ICLR 2026 论文列表

Despite the flourishing in time series (TS) forecasting backbones, the training mostly relies on regression losses like Mean Square Error (MSE). However, MSE assumes a one-mode Gaussian distribution, which struggles to capture complex patterns, especially for real-world scenarios where multiple diverse outcomes are possible. We propose the Multi-Mode Patch Diffusion (MMPD) loss, which can be applied to any patch-based backbone that outputs latent tokens for the future. Models trained with MMPD loss generate diverse predictions (modes) with the corresponding probabilities. Technically, MMPD loss models the future distribution with a diffusion model conditioned on latent tokens from the backbone. A lightweight Patch Consistent MLP is introduced as the denoising network to ensure consistency across denoised patches. Multi-mode predictions are generated by a multi-mode inference algorithm that fits an evolving variational Gaussian Mixture Model (GMM) during diffusion. Experiments on eight datasets show its superiority in diverse forecasting. Its deterministic and probabilistic capabilities also match the strong competitor losses, MSE and Student-T, respectively.

Transformers have demonstrated strong performance in time series forecasting, yet they often fail to capture the intrinsic structure of temporal data, making them susceptible to real-world noise and anomalies. Unlike in vision or language, the local geometry of temporal patterns is a critical feature in time series forecasting, but it is frequently disrupted by corruptions. In this work, we address this gap with two key contributions. First, we propose Local Geometry Attention (LGA), a novel attention mechanism theoretically grounded in local Gaussian process theory. LGA adapts to the intrinsic data geometry by learning query-specific distance metrics, enabling it to model complex temporal dependencies and enhance resilience to noise. Second, we introduce TSRBench, the first comprehensive benchmark for evaluating forecasting robustness under realistic, statistically-grounded corruptions. Experiments on TSRBench show that LGA significantly reduces performance degradation, consistently outperforming both Transformer and linear model. These results establish a foundation for developing robust time series models that can be deployed in real-world applications where data quality is not guaranteed. Our code is available at: https://anonymous.4open.science/r/LGA-5454.

With the rapid growth of spatio-temporal data fueled by IoT deployments and urban infrastructure expansion, accurate and efficient continual forecasting has become a critical challenge. Most existing Spatio-Temporal Graph Neural Networks rely on static graph structures and offline training, rendering them inadequate for real-world streaming scenarios characterized by graph expansion and distribution shifts. Although Continual Spatio-Temporal Forecasting methods have been proposed to tackle these issues, they often adopt backbones with limited modeling capacity and lack effective mechanisms to balance stability and adaptability. To overcome these limitations, we propose STBP, a novel framework that integrates a general spatio-temporal backbone with a scalable contextual pattern bank. The backbone extracts stable representations in the frequency domain and captures dynamic spatial correlations through lightweight linear graph attention. To support continual adaptation and mitigate catastrophic forgetting, the contextual pattern bank is updated incrementally via parameter expansion, enabling the capture of evolving node-level heterogeneity and relevance. During incremental training, the backbone remains fixed to preserve general knowledge, while the pattern bank adapts to new scenarios and distributions. Extensive experiments demonstrate that STBP outperforms state-of-the-art baselines in both forecasting accuracy and scalability, validating its effectiveness for continual spatio-temporal forecasting. Code is available at https://github.com/Aoyu-Liu/STBP.

Accurate weather forecasting is crucial for climate research, disaster mitigation, and societal planning. Despite recent progress with deep learning, global atmospheric data remain uniquely challenging since weather dynamics evolve across heterogeneous spatial and temporal scales ranging from planetary circulations to localized phenomena. Capturing such cross-scale interactions within a unified framework remains an open problem. To address this gap, we propose \textbf{STORM}, a spatio-temporal model that disentangles atmospheric variations into multiple scales to uncover scale-specific dependencies. In addition, it enables coherent forecasting across multiple resolutions, maintaining consistent temporal evolution. Experiments on benchmark datasets demonstrate that STORM consistently delivers superior performance across both global and regional settings, as well as for short- and long-term forecasts.

Irregular Multivariate Time Series (IMTS) are characterized by uneven intervals between consecutive timestamps, which carry sampling pattern information valuable and informative for learning temporal and variable dependencies. In addition, IMTS often exhibit diverse dependencies across multiple time scales. However, many existing multi-scale IMTS methods use resampling to obtain the coarse series, which can alter the original timestamps and disrupt the sampling pattern information. To address the challenge, we propose ReIMTS, a **Re**cursive multi-scale modeling approach for **I**rregular **M**ultivariate **T**ime **S**eries forecasting. Instead of resampling, ReIMTS keeps timestamps unchanged and recursively splits each sample into subsamples with progressively shorter time periods. Based on the original sampling timestamps in these long-to-short subsamples, an irregularity-aware representation fusion mechanism is proposed to capture global-to-local dependencies for accurate forecasting. Extensive experiments demonstrate an average performance improvement of 27.1\% in the forecasting task across different models and real-world datasets. Our code is available at [https://github.com/Ladbaby/PyOmniTS](https://github.com/Ladbaby/PyOmniTS).

While deep learning has achieved impressive performance in time series forecasting, it becomes increasingly crucial to understand its decision-making process for building trust in high-stakes scenarios. Existing interpretable models often provide only local and partial explanations, lacking the capability to reveal how heterogeneous and interacting input variables jointly shape the overall temporal patterns in the forecast curve. We propose ProtoTS, a novel interpretable forecasting framework that achieves both high accuracy and transparent decision-making through modeling prototypical temporal patterns. ProtoTS computes instance-prototype similarity based on a denoised representation that preserves abundant heterogeneous information. The prototypes are organized hierarchically to capture global temporal patterns with coarse prototypes while capturing finer-grained local variations with detailed prototypes, enabling expert steering and multi-level interpretability. Experiments on multiple realistic benchmarks, including a newly released LOF dataset, show that ProtoTS not only exceeds existing methods in forecast accuracy but also delivers expert-steerable interpretations for better model understanding and decision support. The source code is available at https://anonymous.4open.science/r/ProtoTS-D791/.

Accurate prediction of extreme wind velocities has substantial significance in industry, particularly for the operation management of wind power plants. Although the state-of-the-art data-driven models perform well for general meteorological forecasting, they may exhibit large errors for extreme weather—for example, systematically underestimating the magnitudes and short-term variation of extreme winds. To address this issue, we conduct a theoretical analysis of how the data frequency spectrum influences errors in extreme wind prediction. Based on these insights, we propose a novel loss function that incorporates a gradient penalty to mitigate the magnitude shrinkage of extreme weather, and we theoretically justify its effectiveness via a PDE-based energy–enstrophy analysis. To capture more precise short-term wind velocity variations, we design a novel structure of physics-embedded machine learning models with frequency reweighting. Experiments demonstrate that, compared to the baseline models, our approach achieves significant improvements in predicting extreme wind velocities while maintaining robust overall performance.

Time series forecasting plays a significant role in finance, energy, meteorology, and IoT applications. Recent studies have leveraged the generalization capabilities of large language models (LLMs) to adapt to time series forecasting, achieving promising performance. However, existing studies focus on token-level modal alignment, instead of bridging the intrinsic modality gap between linguistic knowledge structures and time series data patterns, greatly limiting the semantic representation. To address this issue, we propose a novel Semantic-Enhanced LLM (SE-LLM) that explores the inherent periodicity and anomalous characteristics of time series to embed into the semantic space to enhance the token embedding. This process enhances the interpretability of tokens for LLMs, thereby activating the potential of LLMs for temporal sequence analysis. Moreover, existing Transformer-based LLMs excel at capturing long-range dependencies but are weak at modeling short-term anomalies in time-series data. Hence, we propose a plugin module embedded within self-attention that models long-term and short-term dependencies to effectively adapt LLMs to time-series analysis. Our approach freezes the LLM and reduces the sequence dimensionality of tokens, greatly reducing computational consumption. Experiments demonstrate the superiority performance of our SE-LLM against the state-of-the-art (SOTA) methods.

Solving primitive equations is essential for accurate weather forecasting. However, traditional numerical weather prediction (NWP) methods often incorporate various simplifications that limit their effectiveness in parameterizing unresolved physical processes. Meanwhile, existing deep learning-based models mostly focus on pure data-driven paradigms, overlooking the fundamental physical principles that govern atmospheric dynamics. To address these challenges, we present DeepPrim, a novel 3D \underline{deep} weather forecaster designed to learn \underline{prim}itive equations of the Earth’s atmosphere. Specifically, DeepPrim aims at accurately modeling 3D atmospheric motion through Navier-Stokes equation in pressure coordinates, and effectively capturing the interactions between the solved advection and key weather variables (e.g., temperature and water vapor) through corresponding equations. By seamlessly integrating fundamental atmospheric physics with advanced data-driven techniques, our model effectively approximates complicated physical processes without relying on empirical simplifications. Experimentally, DeepPrim achieves impressive performance in both short-term global and regional weather forecasting tasks, and exhibits the superior capacity to capture 3D atmospheric dynamics. The code is available at https://github.com/DAMO-DI-ML/DeepPrim.

Exogenous variables offer valuable supplementary information for predicting future endogenous variables. Forecasting with exogenous variables needs to consider both past-to-future dependencies (i.e., temporal correlations) and the influence of exogenous variables on endogenous variables (i.e., channel correlations). This is pivotal when future exogenous variables are available, because they may directly affect the future endogenous variables. Many methods have been proposed for time series forecasting with exogenous variables, focusing on modeling temporal and channel correlations. However, most of them use a two-step strategy, modeling temporal and channel correlations separately, which limits their ability to capture joint correlations across time and channels. Furthermore, in real-world scenarios, recorded time series are frequently affected by various forms of noises, underscoring the critical importance of robustness in such correlations modeling. To address these limitations, we propose GCGNet, a Graph-Consistent Generative Network for time series forecasting with exogenous variables. Specifically, GCGNet first employs a Variational Generator to produce coarse predictions. A Graph Discriminator then further guides it by evaluating the consistency between the generated and true correlations, where the correlations are represented as graphs, and are robust to noises. Finally, a Graph Refiner is proposed to refine the predictions to prevent degeneration and improve accuracy. Extensive experiments on 12 real-world datasets demonstrate that GCGNet outperforms state-of-the-art baselines.

Time-series forecasting is an essential task with wide real-world applications across domains. While recent advances in deep learning have enabled time-series forecasting models with accurate predictions, there remains considerable debate over which architectures and design components, such as series decomposition or normalization, are most effective under varying conditions. Existing benchmarks primarily evaluate models at a high level, offering limited insight into why certain designs work better. To mitigate this gap, we propose TIMERECIPE, a unified benchmarking framework that systematically evaluates time-series forecasting methods at the module level. TIMERECIPE conducts over 10,000 experiments to assess the effectiveness of individual components across a diverse range of datasets, forecasting horizons, and task settings. Our results reveal that exhaustive exploration of the design space can yield models that outperform existing state-of-the-art methods and uncover meaningful intuitions linking specific design choices to forecasting scenarios. Furthermore, we release a practical toolkit within TIMERECIPE that recommends suitable model architectures based on these empirical insights.

Accurate Subseasonal-to-Seasonal (S2S) forecasting is vital for decision-making in agriculture, energy production, and emergency management. However, it remains a challenging and underexplored problem due to the chaotic nature of the weather system. Recent data-driven studies have shown promising results, but their performance is limited by the inadequate incorporation of climate states and a model tendency to degrade, progressively losing fine-scale details and yielding over-smoothed forecasts. To overcome these limitations, we propose TianQuan-S2S, a global S2S forecasting model that integrates initial weather states with climatological means via incorporating climatology into patch embedding and enhancing variability capture through an uncertainty-augmented Transformer. Extensive experiments on the Earth Reanalysis 5 (ERA5) reanalysis dataset demonstrate that our model yields a significant improvement in both deterministic and ensemble forecasting over the climatology mean, traditional numerical methods, and data-driven models. Ablation studies empirically show the effectiveness of our model designs. Remarkably, our model outperforms skillful numerical ECMWF-S2S and advanced data-driven Fuxi-S2S in key meteorological variables. The code implementation can be found in https://github.com/zhangminglang42/TianQuan.

Many methods aim to enhance time series forecasting by decomposing the series through intricate model structures and prior knowledge, yet they are inevitably limited by computational complexity and the robustness of the assumptions. Our research uncovers that in the complex domain and higher-order hypercomplex spaces, the characteristic frequencies of time series naturally decrease. Leveraging this insight, we propose Numerion, a time series forecasting model based on multiple hypercomplex spaces. Specifically, grounded in theoretical support, we generalize linear layers and activation functions to hypercomplex spaces of arbitrary power-of-two dimensions and introduce a novel Real-Hypercomplex-Real Domain Multi-Layer Perceptron (RHR-MLP) architecture. Numerion utilizes multiple RHR-MLPs to map time series into hypercomplex spaces of varying dimensions, naturally decomposing and independently modeling the series, and adaptively fuses the latent patterns exhibited in different spaces through a dynamic fusion mechanism. Experiments validate the model’s performance, achieving state-of-the-art results on multiple public datasets. Visualizations and quantitative analyses comprehensively demonstrate the ability of multi-dimensional RHR-MLPs to naturally decompose time series and reveal the tendency of higher-dimensional hypercomplex spaces to capture lower-frequency features.