrate that RITA outperforms the state-of-the-art in accuracy and is significantly faster -- with speedups of up to 63X.

In recent years, the introduction of self-supervised contrastive learning (SSCL) has demonstrated remarkable improvements in representation learning across various domains, including natural language processing and computer vision. By leveraging the inherent benefits of self-supervision, SSCL enables the pre-training of representation models using vast amounts of unlabeled data. Despite these advances, there remains a significant gap in understanding the impact of different SSCL strategies on time series forecasting performance, as well as the specific benefits that SSCL can bring. This paper aims to address these gaps by conducting a comprehensive analysis of the effectiveness of various training variables, including different SSCL algorithms, learning strategies, model architectures, and their interplay. Additionally, to gain deeper insights into the improvements brought about by SSCL in the context of time-series forecasting, a qualitative analysis of the empirical receptive field is performed. Through our experiments, we demonstrate that the end-to-end training of a Transformer model using the Mean Squared Error (MSE) loss and SSCL emerges as the most effective approach in time series forecasting. Notably, the incorporation of the contrastive objective enables the model to prioritize more pertinent information for forecasting, such as scale and periodic relationships. These findings contribute to a better understanding of the benefits of SSCL in time series forecasting and provide valuable insights for future research in this area. Our codes are available at https://github.com/chiyuzhang94/contrastive_learning_time-series_e2e.

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local temporal dynamics and the decoding heterogeneity of forecasting. Such designs lose details in information-dense regions, introduce redundancy in stable segments, and fail to capture the distinct complexities of short-term and long-term horizons. We propose TimeMosaic, a forecasting framework that aims to address temporal heterogeneity. TimeMosaic employs adaptive patch embedding to dynamically adjust granularity according to local information density, balancing motif reuse with structural clarity while preserving temporal continuity. In addition, it introduces segment-wise decoding that treats each prediction horizon as a related subtask and adapts to horizon-specific difficulty and information requirements, rather than applying a single uniform decoder. Extensive evaluations on benchmark datasets demonstrate that TimeMosaic delivers consistent improvements over existing methods, and our model trained on the large-scale corpus with 321 billion observations achieves performance competitive with state-of-the-art TSFMs.

Spatiotemporal forecasting techniques are significant for various domains such as transportation, energy, and weather. Accurate prediction of spatiotemporal series remains challenging due to the complex spatiotemporal heterogeneity. In particular, current end-to-end models are limited by input length and thus often fall into spatiotemporal mirage, i.e., similar input time series followed by dissimilar future values and vice versa. To address these problems, we propose a novel self-supervised pre-training framework Spatial-Temporal-Decoupled Masked Pre-training (STD-MAE) that employs two decoupled masked autoencoders to reconstruct spatiotemporal series along the spatial and temporal dimensions. Rich-context representations learned through such reconstruction could be seamlessly integrated by downstream predictors with arbitrary architectures to augment their performances. A series of quantitative and qualitative evaluations on six widely used benchmarks (PEMS03, PEMS04, PEMS07, PEMS08, METR-LA, and PEMS-BAY) are conducted to validate the state-of-the-art performance of STD-MAE. Codes are available at https://github.com/Jimmy-7664/STD-MAE.

Missing data in time series is a pervasive problem that puts obstacles in the way of advanced analysis. A popular solution is imputation, where the fundamental challenge is to determine what values should be filled in. This paper proposes SAITS, a novel method based on the self-attention mechanism for missing value imputation in multivariate time series. Trained by a joint-optimization approach, SAITS learns missing values from a weighted combination of two diagonally-masked self-attention (DMSA) blocks. DMSA explicitly captures both the temporal dependencies and feature correlations between time steps, which improves imputation accuracy and training speed. Meanwhile, the weighted-combination design enables SAITS to dynamically assign weights to the learned representations from two DMSA blocks according to the attention map and the missingness information. Extensive experiments quantitatively and qualitatively demonstrate that SAITS outperforms the state-of-the-art methods on the time-series imputation task efficiently and reveal SAITS' potential to improve the learning performance of pattern recognition models on incomplete time-series data from the real world. The code is open source on GitHub at https://github.com/WenjieDu/SAITS.

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.

We present an unsupervised representation learning approach that compactly encodes the motion dependencies in videos. Given a pair of images from a video clip, our framework learns to predict the long-term 3D motions. To reduce the complexity of the learning framework, we propose to describe the motion as a sequence of atomic 3D flows computed with RGB-D modality. We use a Recurrent Neural Network based Encoder-Decoder framework to predict these sequences of flows. We argue that in order for the decoder to reconstruct these sequences, the encoder must learn a robust video representation that captures long-term motion dependencies and spatial-temporal relations. We demonstrate the effectiveness of our learned temporal representations on activity classification across multiple modalities and datasets such as NTU RGB+D and MSR Daily Activity 3D. Our framework is generic to any input modality, i.e., RGB, Depth, and RGB-D videos.

Time series forecasting is a fundamental problem with applications in climate, energy, healthcare, and finance. Many existing approaches require domain-specific feature engineering and substantial labeled data for each task. We introduce PatchFormer, a patch-based time series foundation model that uses hierarchical masked reconstruction for self-supervised pretraining and lightweight adapters for efficient transfer. PatchFormer segments time series into patches and learns multiscale temporal representations with learnable aggregation across temporal scales. Pretraining uses masked patch reconstruction with dynamic masking and objectives that encourage both local accuracy and global consistency, followed by cross-domain knowledge distillation. Experiments on 24 benchmark datasets spanning weather, energy, traffic, finance, and healthcare demonstrate state-of-the-art zero-shot multi-horizon forecasting, reducing mean squared error by 27.3 percent relative to strong baselines while requiring 94 percent less task-specific training data. The model exhibits near log-linear scaling with more pretraining data up to 100 billion points and processes length-512 sequences 3.8x faster than full-sequence transformers.

Learning time series foundation models has been shown to be a promising approach for zero-shot time series forecasting across diverse time series domains. Insofar as scaling has been a critical driver of performance of foundation models in other modalities such as language and vision, much recent work on time series foundation modeling has focused on scaling. This has resulted in time series foundation models with hundreds of millions of parameters that are, while performant, inefficient and expensive to use in practice. This paper describes a simple recipe for learning efficient foundation models for zero-shot time series forecasting that are orders of magnitude smaller. We show that large-scale transformers are not necessary: small hybrid models that interleave long convolution and linear RNN layers (in particular DeltaNet layers) can match the performance of larger transformer-based models while being more than a hundred times smaller. We also describe several data augmentation and inference strategies that further improve performance. This recipe results in Reverso, a family of efficient time series foundation models for zero-shot forecasting that significantly push the performance-efficiency Pareto frontier.

Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets will be released.

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.

One of the key components within diffusion models is the UNet for noise prediction. While several works have explored basic properties of the UNet decoder, its encoder largely remains unexplored. In this work, we conduct the first comprehensive study of the UNet encoder. We empirically analyze the encoder features and provide insights to important questions regarding their changes at the inference process. In particular, we find that encoder features change gently, whereas the decoder features exhibit substantial variations across different time-steps. This finding inspired us to omit the encoder at certain adjacent time-steps and reuse cyclically the encoder features in the previous time-steps for the decoder. Further based on this observation, we introduce a simple yet effective encoder propagation scheme to accelerate the diffusion sampling for a diverse set of tasks. By benefiting from our propagation scheme, we are able to perform in parallel the decoder at certain adjacent time-steps. Additionally, we introduce a prior noise injection method to improve the texture details in the generated image. Besides the standard text-to-image task, we also validate our approach on other tasks: text-to-video, personalized generation and reference-guided generation. Without utilizing any knowledge distillation technique, our approach accelerates both the Stable Diffusion (SD) and the DeepFloyd-IF models sampling by 41% and 24% respectively, while maintaining high-quality generation performance. Our code is available in https://github.com/hutaiHang/Faster-Diffusion{FasterDiffusion}.

Recent advances in video-based multimodal large language models (Video-LLMs) have significantly improved video understanding by processing videos as sequences of image frames. However, many existing methods treat frames independently in the vision backbone, lacking explicit temporal modeling, which limits their ability to capture dynamic patterns and efficiently handle long videos. To address these limitations, we introduce STORM (Spatiotemporal TOken Reduction for Multimodal LLMs), a novel architecture incorporating a dedicated temporal encoder between the image encoder and the LLM. Our temporal encoder leverages the Mamba State Space Model to integrate temporal information into image tokens, generating enriched representations that preserve inter-frame dynamics across the entire video sequence. This enriched encoding not only enhances video reasoning capabilities but also enables effective token reduction strategies, including test-time sampling and training-based temporal and spatial pooling, substantially reducing computational demands on the LLM without sacrificing key temporal information. By integrating these techniques, our approach simultaneously reduces training and inference latency while improving performance, enabling efficient and robust video understanding over extended temporal contexts. Extensive evaluations show that STORM achieves state-of-the-art results across various long video understanding benchmarks (more than 5\% improvement on MLVU and LongVideoBench) while reducing the computation costs by up to 8times and the decoding latency by 2.4-2.9times for the fixed numbers of input frames. Project page is available at https://research.nvidia.com/labs/lpr/storm

Time series classification (TSC) is a cornerstone of modern web applications, powering tasks such as financial data analysis, network traffic monitoring, and user behavior analysis. In recent years, deep neural networks (DNNs) have greatly enhanced the performance of TSC models in these critical domains. However, DNNs are vulnerable to backdoor attacks, where attackers can covertly implant triggers into models to induce malicious outcomes. Existing backdoor attacks targeting DNN-based TSC models remain elementary. In particular, early methods borrow trigger designs from computer vision, which are ineffective for time series data. More recent approaches utilize generative models for trigger generation, but at the cost of significant computational complexity. In this work, we analyze the limitations of existing attacks and introduce an enhanced method, FreqBack. Drawing inspiration from the fact that DNN models inherently capture frequency domain features in time series data, we identify that improper perturbations in the frequency domain are the root cause of ineffective attacks. To address this, we propose to generate triggers both effectively and efficiently, guided by frequency analysis. FreqBack exhibits substantial performance across five models and eight datasets, achieving an impressive attack success rate of over 90%, while maintaining less than a 3% drop in model accuracy on clean data.