Daily Papers

The goal of precipitation nowcasting is to predict the future rainfall intensity in a local region over a relatively short period of time. Very few previous studies have examined this crucial and challenging weather forecasting problem from the machine learning perspective. In this paper, we formulate precipitation nowcasting as a spatiotemporal sequence forecasting problem in which both the input and the prediction target are spatiotemporal sequences. By extending the fully connected LSTM (FC-LSTM) to have convolutional structures in both the input-to-state and state-to-state transitions, we propose the convolutional LSTM (ConvLSTM) and use it to build an end-to-end trainable model for the precipitation nowcasting problem. Experiments show that our ConvLSTM network captures spatiotemporal correlations better and consistently outperforms FC-LSTM and the state-of-the-art operational ROVER algorithm for precipitation nowcasting.

Weather nowcasting is an essential task that involves predicting future radar echo sequences based on current observations, offering significant benefits for disaster management, transportation, and urban planning. Current prediction methods are limited by training and storage efficiency, mainly focusing on 2D spatial predictions at specific altitudes. Meanwhile, 3D volumetric predictions at each timestamp remain largely unexplored. To address such a challenge, we introduce a comprehensive framework for 3D radar sequence prediction in weather nowcasting, using the newly proposed SpatioTemporal Coherent Gaussian Splatting (STC-GS) for dynamic radar representation and GauMamba for efficient and accurate forecasting. Specifically, rather than relying on a 4D Gaussian for dynamic scene reconstruction, STC-GS optimizes 3D scenes at each frame by employing a group of Gaussians while effectively capturing their movements across consecutive frames. It ensures consistent tracking of each Gaussian over time, making it particularly effective for prediction tasks. With the temporally correlated Gaussian groups established, we utilize them to train GauMamba, which integrates a memory mechanism into the Mamba framework. This allows the model to learn the temporal evolution of Gaussian groups while efficiently handling a large volume of Gaussian tokens. As a result, it achieves both efficiency and accuracy in forecasting a wide range of dynamic meteorological radar signals. The experimental results demonstrate that our STC-GS can efficiently represent 3D radar sequences with over 16times higher spatial resolution compared with the existing 3D representation methods, while GauMamba outperforms state-of-the-art methods in forecasting a broad spectrum of high-dynamic weather conditions.

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.

Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often exhibiting limited cross-domain transferability. We analyze this bottleneck through spatial and temporal entropy measures, which are used as diagnostic indicators of spatiotemporal complexity mismatch rather than as guarantees that entropy alignment alone yields better forecasting. Empirically, larger mismatch is often accompanied by higher prediction uncertainty, especially under a fixed model-capacity budget. Guided by this diagnostic, we propose a scalable, adaptive framework that harmonizes spatial and temporal feature representations. Spatial dimensionality is compressed via low-rank matrix embedding to preserve essential structure, while an extended temporal horizon captures long-range dependencies and mitigates cumulative errors arising from temporal heterogeneity. Extensive experiments on urban traffic, meteorological, and epidemic datasets demonstrate substantial accuracy gains and broad applicability across the evaluated domains, suggesting that the framework is promising for a wide range of spatiotemporal tasks beyond the current study. The code is available on GitHub at https://github.com/ST-Balance/ST-Balance.

Spatio-temporal predictive learning is a learning paradigm that enables models to learn spatial and temporal patterns by predicting future frames from given past frames in an unsupervised manner. Despite remarkable progress in recent years, a lack of systematic understanding persists due to the diverse settings, complex implementation, and difficult reproducibility. Without standardization, comparisons can be unfair and insights inconclusive. To address this dilemma, we propose OpenSTL, a comprehensive benchmark for spatio-temporal predictive learning that categorizes prevalent approaches into recurrent-based and recurrent-free models. OpenSTL provides a modular and extensible framework implementing various state-of-the-art methods. We conduct standard evaluations on datasets across various domains, including synthetic moving object trajectory, human motion, driving scenes, traffic flow and weather forecasting. Based on our observations, we provide a detailed analysis of how model architecture and dataset properties affect spatio-temporal predictive learning performance. Surprisingly, we find that recurrent-free models achieve a good balance between efficiency and performance than recurrent models. Thus, we further extend the common MetaFormers to boost recurrent-free spatial-temporal predictive learning. We open-source the code and models at https://github.com/chengtan9907/OpenSTL.

Effectively modeling long spatiotemporal sequences is challenging due to the need to model complex spatial correlations and long-range temporal dependencies simultaneously. ConvLSTMs attempt to address this by updating tensor-valued states with recurrent neural networks, but their sequential computation makes them slow to train. In contrast, Transformers can process an entire spatiotemporal sequence, compressed into tokens, in parallel. However, the cost of attention scales quadratically in length, limiting their scalability to longer sequences. Here, we address the challenges of prior methods and introduce convolutional state space models (ConvSSM) that combine the tensor modeling ideas of ConvLSTM with the long sequence modeling approaches of state space methods such as S4 and S5. First, we demonstrate how parallel scans can be applied to convolutional recurrences to achieve subquadratic parallelization and fast autoregressive generation. We then establish an equivalence between the dynamics of ConvSSMs and SSMs, which motivates parameterization and initialization strategies for modeling long-range dependencies. The result is ConvS5, an efficient ConvSSM variant for long-range spatiotemporal modeling. ConvS5 significantly outperforms Transformers and ConvLSTM on a long horizon Moving-MNIST experiment while training 3X faster than ConvLSTM and generating samples 400X faster than Transformers. In addition, ConvS5 matches or exceeds the performance of state-of-the-art methods on challenging DMLab, Minecraft and Habitat prediction benchmarks and enables new directions for modeling long spatiotemporal sequences.

Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish the forecasting. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods.

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current inputs and historical patterns. These deviations contain critical signals that can significantly affect model performance. To fill this gap, we propose ST-SSDL, a Spatio-Temporal time series forecasting framework that incorporates a Self-Supervised Deviation Learning scheme to capture and utilize such deviations. ST-SSDL anchors each input to its historical average and discretizes the latent space using learnable prototypes that represent typical spatio-temporal patterns. Two auxiliary objectives are proposed to refine this structure: a contrastive loss that enhances inter-prototype discriminability and a deviation loss that regularizes the distance consistency between input representations and corresponding prototypes to quantify deviation. Optimized jointly with the forecasting objective, these components guide the model to organize its hidden space and improve generalization across diverse input conditions. Experiments on six benchmark datasets show that ST-SSDL consistently outperforms state-of-the-art baselines across multiple metrics. Visualizations further demonstrate its ability to adaptively respond to varying levels of deviation in complex spatio-temporal scenarios. Our code and datasets are available at https://github.com/Jimmy-7664/ST-SSDL.

Accuracy and timeliness are indeed often conflicting goals in prediction tasks. Premature predictions may yield a higher rate of false alarms, whereas delaying predictions to gather more information can render them too late to be useful. In applications such as wildfires, crimes, and traffic jams, timely forecasting are vital for safeguarding human life and property. Consequently, finding a balance between accuracy and timeliness is crucial. In this paper, we propose an early spatio-temporal forecasting model based on Multi-Objective reinforcement learning that can either implement an optimal policy given a preference or infer the preference based on a small number of samples. The model addresses two primary challenges: 1) enhancing the accuracy of early forecasting and 2) providing the optimal policy for determining the most suitable prediction time for each area. Our method demonstrates superior performance on three large-scale real-world datasets, surpassing existing methods in early spatio-temporal forecasting tasks.

Spatiotemporal predictive learning (STPL) aims to forecast future frames from past observations and is essential across a wide range of applications. Compared with recurrent or hybrid architectures, pure convolutional models offer superior efficiency and full parallelism, yet their fixed receptive fields limit their ability to adaptively capture spatially varying motion patterns. Inspired by biological center-surround organization and frequency-selective signal processing, we propose PFGNet, a fully convolutional framework that dynamically modulates receptive fields through pixel-wise frequency-guided gating. The core Peripheral Frequency Gating (PFG) block extracts localized spectral cues and adaptively fuses multi-scale large-kernel peripheral responses with learnable center suppression, effectively forming spatially adaptive band-pass filters. To maintain efficiency, all large kernels are decomposed into separable 1D convolutions (1 times k followed by k times 1), reducing per-channel computational cost from O(k^2) to O(2k). PFGNet enables structure-aware spatiotemporal modeling without recurrence or attention. Experiments on Moving MNIST, TaxiBJ, Human3.6M, and KTH show that PFGNet delivers SOTA or near-SOTA forecasting performance with substantially fewer parameters and FLOPs. Our code is available at https://github.com/fhjdqaq/PFGNet.

Machine learning architectures, including transformers and recurrent neural networks (RNNs) have revolutionized forecasting in applications ranging from text processing to extreme weather. Notably, advanced network architectures, tuned for applications such as natural language processing, are transferable to other tasks such as spatiotemporal forecasting tasks. However, there is a scarcity of ablation studies to illustrate the key components that enable this forecasting accuracy. The absence of such studies, although explainable due to the associated computational cost, intensifies the belief that these models ought to be considered as black boxes. In this work, we decompose the key architectural components of the most powerful neural architectures, namely gating and recurrence in RNNs, and attention mechanisms in transformers. Then, we synthesize and build novel hybrid architectures from the standard blocks, performing ablation studies to identify which mechanisms are effective for each task. The importance of considering these components as hyper-parameters that can augment the standard architectures is exhibited on various forecasting datasets, from the spatiotemporal chaotic dynamics of the multiscale Lorenz 96 system, the Kuramoto-Sivashinsky equation, as well as standard real world time-series benchmarks. A key finding is that neural gating and attention improves the performance of all standard RNNs in most tasks, while the addition of a notion of recurrence in transformers is detrimental. Furthermore, our study reveals that a novel, sparsely used, architecture which integrates Recurrent Highway Networks with neural gating and attention mechanisms, emerges as the best performing architecture in high-dimensional spatiotemporal forecasting of dynamical systems.

Accurate predictions using sequential spatiotemporal data are crucial for various applications. Utilizing real-world data, we aim to learn the intent of a smart device user within confined areas of a vehicle's surroundings. However, in real-world scenarios, environmental factors and sensor limitations result in non-stationary and irregularly sampled data, posing significant challenges. To address these issues, we developed a Transformer-based approach, STaRFormer, which serves as a universal framework for sequential modeling. STaRFormer employs a novel, dynamic attention-based regional masking scheme combined with semi-supervised contrastive learning to enhance task-specific latent representations. Comprehensive experiments on 15 datasets varying in types (including non-stationary and irregularly sampled), domains, sequence lengths, training samples, and applications, demonstrate the efficacy and practicality of STaRFormer. We achieve notable improvements over state-of-the-art approaches. Code and data will be made available.

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.

Recent advancements in time series forecasting have explored augmenting models with text or vision modalities to improve accuracy. While text provides contextual understanding, it often lacks fine-grained temporal details. Conversely, vision captures intricate temporal patterns but lacks semantic context, limiting the complementary potential of these modalities. To address this, we propose \method, a novel multimodal framework that leverages pre-trained Vision-Language Models (VLMs) to bridge temporal, visual, and textual modalities for enhanced forecasting. Our framework comprises three key components: (1) a Retrieval-Augmented Learner, which extracts enriched temporal features through memory bank interactions; (2) a Vision-Augmented Learner, which encodes time series as informative images; and (3) a Text-Augmented Learner, which generates contextual textual descriptions. These components collaborate with frozen pre-trained VLMs to produce multimodal embeddings, which are then fused with temporal features for final prediction. Extensive experiments demonstrate that Time-VLM achieves superior performance, particularly in few-shot and zero-shot scenarios, thereby establishing a new direction for multimodal time series forecasting. Code is available at https://github.com/CityMind-Lab/ICML25-TimeVLM.

Spatio-temporal prediction is a pivotal task with broad applications in traffic management, climate monitoring, energy scheduling, etc. However, existing methodologies often struggle to balance model expressiveness and computational efficiency, especially when scaling to large real-world datasets. To tackle these challenges, we propose STH-SepNet (Spatio-Temporal Hypergraph Separation Networks), a novel framework that decouples temporal and spatial modeling to enhance both efficiency and precision. Therein, the temporal dimension is modeled using lightweight large language models, which effectively capture low-rank temporal dynamics. Concurrently, the spatial dimension is addressed through an adaptive hypergraph neural network, which dynamically constructs hyperedges to model intricate, higher-order interactions. A carefully designed gating mechanism is integrated to seamlessly fuse temporal and spatial representations. By leveraging the fundamental principles of low-rank temporal dynamics and spatial interactions, STH-SepNet offers a pragmatic and scalable solution for spatio-temporal prediction in real-world applications. Extensive experiments on large-scale real-world datasets across multiple benchmarks demonstrate the effectiveness of STH-SepNet in boosting predictive performance while maintaining computational efficiency. This work may provide a promising lightweight framework for spatio-temporal prediction, aiming to reduce computational demands and while enhancing predictive performance. Our code is avaliable at https://github.com/SEU-WENJIA/ST-SepNet-Lightweight-LLMs-Meet-Adaptive-Hypergraphs.

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.

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.

Spatiotemporal predictive learning methods generally fall into two categories: recurrent-based approaches, which face challenges in parallelization and performance, and recurrent-free methods, which employ convolutional neural networks (CNNs) as encoder-decoder architectures. These methods benefit from strong inductive biases but often at the expense of scalability and generalization. This paper proposes PredFormer, a pure transformer-based framework for spatiotemporal predictive learning. Motivated by the Vision Transformers (ViT) design, PredFormer leverages carefully designed Gated Transformer blocks, following a comprehensive analysis of 3D attention mechanisms, including full-, factorized-, and interleaved-spatial-temporal attention. With its recurrent-free, transformer-based design, PredFormer is both simple and efficient, significantly outperforming previous methods by large margins. Extensive experiments on synthetic and real-world datasets demonstrate that PredFormer achieves state-of-the-art performance. On Moving MNIST, PredFormer achieves a 51.3% reduction in MSE relative to SimVP. For TaxiBJ, the model decreases MSE by 33.1% and boosts FPS from 533 to 2364. Additionally, on WeatherBench, it reduces MSE by 11.1% while enhancing FPS from 196 to 404. These performance gains in both accuracy and efficiency demonstrate PredFormer's potential for real-world applications. The source code will be released at https://github.com/yyyujintang/PredFormer .

Forecasting multiple future events within a given time horizon is essential for applications in finance, retail, social networks, and healthcare. Marked Temporal Point Processes (MTPP) provide a principled framework to model both the timing and labels of events. However, most existing research focuses on predicting only the next event, leaving long-horizon forecasting largely underexplored. To address this gap, we introduce HoTPP, the first benchmark specifically designed to rigorously evaluate long-horizon predictions. We identify shortcomings in widely used evaluation metrics, propose a theoretically grounded T-mAP metric, present strong statistical baselines, and offer efficient implementations of popular models. Our empirical results demonstrate that modern MTPP approaches often underperform simple statistical baselines. Furthermore, we analyze the diversity of predicted sequences and find that most methods exhibit mode collapse. Finally, we analyze the impact of autoregression and intensity-based losses on prediction quality, and outline promising directions for future research. The HoTPP source code, hyperparameters, and full evaluation results are available at GitHub.

Spatio-Temporal Graph (STG) forecasting is a fundamental task in many real-world applications. Spatio-Temporal Graph Neural Networks have emerged as the most popular method for STG forecasting, but they often struggle with temporal out-of-distribution (OoD) issues and dynamic spatial causation. In this paper, we propose a novel framework called CaST to tackle these two challenges via causal treatments. Concretely, leveraging a causal lens, we first build a structural causal model to decipher the data generation process of STGs. To handle the temporal OoD issue, we employ the back-door adjustment by a novel disentanglement block to separate invariant parts and temporal environments from input data. Moreover, we utilize the front-door adjustment and adopt the Hodge-Laplacian operator for edge-level convolution to model the ripple effect of causation. Experiments results on three real-world datasets demonstrate the effectiveness and practicality of CaST, which consistently outperforms existing methods with good interpretability.

Recent years have witnessed remarkable advances in spatiotemporal predictive learning, with methods incorporating auxiliary inputs, complex neural architectures, and sophisticated training strategies. While SimVP has introduced a simpler, CNN-based baseline for this task, it still relies on heavy Unet-like architectures for spatial and temporal modeling, which still suffers from high complexity and computational overhead. In this paper, we propose SimVPv2, a streamlined model that eliminates the need for Unet architectures and demonstrates that plain stacks of convolutional layers, enhanced with an efficient Gated Spatiotemporal Attention mechanism, can deliver state-of-the-art performance. SimVPv2 not only simplifies the model architecture but also improves both performance and computational efficiency. On the standard Moving MNIST benchmark, SimVPv2 achieves superior performance compared to SimVP, with fewer FLOPs, about half the training time, and 60% faster inference efficiency. Extensive experiments across eight diverse datasets, including real-world tasks such as traffic forecasting and climate prediction, further demonstrate that SimVPv2 offers a powerful yet straightforward solution, achieving robust generalization across various spatiotemporal learning scenarios. We believe the proposed SimVPv2 can serve as a solid baseline to benefit the spatiotemporal predictive learning community.

Integrating CNNs and RNNs to capture spatiotemporal dependencies is a prevalent strategy for spatiotemporal prediction tasks. However, the property of CNNs to learn local spatial information decreases their efficiency in capturing spatiotemporal dependencies, thereby limiting their prediction accuracy. In this paper, we propose a new recurrent cell, SwinLSTM, which integrates Swin Transformer blocks and the simplified LSTM, an extension that replaces the convolutional structure in ConvLSTM with the self-attention mechanism. Furthermore, we construct a network with SwinLSTM cell as the core for spatiotemporal prediction. Without using unique tricks, SwinLSTM outperforms state-of-the-art methods on Moving MNIST, Human3.6m, TaxiBJ, and KTH datasets. In particular, it exhibits a significant improvement in prediction accuracy compared to ConvLSTM. Our competitive experimental results demonstrate that learning global spatial dependencies is more advantageous for models to capture spatiotemporal dependencies. We hope that SwinLSTM can serve as a solid baseline to promote the advancement of spatiotemporal prediction accuracy. The codes are publicly available at https://github.com/SongTang-x/SwinLSTM.

Autoregressive models for video generation typically operate frame-by-frame, extending next-token prediction from language to video's temporal dimension. We question that unlike word as token is universally agreed in language if frame is a appropriate prediction unit? To address this, we present VideoAR, a unified framework that supports a spectrum of prediction units including full frames, key-detail frames, multiscale refinements, and spatiotemporal cubes. Among these designs, we find model video generation using spatiotemporal cubes as prediction units, which allows autoregressive models to operate across both spatial and temporal dimensions simultaneously. This approach eliminates the assumption that frames are the natural atomic units for video autoregression. We evaluate VideoAR across diverse prediction strategies, finding that cube-based prediction consistently delivers superior quality, speed, and temporal coherence. By removing the frame-by-frame constraint, our video generator surpasses state-of-the-art baselines on VBench while achieving faster inference and enabling seamless scaling to minute-long sequences. We hope this work will motivate rethinking sequence decomposition in video and other spatiotemporal domains.

Although the rise of large language models (LLMs) has introduced new opportunities for time series forecasting, existing LLM-based solutions require excessive training and exhibit limited transferability. In view of these challenges, we propose TimeRAG, a framework that incorporates Retrieval-Augmented Generation (RAG) into time series forecasting LLMs, which constructs a time series knowledge base from historical sequences, retrieves reference sequences from the knowledge base that exhibit similar patterns to the query sequence measured by Dynamic Time Warping (DTW), and combines these reference sequences and the prediction query as a textual prompt to the time series forecasting LLM. Experiments on datasets from various domains show that the integration of RAG improved the prediction accuracy of the original model by 2.97% on average.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5times training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

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.

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.

Spatial-temporal forecasting and imputation are important for real-world intelligent systems. Most existing methods are tailored for individual forecasting or imputation tasks but are not designed for both. Additionally, they are less effective for zero-shot and few-shot learning. While pre-trained language model (PLM) have exhibited strong pattern recognition and reasoning abilities across various tasks, including few-shot and zero-shot learning, their applications in spatial-temporal data understanding has been constrained by insufficient modeling of complex correlations such as the temporal correlations, spatial connectivity, non-pairwise and high-order spatial-temporal correlations within data. In this paper, we propose STD-PLM for understanding both spatial and temporal properties of Spatial-Temporal Data with PLM, which is capable of implementing both spatial-temporal forecasting and imputation tasks. STD-PLM understands spatial-temporal correlations via explicitly designed spatial and temporal tokenizers. Topology-aware node embeddings are designed for PLM to comprehend and exploit the topology structure of data in inductive manner. Furthermore, to mitigate the efficiency issues introduced by the PLM, we design a sandglass attention module (SGA) combined with a specific constrained loss function, which significantly improves the model's efficiency while ensuring performance. Extensive experiments demonstrate that STD-PLM exhibits competitive performance and generalization capabilities across the forecasting and imputation tasks on various datasets. Moreover, STD-PLM achieves promising results on both few-shot and zero-shot tasks.The code is made available at https://anonymous.4open.science/r/STD-PLM-F3BA{https://anonymous.4open.science/r/STD-PLM-F3BA}

Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.

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.

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.

Time series forecasting traditionally relies on unimodal numerical inputs, which often struggle to capture high-level semantic patterns due to their dense and unstructured nature. While recent approaches have explored representing time series as text using large language models (LLMs), these methods remain limited by the discrete nature of token sequences and lack the perceptual intuition humans typically apply, such as interpreting visual patterns. In this paper, we propose a multimodal contrastive learning framework that transforms raw time series into structured visual and textual perspectives. Rather than using natural language or real-world images, we construct both modalities directly from numerical sequences. We then align these views in a shared semantic space via contrastive learning, enabling the model to capture richer and more complementary representations. Furthermore, we introduce a variate selection module that leverages the aligned representations to identify the most informative variables for multivariate forecasting. Extensive experiments on fifteen short-term and six long-term forecasting benchmarks demonstrate that our approach consistently outperforms strong unimodal and cross-modal baselines, highlighting the effectiveness of multimodal alignment in enhancing time series forecasting. Code is available at: https://github.com/Ironieser/TimesCLIP.

The predictive learning of spatiotemporal sequences aims to generate future images by learning from the historical context, where the visual dynamics are believed to have modular structures that can be learned with compositional subsystems. This paper models these structures by presenting PredRNN, a new recurrent network, in which a pair of memory cells are explicitly decoupled, operate in nearly independent transition manners, and finally form unified representations of the complex environment. Concretely, besides the original memory cell of LSTM, this network is featured by a zigzag memory flow that propagates in both bottom-up and top-down directions across all layers, enabling the learned visual dynamics at different levels of RNNs to communicate. It also leverages a memory decoupling loss to keep the memory cells from learning redundant features. We further propose a new curriculum learning strategy to force PredRNN to learn long-term dynamics from context frames, which can be generalized to most sequence-to-sequence models. We provide detailed ablation studies to verify the effectiveness of each component. Our approach is shown to obtain highly competitive results on five datasets for both action-free and action-conditioned predictive learning scenarios.

Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.

Forecasting future events based on evidence of current conditions is an innate skill of human beings, and key for predicting the outcome of any decision making. In artificial vision for example, we would like to predict the next human action before it happens, without observing the future video frames associated to it. Computer vision models for action anticipation are expected to collect the subtle evidence in the preamble of the target actions. In prior studies recurrence modeling often leads to better performance, the strong temporal inference is assumed to be a key element for reasonable prediction. To this end, we propose a unified recurrence modeling for video action anticipation via message passing framework. The information flow in space-time can be described by the interaction between vertices and edges, and the changes of vertices for each incoming frame reflects the underlying dynamics. Our model leverages self-attention as the building blocks for each of the message passing functions. In addition, we introduce different edge learning strategies that can be end-to-end optimized to gain better flexibility for the connectivity between vertices. Our experimental results demonstrate that our proposed method outperforms previous works on the large-scale EPIC-Kitchen dataset.

Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including recommender systems and social networks. However, this performance is based on static graph structures assumption which limits the Graph Neural Networks performance when the data varies with time. Spatiotemporal Graph Neural Networks are extension of Graph Neural Networks that takes the time factor into account. Recently, various Spatiotemporal Graph Neural Network algorithms were proposed and achieved superior performance compared to other deep learning algorithms in several time dependent applications. This survey discusses interesting topics related to Spatiotemporal Graph Neural Networks, including algorithms, applications, and open challenges.

Video Question Answering (VideoQA) task serves as a critical playground for evaluating whether foundation models can effectively perceive, understand, and reason about dynamic real-world scenarios. However, existing Multimodal Large Language Models (MLLMs) struggle with simultaneously modeling spatial relationships within video frames and understanding the causal dynamics of temporal evolution on complex and reasoning-intensive VideoQA task. In this work, we equip MLLM with a comprehensive and extensible Video Toolkit, to enhance MLLM's spatiotemporal reasoning capabilities and ensure the harmony between the quantity and diversity of tools. To better control the tool invocation sequence and avoid toolchain shortcut issues, we propose a Spatiotemporal Reasoning Framework (STAR) that strategically schedules temporal and spatial tools, thereby progressively localizing the key area in the video. Our STAR framework enhances GPT-4o using lightweight tools, achieving an 8.2% gain on VideoMME and 4.6% on LongVideoBench. We believe that our proposed Video Toolkit and STAR framework make an important step towards building autonomous and intelligent video analysis assistants. The code is publicly available at https://github.com/fansunqi/VideoTool.

Spatiotemporal reasoning plays a key role in Cyber-Physical Systems (CPS). Despite advances in Large Language Models (LLMs) and Large Reasoning Models (LRMs), their capacity to reason about complex spatiotemporal signals remains underexplored. This paper proposes a hierarchical SpatioTemporal reAsoning benchmaRK, STARK, to systematically evaluate LLMs across three levels of reasoning complexity: state estimation (e.g., predicting field variables, localizing and tracking events in space and time), spatiotemporal reasoning over states (e.g., inferring spatial-temporal relationships), and world-knowledge-aware reasoning that integrates contextual and domain knowledge (e.g., intent prediction, landmark-aware navigation). We curate 26 distinct spatiotemporal tasks with diverse sensor modalities, comprising 14,552 challenges where models answer directly or by Python Code Interpreter. Evaluating 3 LRMs and 8 LLMs, we find LLMs achieve limited success in tasks requiring geometric reasoning (e.g., multilateration or triangulation), particularly as complexity increases. Surprisingly, LRMs show robust performance across tasks with various levels of difficulty, often competing or surpassing traditional first-principle-based methods. Our results show that in reasoning tasks requiring world knowledge, the performance gap between LLMs and LRMs narrows, with some LLMs even surpassing LRMs. However, the LRM o3 model continues to achieve leading performance across all evaluated tasks, a result attributed primarily to the larger size of the reasoning models. STARK motivates future innovations in model architectures and reasoning paradigms for intelligent CPS by providing a structured framework to identify limitations in the spatiotemporal reasoning of LLMs and LRMs.

Large language models (LLMs) are attractive for context-aware time series forecasting because they can integrate heterogeneous textual signals, yet their discrete, language-oriented tokenization and embedding interfaces are misaligned with continuous numerical values, often harming numerical ordering and forecasting reliability. We propose TempoWave, a plug-and-play temporal wavelet digit interface that maps each scalar observation into digit-wise embeddings constructed from multi-wavelet, multi-scale coefficients. By directly overriding standard token representations, TempoWave seamlessly exposes both fine-grained local fluctuations and macro global structures in a transformer-compatible form, ensuring that precise numerical formatting, distinct digit identity, and robustness to common normalization operations are maintained throughout the LLM pipeline. Experiments across five context-enriched forecasting benchmarks demonstrate that TempoWave consistently improves LLM-based forecasters over standard numeric tokenization and alternative embedding interfaces, achieving a new state-of-the-art. These results highlight the numeric interface as a key bottleneck and suggest that principled multi-resolution embeddings can better couple LLMs' contextual reasoning with precise forecasting. Our code is available at https://github.com/DC-research/TempoWAVE and our model can be accessed at https://huggingface.co/Melady/TempoWAVE.

Large Language Models (LLMs) have recently demonstrated impressive capabilities in natural language processing due to their strong generalization and sequence modeling capabilities. However, their direct application to time series forecasting remains challenging due to two fundamental issues: the inherent heterogeneity of temporal patterns and the modality gap between continuous numerical signals and discrete language representations. In this work, we propose TALON, a unified framework that enhances LLM-based forecasting by modeling temporal heterogeneity and enforcing semantic alignment. Specifically, we design a Heterogeneous Temporal Encoder that partitions multivariate time series into structurally coherent segments, enabling localized expert modeling across diverse temporal patterns. To bridge the modality gap, we introduce a Semantic Alignment Module that aligns temporal features with LLM-compatible representations, enabling effective integration of time series into language-based models while eliminating the need for handcrafted prompts during inference. Extensive experiments on seven real-world benchmarks demonstrate that TALON achieves superior performance across all datasets, with average MSE improvements of up to 11\% over recent state-of-the-art methods. These results underscore the effectiveness of incorporating both pattern-aware and semantic-aware designs when adapting LLMs for time series forecasting. The code is available at: https://github.com/syrGitHub/TALON.

Time series forecasting plays a vital role in supporting decision-making across a wide range of critical applications, including energy, healthcare, and finance. Despite recent advances, forecasting accuracy remains limited due to the challenge of integrating historical numerical sequences with contextual features, which often comprise unstructured textual data. To address this challenge, we propose TokenCast, an LLM-driven framework that leverages language-based symbolic representations as a unified intermediary for context-aware time series forecasting. Specifically, TokenCast employs a discrete tokenizer to transform continuous numerical sequences into temporal tokens, enabling structural alignment with language-based inputs. To bridge the semantic gap between modalities, both temporal and contextual tokens are embedded into a shared representation space via a pre-trained large language model (LLM), further optimized with autoregressive generative objectives. Building upon this unified semantic space, the aligned LLM is subsequently fine-tuned in a supervised manner to predict future temporal tokens, which are then decoded back into the original numerical space. Extensive experiments on diverse real-world datasets enriched with contextual features demonstrate the effectiveness and generalizability of TokenCast.

The rapid evolution of large language models (LLMs) holds promise for reforming the methodology of spatio-temporal data mining. However, current works for evaluating the spatio-temporal understanding capability of LLMs are somewhat limited and biased. These works either fail to incorporate the latest language models or only focus on assessing the memorized spatio-temporal knowledge. To address this gap, this paper dissects LLMs' capability of spatio-temporal data into four distinct dimensions: knowledge comprehension, spatio-temporal reasoning, accurate computation, and downstream applications. We curate several natural language question-answer tasks for each category and build the benchmark dataset, namely STBench, containing 13 distinct tasks and over 60,000 QA pairs. Moreover, we have assessed the capabilities of 13 LLMs, such as GPT-4o, Gemma and Mistral. Experimental results reveal that existing LLMs show remarkable performance on knowledge comprehension and spatio-temporal reasoning tasks, with potential for further enhancement on other tasks through in-context learning, chain-of-though prompting, and fine-tuning. The code and datasets of STBench are released on https://github.com/LwbXc/STBench.

Remote sensing world models aim to both explain observed changes and forecast plausible futures, two tasks that share spatiotemporal priors. Existing methods, however, typically address them separately, limiting cross-task transfer. We present RS-WorldModel, a unified world model for remote sensing that jointly handles spatiotemporal change understanding and text-guided future scene forecasting, and we build RSWBench-1.1M, a 1.1 million sample dataset with rich language annotations covering both tasks. RS-WorldModel is trained in three stages: (1) Geo-Aware Generative Pre-training (GAGP) conditions forecasting on geographic and acquisition metadata; (2) synergistic instruction tuning (SIT) jointly trains understanding and forecasting; (3) verifiable reinforcement optimization (VRO) refines outputs with verifiable, task-specific rewards. With only 2B parameters, RS-WorldModel surpasses open-source models up to 120 times larger on most spatiotemporal change question-answering metrics. It achieves an FID of 43.13 on text-guided future scene forecasting, outperforming all open-source baselines as well as the closed-source Gemini-2.5-Flash Image (Nano Banana).

The prediction of ship trajectories is a growing field of study in artificial intelligence. Traditional methods rely on the use of LSTM, GRU networks, and even Transformer architectures for the prediction of spatio-temporal series. This study proposes a viable alternative for predicting these trajectories using only GNSS positions. It considers this spatio-temporal problem as a natural language processing problem. The latitude/longitude coordinates of AIS messages are transformed into cell identifiers using the H3 index. Thanks to the pseudo-octal representation, it becomes easier for language models to learn the spatial hierarchy of the H3 index. The method is compared with a classical Kalman filter, widely used in the maritime domain, and introduces the Fr\'echet distance as the main evaluation metric. We show that it is possible to predict ship trajectories quite precisely up to 8 hours with 30 minutes of context. We demonstrate that this alternative works well enough to predict trajectories worldwide.

Motion prediction is crucial for autonomous vehicles to operate safely in complex traffic environments. Extracting effective spatiotemporal relationships among traffic elements is key to accurate forecasting. Inspired by the successful practice of pretrained large language models, this paper presents SEPT, a modeling framework that leverages self-supervised learning to develop powerful spatiotemporal understanding for complex traffic scenes. Specifically, our approach involves three masking-reconstruction modeling tasks on scene inputs including agents' trajectories and road network, pretraining the scene encoder to capture kinematics within trajectory, spatial structure of road network, and interactions among roads and agents. The pretrained encoder is then finetuned on the downstream forecasting task. Extensive experiments demonstrate that SEPT, without elaborate architectural design or manual feature engineering, achieves state-of-the-art performance on the Argoverse 1 and Argoverse 2 motion forecasting benchmarks, outperforming previous methods on all main metrics by a large margin.

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in world modeling. However, unlike typical generation tasks that encourage sample diversity, world models entail different sources of uncertainty and require consistent samples aligned with the ground-truth trajectory, which is a limitation we empirically observe in diffusion models. We argue that a key bottleneck in learning consistent diffusion-based world models lies in the suboptimal predictive ability, which we attribute to the entanglement of condition understanding and target denoising within shared architectures and co-training schemes. To address this, we propose Foresight Diffusion (ForeDiff), a diffusion-based world modeling framework that enhances consistency by decoupling condition understanding from target denoising. ForeDiff incorporates a separate deterministic predictive stream to process conditioning inputs independently of the denoising stream, and further leverages a pretrained predictor to extract informative representations that guide generation. Extensive experiments on robot video prediction and scientific spatiotemporal forecasting show that ForeDiff improves both predictive accuracy and sample consistency over strong baselines, offering a promising direction for diffusion-based world models.

Accurate air quality forecasts are vital for public health alerts, exposure assessment, and emissions control. In practice, observational data are often missing in varying proportions and patterns due to collection and transmission issues. These incomplete spatiotemporal records impede reliable inference and risk assessment and can lead to overconfident extrapolation. To address these challenges, we propose an end to end framework, the channel gated learning unit based spatiotemporal bayesian neural field (CGLUBNF). It uses Fourier features with a graph attention encoder to capture multiscale spatial dependencies and seasonal temporal dynamics. A channel gated learning unit, equipped with learnable activations and gated residual connections, adaptively filters and amplifies informative features. Bayesian inference jointly optimizes predictive distributions and parameter uncertainty, producing point estimates and calibrated prediction intervals. We conduct a systematic evaluation on two real world datasets, covering four typical missing data patterns and comparing against five state of the art baselines. CGLUBNF achieves superior prediction accuracy and sharper confidence intervals. In addition, we further validate robustness across multiple prediction horizons and analysis the contribution of extraneous variables. This research lays a foundation for reliable deep learning based spatio-temporal forecasting with incomplete observations in emerging sensing paradigms, such as real world vehicle borne mobile monitoring.

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.

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.

Traffic prediction is a typical spatio-temporal data mining task and has great significance to the public transportation system. Considering the demand for its grand application, we recognize key factors for an ideal spatio-temporal prediction method: efficient, lightweight, and effective. However, the current deep model-based spatio-temporal prediction solutions generally own intricate architectures with cumbersome optimization, which can hardly meet these expectations. To accomplish the above goals, we propose an intuitive and novel framework, MLPST, a pure multi-layer perceptron architecture for traffic prediction. Specifically, we first capture spatial relationships from both local and global receptive fields. Then, temporal dependencies in different intervals are comprehensively considered. Through compact and swift MLP processing, MLPST can well capture the spatial and temporal dependencies while requiring only linear computational complexity, as well as model parameters that are more than an order of magnitude lower than baselines. Extensive experiments validated the superior effectiveness and efficiency of MLPST against advanced baselines, and among models with optimal accuracy, MLPST achieves the best time and space efficiency.

Recently, large language models (LLMs) have shown great promise in time series forecasting. However, most existing LLM-based forecasting methods still follow a static generative paradigm that directly maps historical observations to future values in a single pass. Under this paradigm, forecasting is constrained by limited temporal pattern extraction, single-round acquisition of contextual features, one-shot forecast generation, and lack of support from ensemble forecasts. To address these limitations, in this work, we propose CastFlow, a dynamic agentic forecasting framework that enables multi-view temporal pattern extraction, multi-round contextual features acquisition, iterative forecast refinement, and forecasting with ensemble forecasts. First, CastFlow organizes the forecasting process into planning, action, forecasting, and reflection, establishing an agentic workflow. Second, this workflow is supported by a memory module that retrieves prior experience and a multi-view toolkit that constructs diagnostic evidence and provides a reliable ensemble forecast baseline. Third, CastFlow adopts a role-specialized design that combines general-purpose reasoning with specialized numerical forecasting. Under this design, a frozen LLM preserves general-purpose reasoning, while a fine-tuned domain-specific LLM performs evidence-guided numerical forecasting based on the ensemble forecast baseline, rather than from scratch. To optimize a fine-tuned domain-specific LLM, we further develop a two-stage workflow-oriented training that combines supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). To evaluate the effectiveness of CastFlow, we conduct extensive experiments on diverse datasets and show that it achieves superior overall results against strong baselines. We hope that this work can serve as a step toward more adaptive and accurate time series forecasting.

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

Precise geocoding and time normalization for text requires that location and time phrases be identified. Many state-of-the-art geoparsers and temporal parsers suffer from low recall. Categories commonly missed by parsers are: nouns used in a non- spatiotemporal sense, adjectival and adverbial phrases, prepositional phrases, and numerical phrases. We collected and annotated data set by querying commercial web searches API with such spatiotemporal expressions as were missed by state-of-the- art parsers. Due to the high cost of sentence annotation, active learning was used to label training data, and a new strategy was designed to better select training examples to reduce labeling cost. For the learning algorithm, we applied an average perceptron trained Featurized Hidden Markov Model (FHMM). Five FHMM instances were used to create an ensemble, with the output phrase selected by voting. Our ensemble model was tested on a range of sequential labeling tasks, and has shown competitive performance. Our contributions include (1) an new dataset annotated with named entities and expanded spatiotemporal expressions; (2) a comparison of inference algorithms for ensemble models showing the superior accuracy of Belief Propagation over Viterbi Decoding; (3) a new example re-weighting method for active ensemble learning that 'memorizes' the latest examples trained; (4) a spatiotemporal parser that jointly recognizes expanded spatiotemporal expressions as well as named entities.

Recently, there has been a growing interest in leveraging pre-trained large language models (LLMs) for various time series applications. However, the semantic space of LLMs, established through the pre-training, is still underexplored and may help yield more distinctive and informative representations to facilitate time series forecasting. To this end, we propose Semantic Space Informed Prompt learning with LLM (S^2IP-LLM) to align the pre-trained semantic space with time series embeddings space and perform time series forecasting based on learned prompts from the joint space. We first design a tokenization module tailored for cross-modality alignment, which explicitly concatenates patches of decomposed time series components to create embeddings that effectively encode the temporal dynamics. Next, we leverage the pre-trained word token embeddings to derive semantic anchors and align selected anchors with time series embeddings by maximizing the cosine similarity in the joint space. This way, S^2IP-LLM can retrieve relevant semantic anchors as prompts to provide strong indicators (context) for time series that exhibit different temporal dynamics. With thorough empirical studies on multiple benchmark datasets, we demonstrate that the proposed S^2IP-LLM can achieve superior forecasting performance over state-of-the-art baselines. Furthermore, our ablation studies and visualizations verify the necessity of prompt learning informed by semantic space.

Diffusion models have demonstrated exceptional visual quality in video generation, making them promising for autonomous driving world modeling. However, existing video diffusion-based world models struggle with flexible-length, long-horizon predictions and integrating trajectory planning. This is because conventional video diffusion models rely on global joint distribution modeling of fixed-length frame sequences rather than sequentially constructing localized distributions at each timestep. In this work, we propose Epona, an autoregressive diffusion world model that enables localized spatiotemporal distribution modeling through two key innovations: 1) Decoupled spatiotemporal factorization that separates temporal dynamics modeling from fine-grained future world generation, and 2) Modular trajectory and video prediction that seamlessly integrate motion planning with visual modeling in an end-to-end framework. Our architecture enables high-resolution, long-duration generation while introducing a novel chain-of-forward training strategy to address error accumulation in autoregressive loops. Experimental results demonstrate state-of-the-art performance with 7.4\% FVD improvement and minutes longer prediction duration compared to prior works. The learned world model further serves as a real-time motion planner, outperforming strong end-to-end planners on NAVSIM benchmarks. Code will be publicly available at https://github.com/Kevin-thu/Epona/{https://github.com/Kevin-thu/Epona/}.

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.

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to O(1), effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of O(L), ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: https://github.com/Water2sea/TPGN.

Geo-temporal understanding, the ability to infer location, time, and contextual properties from visual input alone, underpins applications such as disaster management, traffic planning, embodied navigation, world modeling, and geography education. Although recent vision-language models (VLMs) have advanced image geo-localization using cues like landmarks and road signs, their ability to reason about temporal signals and physically grounded spatial cues remains limited. To address this gap, we introduce TimeSpot, a benchmark for evaluating real-world geo-temporal reasoning in VLMs. TimeSpot comprises 1,455 ground-level images from 80 countries and requires structured prediction of temporal attributes (season, month, time of day, daylight phase) and geographic attributes (continent, country, climate zone, environment type, latitude-longitude) directly from visual evidence. It also includes spatial-temporal reasoning tasks that test physical plausibility under real-world uncertainty. Evaluations of state-of-the-art open- and closed-source VLMs show low performance, particularly for temporal inference. While supervised fine-tuning yields improvements, results remain insufficient, highlighting the need for new methods to achieve robust, physically grounded geo-temporal understanding. TimeSpot is available at: https://TimeSpot-GT.github.io.

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and finance. However, with machine learning shifting towards neural autoregressive models such as RNNs and transformers, probabilistic querying has been largely restricted to simple cases such as next-event prediction. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

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

Satellite image time series (SITS) provide continuous observations of the Earth's surface, making them essential for applications such as environmental management and disaster assessment. However, existing spatiotemporal foundation models rely on plain vision transformers, which encode entire temporal sequences without explicitly capturing multiscale spatiotemporal relationships between land objects. This limitation hinders their effectiveness in downstream tasks. To overcome this challenge, we propose TiMo, a novel hierarchical vision transformer foundation model tailored for SITS analysis. At its core, we introduce a spatiotemporal gyroscope attention mechanism that dynamically captures evolving multiscale patterns across both time and space. For pre-training, we curate MillionST, a large-scale dataset of one million images from 100,000 geographic locations, each captured across 10 temporal phases over five years, encompassing diverse geospatial changes and seasonal variations. Leveraging this dataset, we adapt masked image modeling to pre-train TiMo, enabling it to effectively learn and encode generalizable spatiotemporal representations.Extensive experiments across multiple spatiotemporal tasks-including deforestation monitoring, land cover segmentation, crop type classification, and flood detection-demonstrate TiMo's superiority over state-of-the-art methods. Code, model, and dataset will be released at https://github.com/MiliLab/TiMo.

Transformer-based models have recently made significant advances in accurate time-series forecasting, but even these architectures struggle to scale efficiently while capturing long-term temporal dynamics. Mixture-of-Experts (MoE) layers are a proven solution to scaling problems in natural language processing. However, existing MoE approaches for time-series forecasting rely on token-wise routing mechanisms, which may fail to exploit the natural locality and continuity of temporal data. In this work, we introduce Seg-MoE, a sparse MoE design that routes and processes contiguous time-step segments rather than making independent expert decisions. Token segments allow each expert to model intra-segment interactions directly, naturally aligning with inherent temporal patterns. We integrate Seg-MoE layers into a time-series Transformer and evaluate it on multiple multivariate long-term forecasting benchmarks. Seg-MoE consistently achieves state-of-the-art forecasting accuracy across almost all prediction horizons, outperforming both dense Transformers and prior token-wise MoE models. Comprehensive ablation studies confirm that segment-level routing is the key factor driving these gains. Our results show that aligning the MoE routing granularity with the inherent structure of time series provides a powerful, yet previously underexplored, inductive bias, opening new avenues for conditionally sparse architectures in sequential data modeling.

We introduce TiRex-2, a recurrent xLSTM-based time series foundation model that generalizes the univariate TiRex to multivariate forecasting with both past and future covariates. Real-world forecasting is inherently sequential: observations arrive continuously, variables evolve jointly, and a subset of covariates is known ahead of time. Existing Transformer-based time series foundation models capture cross-variate dependencies but incur quadratic complexity in context length and require full-history recomputation as new observations arrive. TiRex-2 addresses these limitations through a memory-centric recurrent design that operates at constant per-patch cost under streaming. The model combines a bidirectional time mixer with an asymmetric grouped-attention variate mixer, enabling the integration of future-known covariates while preserving strict causality over target variables. To our knowledge, this is the first time series foundation model that achieves this combination of properties. To support scalable multivariate pretraining, we propose a synthetic coupling pipeline that composes diverse multivariate samples on the fly from large univariate corpora. Empirically, TiRex-2 achieves state-of-the-art zero-shot performance on GIFT-Eval and fev-bench, remains stable when streamed to arbitrary context lengths, and maintains constant inference cost per patch. The model uses 38.4M active parameters in univariate mode, with an additional 44.1M parameters activated for multivariate forecasting.

Remote sensing offers an unparalleled vantage point for observing the Earth's long-term surface evolution, yet it demands that a model not only perceive land cover at isolated moments, but also track changes, memorize evolution histories, and reason across time and space. However, existing studies lack a systematic evaluation that dissects these distinct competencies. To fill this gap, we introduce ChronoBench, a multidimensional benchmark that decomposes this task into four progressive cognitive levels (i.e., Land Cover Perception, Temporal Recognition, Long-Term Memory, and Spatio-Temporal Reasoning). The ChronoBench comprises 12 sub-tasks and 17,689 rigorously validated QA (Question-Answer) pairs. Extensive evaluations reveal that mainstream MLLMs fall drastically behind human experts, with Long-Term Memory emerging as the most critical bottleneck. Motivated by this finding, we further propose GeoChrono, an MLLM with enhanced capabilities for tracing, memorizing, and reasoning about long-term geographic evolution. Leveraging the physical prior that geographic parcels remain spatially fixed while their semantics evolve, we design a Temporal Trajectory Encoder~(TempEnc) that constructs per-location temporal trajectories for dedicated land cover evolution modeling, and we introduce a Coarse-to-Fine Token Compressor~(C2FComp) that adaptively preserves dynamic regions while compressing the static background. To support training, we also construct ChronoInstruct, a 104K-sample instruction-tuning dataset spanning all competency levels for training. GeoChrono achieves state-of-the-art performance on ChronoBench, surpassing the leading commercial MLLMs by over 20%, while C2FComp reduces visual tokens by over 56% while retaining GeoChrono's 94.6% performance. The code and data will be available at https://github.com/IntelliSensing/GeoChrono

While LLMs have demonstrated remarkable potential in time series forecasting, their practical deployment remains constrained by excessive computational demands and memory footprints. Existing LLM-based approaches typically suffer from three critical limitations: Inefficient parameter utilization in handling numerical time series patterns; Modality misalignment between continuous temporal signals and discrete text embeddings; and Inflexibility for real-time expert knowledge integration. We present SMETimes, the first systematic investigation of sub-3B parameter SLMs for efficient and accurate time series forecasting. Our approach centers on three key innovations: A statistically-enhanced prompting mechanism that bridges numerical time series with textual semantics through descriptive statistical features; A adaptive fusion embedding architecture that aligns temporal patterns with language model token spaces through learnable parameters; And a dynamic mixture-of-experts framework enabled by SLMs' computational efficiency, adaptively combining base predictions with domain-specific models. Extensive evaluations across seven benchmark datasets demonstrate that our 3B-parameter SLM achieves state-of-the-art performance on five primary datasets while maintaining 3.8x faster training and 5.2x lower memory consumption compared to 7B-parameter LLM baselines. Notably, the proposed model exhibits better learning capabilities, achieving 12.3% lower MSE than conventional LLM. Ablation studies validate that our statistical prompting and cross-modal fusion modules respectively contribute 15.7% and 18.2% error reduction in long-horizon forecasting tasks. By redefining the efficiency-accuracy trade-off landscape, this work establishes SLMs as viable alternatives to resource-intensive LLMs for practical time series forecasting. Code and models are available at https://github.com/xiyan1234567/SMETimes.

Traffic forecasting represents a crucial problem within intelligent transportation systems. In recent research, Large Language Models (LLMs) have emerged as a promising method, but their intrinsic design, tailored primarily for sequential token processing, introduces notable challenges in effectively capturing spatial dependencies. Specifically, the inherent limitations of LLMs in modeling spatial relationships and their architectural incompatibility with graph-structured spatial data remain largely unaddressed. To overcome these limitations, we introduce ST-LINK, a novel framework that enhances the capability of Large Language Models to capture spatio-temporal dependencies. Its key components are Spatially-Enhanced Attention (SE-Attention) and the Memory Retrieval Feed-Forward Network (MRFFN). SE-Attention extends rotary position embeddings to integrate spatial correlations as direct rotational transformations within the attention mechanism. This approach maximizes spatial learning while preserving the LLM's inherent sequential processing structure. Meanwhile, MRFFN dynamically retrieves and utilizes key historical patterns to capture complex temporal dependencies and improve the stability of long-term forecasting. Comprehensive experiments on benchmark datasets demonstrate that ST-LINK surpasses conventional deep learning and LLM approaches, and effectively captures both regular traffic patterns and abrupt changes.

Time series forecasting has traditionally focused on univariate and multivariate numerical data, often overlooking the benefits of incorporating multimodal information, particularly textual data. In this paper, we propose a novel framework that integrates time series models with Large Language Models to improve high-dimensional time series forecasting. Inspired by multimodal models, our method combines time series and textual data in the dual-tower structure. This fusion of information creates a comprehensive representation, which is then processed through a linear layer to generate the final forecast. Extensive experiments demonstrate that incorporating text enhances high-dimensional time series forecasting performance. This work paves the way for further research in multimodal time series forecasting.

User profiling and region analysis are two tasks of significant commercial value. However, in practical applications, modeling different features typically involves four main steps: data preparation, data processing, model establishment, evaluation, and optimization. This process is time-consuming and labor-intensive. Repeating this workflow for each feature results in abundant development time for tasks and a reduced overall volume of task development. Indeed, human mobility data contains a wealth of information. Several successful cases suggest that conducting in-depth analysis of population movement data could potentially yield meaningful profiles about users and areas. Nonetheless, most related works have not thoroughly utilized the semantic information within human mobility data and trained on a fixed number of the regions. To tap into the rich information within population movement, based on the perspective that Regions Are Who walk them, we propose a large spatiotemporal model based on trajectories (RAW). It possesses the following characteristics: 1) Tailored for trajectory data, introducing a GPT-like structure with a parameter count of up to 1B; 2) Introducing a spatiotemporal fine-tuning module, interpreting trajectories as collection of users to derive arbitrary region embedding. This framework allows rapid task development based on the large spatiotemporal model. We conducted extensive experiments to validate the effectiveness of our proposed large spatiotemporal model. It's evident that our proposed method, relying solely on human mobility data without additional features, exhibits a certain level of relevance in user profiling and region analysis. Moreover, our model showcases promising predictive capabilities in trajectory generation tasks based on the current state, offering the potential for further innovative work utilizing this large spatiotemporal model.

Large Language Models (LLMs) and Foundation Models (FMs) have recently become prevalent for time series forecasting tasks. While fine-tuning LLMs enables domain adaptation, they often struggle to generalize across diverse and unseen datasets. Moreover, existing Time Series Foundation Models (TSFMs) still face challenges in handling non-stationary dynamics and distribution shifts, largely due to the lack of effective mechanisms for adaptation. To this end, we present TS-RAG, a retrieval-augmented generation framework for time series forecasting that enhances the generalization and interpretability of TSFMs. Specifically, TS-RAG leverages pre-trained time series encoders to retrieve semantically relevant segments from a dedicated knowledge base, enriching the contextual representation of the input query. Furthermore, we propose an Adaptive Retrieval Mixer (ARM) module that dynamically fuses the retrieved patterns with the TSFM's internal representation, improving forecasting accuracy without requiring task-specific fine-tuning. Thorough empirical studies on seven public benchmark datasets demonstrate that TS-RAG achieves state-of-the-art zero-shot forecasting performance, outperforming the existing TSFMs by up to 6.84% across diverse domains while also providing desirable interpretability. Our code and data are available at: https://github.com/UConn-DSIS/TS-RAG

Forecasting is a critical task in decision-making across numerous domains. While historical numerical data provide a start, they fail to convey the complete context for reliable and accurate predictions. Human forecasters frequently rely on additional information, such as background knowledge and constraints, which can efficiently be communicated through natural language. However, in spite of recent progress with LLM-based forecasters, their ability to effectively integrate this textual information remains an open question. To address this, we introduce "Context is Key" (CiK), a time-series forecasting benchmark that pairs numerical data with diverse types of carefully crafted textual context, requiring models to integrate both modalities; crucially, every task in CiK requires understanding textual context to be solved successfully. We evaluate a range of approaches, including statistical models, time series foundation models, and LLM-based forecasters, and propose a simple yet effective LLM prompting method that outperforms all other tested methods on our benchmark. Our experiments highlight the importance of incorporating contextual information, demonstrate surprising performance when using LLM-based forecasting models, and also reveal some of their critical shortcomings. This benchmark aims to advance multimodal forecasting by promoting models that are both accurate and accessible to decision-makers with varied technical expertise. The benchmark can be visualized at https://servicenow.github.io/context-is-key-forecasting/v0/.

Knowledge about the hidden factors that determine particular system dynamics is crucial for both explaining them and pursuing goal-directed interventions. Inferring these factors from time series data without supervision remains an open challenge. Here, we focus on spatiotemporal processes, including wave propagation and weather dynamics, for which we assume that universal causes (e.g. physics) apply throughout space and time. A recently introduced DIstributed SpatioTemporal graph Artificial Neural network Architecture (DISTANA) is used and enhanced to learn such processes, requiring fewer parameters and achieving significantly more accurate predictions compared to temporal convolutional neural networks and other related approaches. We show that DISTANA, when combined with a retrospective latent state inference principle called active tuning, can reliably derive location-respective hidden causal factors. In a current weather prediction benchmark, DISTANA infers our planet's land-sea mask solely by observing temperature dynamics and, meanwhile, uses the self inferred information to improve its own future temperature predictions.

Autoregressive models excel in visual generation by treating images as 1D sequences of discrete tokens, mirroring language modeling. However, this flattening discards the intrinsic 2D spatial locality of visual signals, creating severe computational bottlenecks during inference. We introduce Spatially Speculative Decoding (SSD), a framework that aligns the predictive objective with the natural geometry of images. Rather than predicting only the immediate next token in a 1D sequence, our model simultaneously predicts the adjacent horizontal token and the token directly below it. By capitalizing on this 2D spatial correlation, spatially speculative decoding overcomes the memory wall in visual inference. Our approach accelerates autoregressive image generation by up to 13.3x while maintaining high fidelity on DPG-Bench and GenEval. Our results suggest that respecting the underlying geometry of vision unlocks massive computational efficiencies, paving the way for real-time, high-resolution autoregressive generative models.

Satellite image time-series analysis demands fine-grained spatial-temporal reasoning, which remains a challenge for existing multimodal large language models (MLLMs). In this work, we study the capabilities of MLLMs on a novel task that jointly targets temporal change understanding and future scene generation, aiming to assess their potential for modeling complex multimodal dynamics over time. We propose TAMMs, a Temporal-Aware Multimodal Model for satellite image change understanding and forecasting, which enhances frozen MLLMs with lightweight temporal modules for structured sequence encoding and contextual prompting. To guide future image generation, TAMMs introduces a Semantic-Fused Control Injection (SFCI) mechanism that adaptively combines high-level semantic reasoning and structural priors within an enhanced ControlNet. This dual-path conditioning enables temporally consistent and semantically grounded image synthesis. Experiments demonstrate that TAMMs outperforms strong MLLM baselines in both temporal change understanding and future image forecasting tasks, highlighting how carefully designed temporal reasoning and semantic fusion can unlock the full potential of MLLMs for spatio-temporal understanding.

Recent successes in autoregressive (AR) generation models, such as the GPT series in natural language processing, have motivated efforts to replicate this success in visual tasks. Some works attempt to extend this approach to autonomous driving by building video-based world models capable of generating realistic future video sequences and predicting ego states. However, prior works tend to produce unsatisfactory results, as the classic GPT framework is designed to handle 1D contextual information, such as text, and lacks the inherent ability to model the spatial and temporal dynamics essential for video generation. In this paper, we present DrivingWorld, a GPT-style world model for autonomous driving, featuring several spatial-temporal fusion mechanisms. This design enables effective modeling of both spatial and temporal dynamics, facilitating high-fidelity, long-duration video generation. Specifically, we propose a next-state prediction strategy to model temporal coherence between consecutive frames and apply a next-token prediction strategy to capture spatial information within each frame. To further enhance generalization ability, we propose a novel masking strategy and reweighting strategy for token prediction to mitigate long-term drifting issues and enable precise control. Our work demonstrates the ability to produce high-fidelity and consistent video clips of over 40 seconds in duration, which is over 2 times longer than state-of-the-art driving world models. Experiments show that, in contrast to prior works, our method achieves superior visual quality and significantly more accurate controllable future video generation. Our code is available at https://github.com/YvanYin/DrivingWorld.

The spatio-temporal relations of impacts of extreme events and their drivers in climate data are not fully understood and there is a need of machine learning approaches to identify such spatio-temporal relations from data. The task, however, is very challenging since there are time delays between extremes and their drivers, and the spatial response of such drivers is inhomogeneous. In this work, we propose a first approach and benchmarks to tackle this challenge. Our approach is trained end-to-end to predict spatio-temporally extremes and spatio-temporally drivers in the physical input variables jointly. By enforcing the network to predict extremes from spatio-temporal binary masks of identified drivers, the network successfully identifies drivers that are correlated with extremes. We evaluate our approach on three newly created synthetic benchmarks, where two of them are based on remote sensing or reanalysis climate data, and on two real-world reanalysis datasets. The source code and datasets are publicly available at the project page https://hakamshams.github.io/IDE.

Multivariate time series forecasting (MTSF) seeks to model temporal dynamics among variables to predict future trends. Transformer-based models and large language models (LLMs) have shown promise due to their ability to capture long-range dependencies and patterns. However, current methods often rely on rigid inductive biases, ignore intervariable interactions, or apply static fusion strategies that limit adaptability across forecast horizons. These limitations create bottlenecks in capturing nuanced, horizon-specific relationships in time-series data. To solve this problem, we propose T3Time, a novel trimodal framework consisting of time, spectral, and prompt branches, where the dedicated frequency encoding branch captures the periodic structures along with a gating mechanism that learns prioritization between temporal and spectral features based on the prediction horizon. We also proposed a mechanism which adaptively aggregates multiple cross-modal alignment heads by dynamically weighting the importance of each head based on the features. Extensive experiments on benchmark datasets demonstrate that our model consistently outperforms state-of-the-art baselines, achieving an average reduction of 3.28% in MSE and 2.29% in MAE. Furthermore, it shows strong generalization in few-shot learning settings: with 5% training data, we see a reduction in MSE and MAE by 4.13% and 1.91%, respectively; and with 10% data, by 3.62% and 1.98% on average. Code - https://github.com/monaf-chowdhury/T3Time/

Bayesian predictive inference provides a principled framework for uncertainty quantification, data efficiency, and robust generalization. However, exact inference is often intractable, and scalable approximations may remain computationally expensive or require restrictive modeling assumptions that degrade predictive performance. Prior-Data Fitted and in-context models have recently emerged as an amortized alternative by learning to map datasets directly to predictive distributions, but existing approaches are tightly coupled to the support of the training prior and lack explicit mechanisms for adapting to new priors at test time, resulting in limited robustness under distribution shift. We introduce a multi-task in-context learning framework for amortized hierarchical Bayesian predictive inference that explicitly represents prior information as a prefix of in-context datasets. A transformer trained on sequences of prior and target tasks learns to adapt its predictions across families of priors. On a suite of evaluations with increasing difficulty, including out-of-meta-distribution priors and priors with high-dimensional latent structures, our method matches oracle Bayesian predictors while being orders of magnitude faster. We further demonstrate its practical relevance on a real-world spatiotemporal temperature prediction benchmark. Code is available at https://github.com/martianmartina/multi-task-bayesian-icl/.

Pre-training on large-scale video data has become a common recipe for learning transferable spatiotemporal representations in recent years. Despite some progress, existing methods are mostly limited to highly curated datasets (e.g., K400) and exhibit unsatisfactory out-of-the-box representations. We argue that it is due to the fact that they only capture pixel-level knowledge rather than spatiotemporal semantics, which hinders further progress in video understanding. Inspired by the great success of image-text pre-training (e.g., CLIP), we take the first step to exploit language semantics to boost transferable spatiotemporal representation learning. We introduce a new pretext task, Turning to Video for Transcript Sorting (TVTS), which sorts shuffled ASR scripts by attending to learned video representations. We do not rely on descriptive captions and learn purely from video, i.e., leveraging the natural transcribed speech knowledge to provide noisy but useful semantics over time. Our method enforces the vision model to contextualize what is happening over time so that it can re-organize the narrative transcripts, and can seamlessly apply to large-scale uncurated video data in the real world. Our method demonstrates strong out-of-the-box spatiotemporal representations on diverse benchmarks, e.g., +13.6% gains over VideoMAE on SSV2 via linear probing. The code is available at https://github.com/TencentARC/TVTS.

Most existing forecasting systems are memory-based methods, which attempt to mimic human forecasting ability by employing various memory mechanisms and have progressed in temporal modeling for memory dependency. Nevertheless, an obvious weakness of this paradigm is that it can only model limited historical dependence and can not transcend the past. In this paper, we rethink the temporal dependence of event evolution and propose a novel memory-anticipation-based paradigm to model an entire temporal structure, including the past, present, and future. Based on this idea, we present Memory-and-Anticipation Transformer (MAT), a memory-anticipation-based approach, to address the online action detection and anticipation tasks. In addition, owing to the inherent superiority of MAT, it can process online action detection and anticipation tasks in a unified manner. The proposed MAT model is tested on four challenging benchmarks TVSeries, THUMOS'14, HDD, and EPIC-Kitchens-100, for online action detection and anticipation tasks, and it significantly outperforms all existing methods. Code is available at https://github.com/Echo0125/Memory-and-Anticipation-Transformer.

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.

Weather forecasting is one of the cornerstones of meteorological work. In this paper, we present a new benchmark dataset named Weather2K, which aims to make up for the deficiencies of existing weather forecasting datasets in terms of real-time, reliability, and diversity, as well as the key bottleneck of data quality. To be specific, our Weather2K is featured from the following aspects: 1) Reliable and real-time data. The data is hourly collected from 2,130 ground weather stations covering an area of 6 million square kilometers. 2) Multivariate meteorological variables. 20 meteorological factors and 3 constants for position information are provided with a length of 40,896 time steps. 3) Applicable to diverse tasks. We conduct a set of baseline tests on time series forecasting and spatio-temporal forecasting. To the best of our knowledge, our Weather2K is the first attempt to tackle weather forecasting task by taking full advantage of the strengths of observation data from ground weather stations. Based on Weather2K, we further propose Meteorological Factors based Multi-Graph Convolution Network (MFMGCN), which can effectively construct the intrinsic correlation among geographic locations based on meteorological factors. Sufficient experiments show that MFMGCN improves both the forecasting performance and temporal robustness. We hope our Weather2K can significantly motivate researchers to develop efficient and accurate algorithms to advance the task of weather forecasting. The dataset can be available at https://github.com/bycnfz/weather2k/.

Time series forecasting plays a crucial role in data mining, driving rapid advancements across numerous industries. With the emergence of large models, time series foundation models (TSFMs) have exhibited remarkable generalization capabilities, such as zero-shot learning, through large-scale pre-training. Meanwhile, Retrieval-Augmented Generation (RAG) methods have been widely employed to enhance the performance of foundation models on unseen data, allowing models to access to external knowledge. In this paper, we introduce TimeRAF, a Retrieval-Augmented Forecasting model that enhance zero-shot time series forecasting through retrieval-augmented techniques. We develop customized time series knowledge bases that are tailored to the specific forecasting tasks. TimeRAF employs an end-to-end learnable retriever to extract valuable information from the knowledge base. Additionally, we propose Channel Prompting for knowledge integration, which effectively extracts relevant information from the retrieved knowledge along the channel dimension. Extensive experiments demonstrate the effectiveness of our model, showing significant improvement across various domains and datasets.

We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 5 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalisation capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

Short-term demand forecasting models commonly combine convolutional and recurrent layers to extract complex spatiotemporal patterns in data. Long-term histories are also used to consider periodicity and seasonality patterns as time series data. In this study, we propose an efficient architecture, Temporal-Guided Network (TGNet), which utilizes graph networks and temporal-guided embedding. Graph networks extract invariant features to permutations of adjacent regions instead of convolutional layers. Temporal-guided embedding explicitly learns temporal contexts from training data and is substituted for the input of long-term histories from days/weeks ago. TGNet learns an autoregressive model, conditioned on temporal contexts of forecasting targets from temporal-guided embedding. Finally, our model achieves competitive performances with other baselines on three spatiotemporal demand dataset from real-world, but the number of trainable parameters is about 20 times smaller than a state-of-the-art baseline. We also show that temporal-guided embedding learns temporal contexts as intended and TGNet has robust forecasting performances even to atypical event situations.

Modeling human mobility is vital for extensive applications such as transportation planning and epidemic modeling. With the rise of the Artificial Intelligence Generated Content (AIGC) paradigm, recent works explore synthetic trajectory generation using autoregressive and diffusion models. While these methods show promise for generating single-day trajectories, they remain limited by inefficiencies in long-term generation (e.g., weekly trajectories) and a lack of explicit spatiotemporal multi-scale modeling. This study proposes Multi-Scale Spatio-Temporal AutoRegression (M-STAR), a new framework that generates long-term trajectories through a coarse-to-fine spatiotemporal prediction process. M-STAR combines a Multi-scale Spatiotemporal Tokenizer that encodes hierarchical mobility patterns with a Transformer-based decoder for next-scale autoregressive prediction. Experiments on two real-world datasets show that M-STAR outperforms existing methods in fidelity and significantly improves generation speed. The data and codes are available at https://github.com/YuxiaoLuo0013/M-STAR.

Recent advancements in sequence modeling have led to the emergence of Structured State Space Models (SSMs) as an efficient alternative to Recurrent Neural Networks (RNNs) and Transformers, addressing challenges in long-range dependency modeling and computational efficiency. While RNNs suffer from vanishing gradients and sequential inefficiencies, and Transformers face quadratic complexity, SSMs leverage structured recurrence and state-space representations to achieve superior long-sequence processing with linear or near-linear complexity. This survey provides a comprehensive review of SSMs, tracing their evolution from the foundational S4 model to its successors like Mamba, Simplified Structured State Space Sequence Model (S5), and Jamba, highlighting their improvements in computational efficiency, memory optimization, and inference speed. By comparing SSMs with traditional sequence models across domains such as natural language processing (NLP), speech recognition, vision, and time-series forecasting, we demonstrate their advantages in handling long-range dependencies while reducing computational overhead. Despite their potential, challenges remain in areas such as training optimization, hybrid modeling, and interpretability. This survey serves as a structured guide for researchers and practitioners, detailing the advancements, trade-offs, and future directions of SSM-based architectures in AI and deep learning.

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.

We introduce Timer-S1, a strong Mixture-of-Experts (MoE) time series foundation model with 8.3B total parameters, 0.75B activated parameters for each token, and a context length of 11.5K. To overcome the scalability bottleneck in existing pre-trained time series foundation models, we perform Serial Scaling in three dimensions: model architecture, dataset, and training pipeline. Timer-S1 integrates sparse TimeMoE blocks and generic TimeSTP blocks for Serial-Token Prediction (STP), a generic training objective that adheres to the serial nature of forecasting. The proposed paradigm introduces serial computations to improve long-term predictions while avoiding costly rolling-style inference and pronounced error accumulation in the standard next-token prediction. Pursuing a high-quality and unbiased training dataset, we curate TimeBench, a corpus with one trillion time points, and apply meticulous data augmentation to mitigate predictive bias. We further pioneer a post-training stage, including continued pre-training and long-context extension, to enhance short-term and long-context performance. Evaluated on the large-scale GIFT-Eval leaderboard, Timer-S1 achieves state-of-the-art forecasting performance, attaining the best MASE and CRPS scores as a pre-trained model. Timer-S1 will be released to facilitate further research.

Recent advances in Large Language Models (LLMs) have demonstrated new possibilities for accurate and efficient time series analysis, but prior work often required heavy fine-tuning and/or ignored inter-series correlations. In this work, we explore simple and flexible prompt-based strategies that enable LLMs to perform time series forecasting without extensive retraining or the use of a complex external architecture. Through the exploration of specialized prompting methods that leverage time series decomposition, patch-based tokenization, and similarity-based neighbor augmentation, we find that it is possible to enhance LLM forecasting quality while maintaining simplicity and requiring minimal preprocessing of data. To this end, we propose our own method, PatchInstruct, which enables LLMs to make precise and effective predictions.

Recent studies have indicated that vision models pre-trained on images can serve as time series foundation models (TSFMs) by reformulating time series forecasting (TSF) as image reconstruction. However, effective cross-modal transfer from vision to time series remains challenging due to three discrepancies: (1) the data-modality gap between structured, bounded image data and unbounded, heterogeneous time series; (2) the multivariate-forecasting gap between fixed RGB-three-channel vision models and time series with arbitrary numbers of variates; and (3) the probabilistic-forecasting gap between the deterministic outputs of vision models and the requirement for uncertainty-aware probabilistic predictions. To bridge these gaps, we propose VisonTS++, a TSFM based on continual pre-training of a vision model on large-scale time series. Our approach introduces three key innovations: (1) vision-model-based filtering to identify high-quality sequences to stabilize pre-training and mitigate modality gap; (2) colorized multivariate conversion, encoding multivariate series as multi-subfigure RGB images to enhance cross-variate modeling; (3) multi-quantile forecasting, using parallel reconstruction heads to generate quantile forecasts without parametric assumptions. Experiments show that VisionTS++ achieves state-of-the-art performance in both in-distribution and out-of-distribution forecasting, outperforming specialized TSFMs by 6%-44% in MSE reduction and ranking first in GIFT-Eval benchmark which comprises 23 datasets across 7 domains. Our work demonstrates that with appropriate adaptation, vision models can effectively generalize to TSF, thus advancing the pursuit of universal TSFMs. Code is available at https://github.com/HALF111/VisionTSpp.

Reasoning about human motion is an important prerequisite to safe and socially-aware robotic navigation. As a result, multi-agent behavior prediction has become a core component of modern human-robot interactive systems, such as self-driving cars. While there exist many methods for trajectory forecasting, most do not enforce dynamic constraints and do not account for environmental information (e.g., maps). Towards this end, we present Trajectron++, a modular, graph-structured recurrent model that forecasts the trajectories of a general number of diverse agents while incorporating agent dynamics and heterogeneous data (e.g., semantic maps). Trajectron++ is designed to be tightly integrated with robotic planning and control frameworks; for example, it can produce predictions that are optionally conditioned on ego-agent motion plans. We demonstrate its performance on several challenging real-world trajectory forecasting datasets, outperforming a wide array of state-of-the-art deterministic and generative methods.

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

Spatio-temporal reasoning is a core capability for Multimodal Large Language Models (MLLMs) operating in the real world. As such, evaluating it precisely has become an essential challenge. However, existing spatio-temporal reasoning benchmark datasets primarily rely on static image sets or passively curated video data, which limits the evaluation of fine-grained reasoning capabilities. In this paper, we introduce VGenST-Bench, a video benchmark that employs generative models to actively synthesize highly controlled and diverse evaluation scenarios. To construct VGenST-Bench, we propose a multi-agent pipeline incorporating a human quality control stage, ensuring the quality of all generated videos and QA pairs. We establish a comprehensive 3x2x2 video taxonomy, encompassing Spatial Scale, Perspective, and Scene Dynamics to span diverse scenarios. Furthermore, we design a hierarchical task suite that decouples low-level visual perception from high-level spatio-temporal reasoning. By shifting the paradigm from passive curation to active synthesis, VGenST-Bench enables fine-grained diagnosis of spatio-temporal understanding in MLLMs.

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.

The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.

We present a novel framework for motion forecasting with Dual Consistency Constraints and Multi-Pseudo-Target supervision. The motion forecasting task predicts future trajectories of vehicles by incorporating spatial and temporal information from the past. A key design of DCMS is the proposed Dual Consistency Constraints that regularize the predicted trajectories under spatial and temporal perturbation during the training stage. In addition, we design a novel self-ensembling scheme to obtain accurate pseudo targets to model the multi-modality in motion forecasting through supervision with multiple targets explicitly, namely Multi-Pseudo-Target supervision. Our experimental results on the Argoverse motion forecasting benchmark show that DCMS significantly outperforms the state-of-the-art methods, achieving 1st place on the leaderboard. We also demonstrate that our proposed strategies can be incorporated into other motion forecasting approaches as general training schemes.

Next POI recommendation intends to forecast users' immediate future movements given their current status and historical information, yielding great values for both users and service providers. However, this problem is perceptibly complex because various data trends need to be considered together. This includes the spatial locations, temporal contexts, user's preferences, etc. Most existing studies view the next POI recommendation as a sequence prediction problem while omitting the collaborative signals from other users. Instead, we propose a user-agnostic global trajectory flow map and a novel Graph Enhanced Transformer model (GETNext) to better exploit the extensive collaborative signals for a more accurate next POI prediction, and alleviate the cold start problem in the meantime. GETNext incorporates the global transition patterns, user's general preference, spatio-temporal context, and time-aware category embeddings together into a transformer model to make the prediction of user's future moves. With this design, our model outperforms the state-of-the-art methods with a large margin and also sheds light on the cold start challenges within the spatio-temporal involved recommendation problems.

Forecasting from partial observations is central to world modeling. Many recent methods represent the world through images, and reduce forecasting to stochastic video generation. Although such methods excel at realism and visual fidelity, predicting pixels is computationally intensive and not directly useful in many applications, as it requires translating RGB into signals useful for decision making. An alternative approach uses features from vision foundation models (VFMs) as world representations, performing deterministic regression to predict future world states. These features can be directly translated into actionable signals such as semantic segmentation and depth, while remaining computationally efficient. However, deterministic regression averages over multiple plausible futures, undermining forecast accuracy by failing to capture uncertainty. To address this crucial limitation, we introduce a generative forecaster that performs autoregressive flow matching in VFM feature space. Our key insight is that generative modeling in this space requires encoding VFM features into a compact latent space suitable for diffusion. We show that this latent space preserves information more effectively than previously used PCA-based alternatives, both for forecasting and other applications, such as image generation. Our latent predictions can be easily decoded into multiple useful and interpretable output modalities: semantic segmentation, depth, surface normals, and even RGB. With matched architecture and compute, our method produces sharper and more accurate predictions than regression across all modalities. Our results suggest that stochastic conditional generation of VFM features offers a promising and scalable foundation for future world models.

Time series forecasting is a foundational task across domains, such as finance, healthcare, and environmental monitoring. While recent advances in Time Series Foundation Models (TSFMs) have demonstrated strong generalisation through large-scale pretraining, existing models operate predominantly in a unimodal setting, ignoring the rich multimodal context, such as visual and textual signals, that often accompanies time series data in real-world scenarios. This paper introduces a novel parameter-efficient multimodal framework, UniCast, that extends TSFMs to jointly leverage time series, vision, and text modalities for enhanced forecasting performance. Our method integrates modality-specific embeddings from pretrained Vision and Text Encoders with a frozen TSFM via soft prompt tuning, enabling efficient adaptation with minimal parameter updates. This design not only preserves the generalisation strength of the foundation model but also enables effective cross-modal interaction. Extensive experiments across diverse time-series forecasting benchmarks demonstrate that UniCast consistently and significantly outperforms all existing TSFM baselines. The findings highlight the critical role of multimodal context in advancing the next generation of general-purpose time series forecasters.

A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of 10000 or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the state matrix \( A \), this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning \( A \) with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation 60times faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.

Recent two-stream deep Convolutional Neural Networks (ConvNets) have made significant progress in recognizing human actions in videos. Despite their success, methods extending the basic two-stream ConvNet have not systematically explored possible network architectures to further exploit spatiotemporal dynamics within video sequences. Further, such networks often use different baseline two-stream networks. Therefore, the differences and the distinguishing factors between various methods using Recurrent Neural Networks (RNN) or convolutional networks on temporally-constructed feature vectors (Temporal-ConvNet) are unclear. In this work, we first demonstrate a strong baseline two-stream ConvNet using ResNet-101. We use this baseline to thoroughly examine the use of both RNNs and Temporal-ConvNets for extracting spatiotemporal information. Building upon our experimental results, we then propose and investigate two different networks to further integrate spatiotemporal information: 1) temporal segment RNN and 2) Inception-style Temporal-ConvNet. We demonstrate that using both RNNs (using LSTMs) and Temporal-ConvNets on spatiotemporal feature matrices are able to exploit spatiotemporal dynamics to improve the overall performance. However, each of these methods require proper care to achieve state-of-the-art performance; for example, LSTMs require pre-segmented data or else they cannot fully exploit temporal information. Our analysis identifies specific limitations for each method that could form the basis of future work. Our experimental results on UCF101 and HMDB51 datasets achieve state-of-the-art performances, 94.1% and 69.0%, respectively, without requiring extensive temporal augmentation.

Time series forecasting is not just numerical extrapolation, but often requires reasoning with unstructured contextual data such as news or events. While specialized Time Series Foundation Models (TSFMs) excel at forecasting based on numerical patterns, they remain unaware to real-world textual signals. Conversely, while LLMs are emerging as zero-shot forecasters, their performance remains uneven across domains and contextual grounding. To bridge this gap, we introduce Nexus, a multi-agent forecasting framework that decomposes prediction into specialized stages: isolating macro-level and micro-level temporal fluctuations, and integrating contextual information when available before synthesizing a final forecast. This decomposition enables Nexus to adapt from seasonal signals to volatile, event-driven information without relying on external statistical anchors or monolithic prompting. We show that current-generation LLMs possess substantially stronger intrinsic forecasting ability than previously recognized, depending critically on how numerical and contextual reasoning are organized. Evaluated on data strictly succeeding LLM knowledge cutoffs spanning Zillow real estate metrics and volatile stock market equities, Nexus consistently matches or outperforms state-of-the-art TSFMs and strong LLM baselines. Beyond numerical accuracy, Nexus produces high-quality reasoning traces that explicitly show the fundamental drivers behind each forecast. Our results establish that real-world forecasting is an agentic reasoning problem extending well beyond only sequence modeling.

Multimodal large language models (MLLMs) have made remarkable progress in either temporal or spatial localization. However, they struggle to perform spatio-temporal video grounding. This limitation stems from two major challenges. Firstly, it is difficult to extract accurate spatio-temporal information of each frame in the video. Secondly, the substantial number of visual tokens makes it challenging to precisely map visual tokens of each frame to their corresponding spatial coordinates. To address these issues, we introduce SpaceVLLM, a MLLM endowed with spatio-temporal video grounding capability. Specifically, we adopt a set of interleaved Spatio-Temporal Aware Queries to capture temporal perception and dynamic spatial information. Moreover, we propose a Query-Guided Space Decoder to establish a corresponding connection between the queries and spatial coordinates. Additionally, due to the lack of spatio-temporal datasets, we construct the Unified Spatio-Temporal Grounding (Uni-STG) dataset, comprising 480K instances across three tasks. This dataset fully exploits the potential of MLLM to simultaneously facilitate localization in both temporal and spatial dimensions. Extensive experiments demonstrate that SpaceVLLM achieves the state-of-the-art performance across 11 benchmarks covering temporal, spatial, spatio-temporal and video understanding tasks, highlighting the effectiveness of our approach. Our code, datasets and model will be released at https://github.com/Jayce1kk/SpaceVLLM.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

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.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

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.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.

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 introduce TimeMCL, a method leveraging the Multiple Choice Learning (MCL) paradigm to forecast multiple plausible time series futures. Our approach employs a neural network with multiple heads and utilizes the Winner-Takes-All (WTA) loss to promote diversity among predictions. MCL has recently gained attention due to its simplicity and ability to address ill-posed and ambiguous tasks. We propose an adaptation of this framework for time-series forecasting, presenting it as an efficient method to predict diverse futures, which we relate to its implicit quantization objective. We provide insights into our approach using synthetic data and evaluate it on real-world time series, demonstrating its promising performance at a light computational cost.

Temporal point processes are the dominant paradigm for modeling sequences of events happening at irregular intervals. The standard way of learning in such models is by estimating the conditional intensity function. However, parameterizing the intensity function usually incurs several trade-offs. We show how to overcome the limitations of intensity-based approaches by directly modeling the conditional distribution of inter-event times. We draw on the literature on normalizing flows to design models that are flexible and efficient. We additionally propose a simple mixture model that matches the flexibility of flow-based models, but also permits sampling and computing moments in closed form. The proposed models achieve state-of-the-art performance in standard prediction tasks and are suitable for novel applications, such as learning sequence embeddings and imputing missing data.

Time Series Foundation Models (TSFMs) excel at numerical forecasting but operate as black boxes lacking qualitative reasoning. Conversely, applying LLMs directly to temporal data introduces a modality gap: text tokenizers fragment continuous numerical values, degrading mathematical relationships and exploding sequence lengths, leading to computational overhead. To resolve this, we introduce STRIDE (Strategic Time-series Reasoning Injected via Distilled Embeddings), a novel framework natively integrating LLM reasoning into the continuous embedding space of TSFMs. Instead of discrete tokens, STRIDE distills reasoning traces into a lightweight LLM, dynamically projecting its mean-pooled hidden states as a cross-modal prior into the target numerical encoder. The architecture is jointly optimized using cross-entropy and quantile losses. Evaluations demonstrate STRIDE establishes state-of-the-art numerical forecasting on GIFT-Eval (0.674 MASE, 0.454 CRPS) compared to TSFMs and exhibits superior in-domain and out-of-domain numerical as well as reasoning performance on TFRBench. Specifically, STRIDE acts as a plug-and-play enhancement, consistently improving diverse TSFMs (e.g., Chronos-2, Timer-S1) across various LLM configurations. Thus, injecting semantic reasoning as a continuous prior equips TSFMs with human-interpretable reasoning while fundamentally improving predictive accuracy.

Recent advances in multimodal time series learning underscore a paradigm shift from analytics centered on basic patterns toward advanced time series understanding and reasoning. However, existing multimodal time series datasets mostly remain at the level of surface alignment and question answering, without reaching the depth of genuine reasoning. The absence of well-defined tasks that genuinely require time series reasoning, along with the scarcity of high-quality data, has limited progress in building practical time series reasoning models (TSRMs). To this end, we introduce Time Series Reasoning Suite (TSR-Suite), which formalizes four atomic tasks that span three fundamental capabilities for reasoning with time series: (1) perception, acquired through scenario understanding and causality discovery; (2) extrapolation, realized via event-aware forecasting; and (3) decision-making, developed through deliberation over perception and extrapolation. TSR-Suite is the first comprehensive time series reasoning suite that supports not only thorough evaluation but also the data pipeline and training of TSRMs. It contains more than 23K samples, of which 2.3K are carefully curated through a human-guided hierarchical annotation process. Building on this foundation, we introduce TimeOmni-1, the first unified reasoning model designed to address diverse real-world problems demanding time series reasoning. The model is trained in multiple stages, integrating a mixture of task scenarios, novel reward functions, and tailored optimizations. Experiments show that TimeOmni-1 delivers strong out-of-distribution generalization across all tasks and achieves a high rate of valid responses. It significantly improves causality discovery accuracy (64.0% vs. 35.9% with GPT-4.1) and raises the valid response rate by over 6% compared to GPT-4.1 on the event-aware forecasting task.

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.

In this paper, we introduce PredBench, a benchmark tailored for the holistic evaluation of spatio-temporal prediction networks. Despite significant progress in this field, there remains a lack of a standardized framework for a detailed and comparative analysis of various prediction network architectures. PredBench addresses this gap by conducting large-scale experiments, upholding standardized and appropriate experimental settings, and implementing multi-dimensional evaluations. This benchmark integrates 12 widely adopted methods with 15 diverse datasets across multiple application domains, offering extensive evaluation of contemporary spatio-temporal prediction networks. Through meticulous calibration of prediction settings across various applications, PredBench ensures evaluations relevant to their intended use and enables fair comparisons. Moreover, its multi-dimensional evaluation framework broadens the analysis with a comprehensive set of metrics, providing deep insights into the capabilities of models. The findings from our research offer strategic directions for future developments in the field. Our codebase is available at https://github.com/OpenEarthLab/PredBench.

Multivariate time series forecasting (MTSF) endeavors to predict future observations given historical data, playing a crucial role in time series data management systems. With advancements in large language models (LLMs), recent studies employ textual prompt tuning to infuse the knowledge of LLMs into MTSF. However, the deployment of LLMs often suffers from low efficiency during the inference phase. To address this problem, we introduce TimeKD, an efficient MTSF framework that leverages the calibrated language models and privileged knowledge distillation. TimeKD aims to generate high-quality future representations from the proposed cross-modality teacher model and cultivate an effective student model. The cross-modality teacher model adopts calibrated language models (CLMs) with ground truth prompts, motivated by the paradigm of Learning Under Privileged Information (LUPI). In addition, we design a subtractive cross attention (SCA) mechanism to refine these representations. To cultivate an effective student model, we propose an innovative privileged knowledge distillation (PKD) mechanism including correlation and feature distillation. PKD enables the student to replicate the teacher's behavior while minimizing their output discrepancy. Extensive experiments on real data offer insight into the effectiveness, efficiency, and scalability of the proposed TimeKD.

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.

Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present Proceed, a novel proactive model adaptation framework for online time series forecasting. Proceed first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, Proceed is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that Proceed brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at https://github.com/SJTU-DMTai/OnlineTSF.

Cross-domain generalization is very important in Time Series Forecasting because similar historical information may lead to distinct future trends due to the domain-specific characteristics. Recent works focus on building unimodal time series foundation models and end-to-end multimodal supervised models. Since domain-specific knowledge is often contained in modalities like texts, the former lacks the explicit utilization of them, thus hindering the performance. The latter is tailored for end-to-end scenarios and does not support zero-shot inference for cross-domain scenarios. In this work, we introduce Aurora, a Multimodal Time Series Foundation Model, which supports multimodal inputs and zero-shot inference. Pretrained on Corss-domain Multimodal Time Series Corpus, Aurora can adaptively extract and focus on key domain knowledge contained in corrsponding text or image modalities, thus possessing strong Cross-domain generalization capability. Through tokenization, encoding, and distillation, Aurora can extract multimodal domain knowledge as guidance and then utilizes a Modality-Guided Multi-head Self-Attention to inject them into the modeling of temporal representations. In the decoding phase, the multimodal representations are used to generate the conditions and prototypes of future tokens, contributing to a novel Prototype-Guided Flow Matching for generative probabilistic forecasting. Comprehensive experiments on well-recognized benchmarks, including TimeMMD, TSFM-Bench and ProbTS, demonstrate the consistent state-of-the-art performance of Aurora on both unimodal and multimodal scenarios.