ICML 2026 Papers

Unlike conventional "black-box" transformers with classical self-attention mechanisms, we build a lightweight and interpretable transformer-like neural network by unrolling a mixed-graph-based optimization algorithm to forecast traffic with spatial and temporal dimensions. We construct two graphs: an undirected graph $\mathcal{G}^u$ capturing spatial correlations across geography, and a directed graph $\mathcal{G}^d$ capturing sequential relationships over time. We predict future samples of signal $\mathbf{x}$, assuming it is "smooth" with respect to both $\mathcal{G}^u$ and $\mathcal{G}^d$, where we design new $\ell_2$- and $\ell_1$-norm variational terms to quantify and promote signal smoothness (low-frequency reconstruction) on a directed graph. We design an iterative algorithm based on alternating direction method of multipliers (ADMM), and unroll it into a feed-forward network for data-driven parameter learning. We periodically insert graph learning modules for $\mathcal{G}^u$ and $\mathcal{G}^d$ that play the role of self-attention. Experiments show that our unrolled networks achieve competitive traffic forecast performance as state-of-the-art prediction schemes, while reducing parameter counts drastically. Code: https://github.com/SingularityUndefined/Unrolling-GSP-STForecast.

We introduce \textsc{Mosaic}, a probabilistic weather forecasting model that addresses two sources of spectral degradation in ML-based weather prediction: training to predict the ensemble mean deterministically and compressive encoding creating an information bottleneck. \textsc{Mosaic} combines learned functional perturbations for ensemble forecasting with block-sparse attention, a hardware-aligned formulation that shares keys and values across spatially adjacent queries, enabling each block to dynamically attend to the most relevant regions. By capturing arbitrarily long-range dependencies at linear cost, \textsc{Mosaic} processes high-resolution weather data without compression. On IFS HRES data, \textsc{Mosaic} at 1.5° resolution matches or outperforms models trained on 0.25° data, with individual ensemble members exhibiting near-perfect spectral alignment across all resolved frequencies.

Incorporating textual information into time-series forecasting holds promise for addressing event- driven non-stationarity; however, a fundamental modality gap hinders effective fusion: textual descriptions express temporal impacts implicitly and qualitatively, whereas forecasting models rely on explicit and quantitative signals. Through controlled semi-synthetic experiments, we show that existing methods over-attend to redundant tokens and struggle to reliably translate textual semantics into usable numerical cues. To bridge this gap, we propose TESS, which introduces a Temporal Evolution Semantic Space as an intermediate bottleneck between modalities. This space consists of interpretable, numerically grounded temporal primitives—distribution shift, volatility, shape, and lag—extracted from text by an LLM via structured prompting and filtered through confidence-aware gating. Experiments on four real-world datasets demonstrate up to a 29% reduction in forecasting error compared to state-of-the-art unimodal and multimodal baselines. Code is available at: https://github.com/olivia3395/TESS.

Most existing time-series forecasters are trained end-to-end with backpropagation, which often increases computational cost and limits structural transparency. As a result, it remains difficult to trace how their predictions are formed. This paper presents FIPN, a forward self-organizing interpretable polynomial network for time-series forecasting. FIPN grows its architecture layer by layer through candidate generation, closed-form estimation, and validation-based selection, without relying on backpropagation-based optimization. Each neuron couples a fuzzy rule antecedent with a Fourier-enhanced polynomial consequent: fuzzy clustering softly partitions the input space and produces interpretable rule weights for local regimes, while the consequent retains access to original features and uses Fourier functions to capture periodic and frequency-related structures. Since forward growth may introduce redundancy, collinearity, and overfitting as depth increases, FIPN further incorporates regularized node scoring, dropout-based redundancy control, and persistent access to raw inputs. Experiments on long-horizon forecasting benchmarks show that FIPN achieves competitive accuracy with a compact model size, while the learned fuzzy rules provide rule- and structure-level explanations. These results suggest that forward self-organizing polynomial networks offer a practical balance among accuracy, efficiency, and interpretability for long-horizon forecasting.

Time series foundation models (TSFMs) have demonstrated impressive generalization capabilities across diverse domains. However, they face significant challenges in long-term and ultra long-term forecasting. These challenges primarily arise from scalability limitations when TSFMs process extensive sequence lengths. To address this, we propose SPRINT, a training-free plug-and-play framework designed to empower TSFMs to see more, forecast better and faster during inference. The core idea is to perform forecasting in a downsampled-resolution space, enabling an extended look-back window with reduced computational costs. To avoid information loss and resolution mismatch caused by downsampling, SPRINT decomposes time series into trend and seasonal components, processing them separately. It predicts the low-frequency trend via a Resolution Interpolation workflow within the downsampled space, while preserving high-frequency details through a Pattern Replication mechanism for seasonality. Extensive experiments show that SPRINT achieves a significant improvement, increasing accuracy by 19\% while enhancing efficiency with a reduction of max memory usage by 6.4$\times$ and inference time by 16.9$\times$ compared to state-of-the-art TSFMs.

Accurate climate forecasting provides critical support for decision-making in agriculture, energy, and disaster preparedness. Current deterministic models often fail to capture climate uncertainty, while existing generative approaches oversimplify the system by neglecting key spatiotemporal dependencies and cross-scale interactions. To address these limitations, we introduce ClimateAR, an AutoRegressive generative model for probabilistic seasonal-to-interannual Climate forecasting. The framework incorporates two novel components: (1) an aligned tokenizer that bridges and aligns heterogeneous simulation and real-world data to improve transferability across domains, and (2) a mixed-scale conditioning mechanism that captures multi-scale climate interactions for robust probabilistic forecasting. Extensive evaluations on the ERA5 reanalysis dataset show that ClimateAR achieves state-of-the-art performance, improving anomaly correlation skill by 37.56\% on average compared to leading baselines.

While deep learning is facing an homogenization across modalities led by Transformers, they are still challenged by shallow linear models in the time series forecasting task. Our hypothesis is that models should learn a direct link from past to future data points, which we identify as a learning dynamics capability. We develop an original $\texttt{PRO-DYN}$ nomenclature to analyze existing models through the lens of dynamics. Two observations thus emerge: **1.** under-performing architectures learn dynamics at most partially, **2.** the location of the dynamics block at the model end is of prime importance. Our systemic and empirical studies both confirm our observations on a set of performance-varying models with diverse backbones. We propose a simple plug-and-play methodology guiding model designs and improvements.

Time Series Foundation Models (TSFMs) have achieved strong performance in univariate time series forecasting. However, most TSFMs rely on channel-independent pre-training that models each variable separately, limiting their ability to leverage inter-channel information that is crucial in real-world multivariate systems. Motivated by this limitation, we propose ChaTSFM, a lightweight plug-and-play channel adapter that allows frozen TSFMs to leverage multivariate correlations in a zero-shot setting. ChaTSFM first builds a budgeted pre-training dataset to cover diverse heterogeneous inter-channel dependency patterns. It then uses data-derived domain descriptors to learn a dataset-conditioned inter-channel similarity measure that reduces cross-domain metric distortion. Finally, it injects sparse inter-channel information via gated refinement, leveraging multivariate information without degrading intra-channel temporal dynamics. Extensive experiments on nine benchmarks validate the effectiveness of ChaTSFM, demonstrating consistent zero-shot improvements over four best-performing TSFMs while maintaining scalable deployment. Code is available at Code is available at https://github.com/Clearloveyuan/ChaTSFM.

The increasing impact of climate change and extreme weather events has spurred growing interest in deep learning for weather research. However, existing studies often rely on weather data in pixel space, which presents several challenges such as smooth outputs in model outputs, limited applicability to a single pressure-variable subset (PVS), and high data storage and computational costs. To address these challenges, we propose a novel Weather Latent Autoencoder (WLA) that transforms weather data from pixel space to latent space, enabling efficient data representation. By decoupling weather reconstruction from downstream tasks, WLA improves the accuracy and sharpness of weather task model results. The incorporated Pressure-Variable Unified Module transforms multiple PVS into a unified representation, enhancing the adaptability of the model in multiple weather scenarios. Furthermore, weather tasks can be performed in a low-storage latent space of WLA rather than a high-storage pixel space, thus significantly reducing data storage and computational costs. Through extensive experimentation, we demonstrate its superior compression and reconstruction performance, enabling the creation of the ERA5-Latent dataset with unified representations of multiple PVS from ERA5 data. The compressed full PVS in the ERA5-Latent dataset reduces the original 244.34 TB of data to 0.43 TB. The downstream task further demonstrates that task models can apply to multiple PVS with low data costs in latent space and achieve superior performance compared to models in pixel space.

Context-aided forecasting (CAF) holds promise for integrating domain knowledge and forward-looking information, enabling AI systems to surpass traditional statistical methods. However, recent empirical studies reveal a puzzling gap: multimodal models often fail to outperform their unimodal counterparts. We hypothesize that this underperformance stems partly from insufficiently verified context usefulness in existing datasets. To address these limitations, we introduce a semi-synthetic data augmentation method that generates contexts both descriptive of temporal dynamics and verifiably complementary to numerical histories. This approach enables massive-scale dataset creation, resulting in CAF-7M, a corpus of 7 million context-augmented time series windows, including a rigorously verified test set. We demonstrate that semi-synthetic pre-training transfers effectively to real-world evaluation, and show clear evidence of context utilization. Our results suggest that dataset quality is a major bottleneck in context-aided forecasting, and that verified context can substantially improve the usefulness of CAF training data.

Mainstream methods for multivariate time-series forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing forecasting reliability. To address this issue, we propose L-Drive, a change-aware forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between forecasting accuracy and computational efficiency.

Multivariate time-series forecasting (MTSF) learns from high-dimensional covariates with strong temporal dependence, periodic structure, and cross-variable correlations. While modern pipelines often mitigate non-stationarity through instance-wise normalization and decomposition, these interventions operate at the data level and do not directly control dependence that can emerge among the parameters during training. We study MTSF optimization from a parameter-decorrelation viewpoint. Modeling stochastic optimization as a Markov chain in parameter space and leveraging its stochastic differential equation interpretation, we use the per-step transition-variance induced by gradient noise as a tractable signal for optimization-induced dependence and update uncertainty. This signal can empirically inflate during training; we theoretically show that such inflation can degrade generalization diagnostics. Motivated by this mechanism, we propose transition-variance alignment (TVA), an architecture-agnostic procedure that regulates transition-variance by smoothly gating the step size based on the mismatch between an estimated noise scale and a chosen target. TVA maintains effective transition-variance near a prescribed scale without architectural changes, incurs negligible overhead, and integrates seamlessly with diverse methods. Across real-world multivariate benchmarks, TVA consistently improves forecasting accuracy.

Time series forecasting under non-stationarity faces a fundamental tension between capturing stable representations and adapting to distribution shifts. Existing methods implicitly rely on static historical assumptions, leading to a critical failure mode we term *Phase Amnesia*, where models become blind to the evolving global context. To resolve this, we formalize non-stationary dynamics through three physical hypotheses: wold decomposition, dynamical phase evolution, and heteroscedastic manifold generation. These principles inspire **PULSE**, a physics-informed, plug-and-play framework adopting a *Disentangle--Evolve--Simulate* design philosophy. Specifically, PULSE utilizes phase-anchored disentanglement to resolve optimization interference caused by dominant trends, employs a Phase Router to actively generate future trajectories, and introduces Statistic-Aware Mixup (SAM) to ensure robustness against out-of-distribution volatility. Empirically, PULSE enables a simple MLP backbone to achieve state-of-the-art or highly competitive performance across 12 real-world benchmarks. This validates that a correct physics-informed inductive bias is far more critical than raw architectural complexity for non-stationary forecasting. The code is available at: https://github.com/Gemost/PULSE.

Existing time series tokenization methods predominantly encode a constant number of samples into individual tokens. This inflexible approach can generate excessive tokens for even simple patterns like extended constant values, resulting in substantial computational overhead. Inspired by the success of byte pair encoding, we propose the first pattern-centric tokenization scheme for time series analysis. Based on a discrete vocabulary of frequent motifs, our method merges samples with underlying patterns into tokens, compressing time series adaptively. Exploiting our finite set of motifs and the continuous properties of time series, we further introduce conditional decoding as a lightweight yet powerful post-hoc optimization method, which requires no gradient computation and adds no computational overhead. On recent time series foundation models, our motif-based tokenization improves forecasting performance by 40% and boosts efficiency by 2314% on average. Conditional decoding further reduces MSE by up to 48%. In an extensive analysis, we demonstrate the adaptiveness of our tokenization to diverse temporal patterns, its generalization to unseen data, and its meaningful token representations capturing distinct time series properties, including statistical moments and trends.

In the era of increasingly complex AI models for time series forecasting, progress is often measured by marginal improvements on benchmark leaderboards. However, standard evaluations rely on aggregate metrics (e.g., MSE) that conflate model capability with the intrinsic difficulty of the evaluated instances. To address this, we propose a diagnostic framework anchored in **Spectral Coherence Predictability (SCP)**, which provides an efficient $\mathcal{O}(N\log N)$ per-instance difficulty reference and yields a corresponding linear MSE lower bound. Complementing this, we introduce the **Linear Utilization Ratio (LUR)** to quantify how effectively models exploit linearly predictable structures across frequencies. Experiments on synthetic and real-world benchmarks show that SCP aligns strongly with realized forecasting errors across diverse state-of-the-art forecasters. Using this lens, we uncover ``predictability drift,'' revealing that task difficulty is not static but fluctuates significantly over time and variables. Furthermore, stratified evaluation exposes complementary architectural strengths across distinct frequency bands and difficulty regimes. Overall, we advocate moving beyond leaderboard-style ranking toward a more insightful, predictability-aware evaluation that fosters fairer model comparisons and a deeper understanding of model behavior. Code and data are available at https://github.com/WanjinVon/TS_Predictability.

Time series forecasting (TSF) plays a critical role in decision-making for many real-world applications. Recently, large language model (LLM)- based forecasters have made promising advancements. Despite their effectiveness, existing methods often lack explicit experience accumulation and continual evolution. In this work, we propose MemCast, a learning-to-memory framework that reformulates TSF as an experience-conditioned reasoning task. Specifically, we learn experience from the training set and organize it into a hierarchical memory. This is achieved by summarizing prediction results into historical patterns, distilling inference trajectories into reasoning wisdom, and inducing extracted temporal features into general laws. Furthermore, during inference, we leverage historical patterns to guide the reasoning process and utilize reasoning wisdom to select better trajectories, while general laws serve as criteria for reflective iteration. Additionally, to enable continual evolution, we design a dynamic confidence adaptation strategy that updates the confidence of individual entries without leaking the test set distribution. Extensive experiments on multiple datasets demonstrate that MemCast consistently outperforms previous methods, validating the effectiveness of our approach. Our code is available at https://github.com/Xiaoyu-Tao/MemCast-TS.

Coupled spatiotemporal forecasting is important for predicting the future evolution of multiple interacting dynamical systems, such as in climate models. However, existing methods are severely constrained by the persistent bottleneck of compounding errors. In coupled systems, errors from each subsystem simulator propagate and amplify one another, a phenomenon we term Reciprocal Error Amplification leading to a rapid collapse of long-range predictions. To address this challenge, we propose a universal framework called PnP-Corrector (Plug-and-Play Corrector). The core idea of our framework is to decouple the physical simulation from the error correction process: it freezes pre-trained physics simulation engines and exclusively trains a correction agent to proactively counteract the systematic biases emerging from the coupled system. Furthermore, we design an efficient predictive model architecture, DSLCast, to serve as the backbone of this framework. Extensive experiments demonstrate that our method significantly enhances the long-term stability and accuracy of coupled forecasting systems. For instance, in the challenging task of a 300-day global ocean-atmosphere coupled forecast, our PnP-Corrector framework reduces the prediction error of the baseline model by 28% and surpasses state-of-the-art models on several key metrics. Codes link: https://github.com/Alexander-wu/PnP-Corrector.

Deep learning has revolutionized weather forecasting, but many challenges remain, including climate modeling. Moreover, the current landscape remains fragmented: highly specialized models are typically trained individually for distinct tasks. To unify this landscape, we introduce WIND, a single pre-trained foundation model capable of replacing specialized baselines across a vast array of tasks. Crucially, in contrast to previous atmospheric foundation models, we achieve this without any task-specific fine-tuning. To learn a robust, task-agnostic prior of the atmosphere, we pre-train WIND with a self-supervised video reconstruction objective, utilizing an unconditional video diffusion model to iteratively reconstruct atmospheric dynamics from a noisy state. At inference, we frame diverse domain-specific problems strictly as inverse problems and solve them via posterior sampling. This unified approach allows us to tackle highly relevant weather and climate problems, including probabilistic forecasting, spatial and temporal downscaling, reconstruction of spatial fields from sparse observations and enforcing global dry air mass conservation. We further demonstrate how WIND can be applied to explore extreme weather events under prescribed out-of-distribution thermodynamic perturbations. By combining generative video modeling with inverse problem solving, WIND offers a computationally efficient alternative for AI-based atmospheric modeling.

The development of Time-Series Forecasting (TSF) models is often constrained by the lack of comprehensive datasets, especially in Global Station Weather Forecasting (GSWF), where existing datasets are small, temporally short, and spatially sparse. To address this, we introduce WEATHER-5K, a large-scale observational weather dataset that better reflects real-world conditions and supports improved model training and evaluation. While recent TSF methods perform well on benchmarks, they still lag behind operational Numerical Weather Prediction (NWP) systems in capturing complex weather dynamics and extreme events. We propose PhysicsFormer, a physics-informed forecasting model that combines a dynamic core with a Transformer residual to predict future weather states. Physical consistency is enforced via pressure–wind alignment and energy-aware smoothness losses, ensuring plausible dynamics while capturing complex temporal patterns. We benchmark PhysicsFormer and other TSF models against operational systems across several weather variables, extreme event prediction, and model complexity, providing a comprehensive assessment of the gap between academic TSF models and operational forecasting. The dataset and benchmark implementation are available at: https://github.com/taohan10200/WEATHER-5K.