NeurIPS 2026 Papers

Multivariate time-series forecasting requires reliable cross-series interaction, yet many attention- and mixing-based models couple heterogeneous variables without explicit entry-stage alignment. Such uncalibrated early interaction can lead to poorly conditioned optimization and degraded generalization when cross-series statistics drift. We propose First-layer Statistical Calibration (FISC), a simple framework that imposes statistical calibration constraints only on the first cross-series coupling layer while leaving deeper coupling layers learnable without repeated calibration. FISC estimates training-set cross-series statistics, converts them into a statistical affinity matrix, and convexly fuses this matrix with learnable coupling parameters. A row-wise simplex projection then yields a nonnegative row-stochastic mixing operator, providing bounded and interpretable entry-layer interaction. By restricting calibration to the first layer, FISC calibrates the entrance interaction without repeatedly constraining deeper feature transformations. To reduce temporal redundancy, FISC further combines a time-domain branch with a data-adaptive orthogonal-domain branch derived from training-time temporal statistics. Experiments on standard long- and short-term forecasting benchmarks show that FISC improves forecasting accuracy while maintaining favorable efficiency. Ablations and non-stationarity analyses further show that first-layer-only calibration consistently outperforms no calibration, last-layer calibration, and all-layer calibration, supporting a simple principle for robust cross-series learning: constrain the entrance interaction with training-set statistics, while letting deeper representations remain data-adaptive.

Air quality prediction at unmonitored locations is challenging because historical AQI observations are unavailable, while conventional spatiotemporal models largely rely on target histories to learn spatial dependencies. Meanwhile, widely available weather covariates provide useful station-specific evidence for target-absent inference. In this paper, we propose \textbf{ExtrapAir}, a lightweight weather-bridged framework for air quality inference at unmonitored locations. ExtrapAir preserves variable-specific weather patterns through per-variable weather encoding and learns adaptive weather and AQI correlations for spatial transfer. To support robust inference, we introduce \textbf{Activation Attention with Prior Inductive Biases}, which enables non-competitive spatial aggregation, incorporates geographic and semantic priors for station-pair guidance, and avoids full station-to-station attention computation for scalability. Extensive experiments on five real-world air-quality datasets against \textbf{32} baselines show that ExtrapAir reduces MAE by up to \textbf{15.24\%} overall and \textbf{16.01\%} on unmonitored stations, while cutting training time by \textbf{84.9\%} and memory usage by \textbf{76.23\%}, achieving a strong accuracy--efficiency trade-off.

As the demand to integrate Artificial Intelligence into high-stakes environments continues to grow, explaining the reasoning behind neural-network predictions has shifted from a theoretical curiosity to a strict operational requirement. Our work is motivated by the explanations of autoregressive neural predictions on dynamic physical fields, as in weather forecasting. Gradient-based feature attribution methods are widely used to explain the predictions on such data, in particular due to their scalability to high-dimensional inputs. It is also interesting to remark that gradient-based techniques such as SmoothGrad are now standard on images to robustify the explanations using pointwise averages of the attribution maps obtained from several noised inputs. Our goal is to efficiently adapt this aggregation strategy to dynamic physical fields. To do so, our first contribution is to identify a fundamental failure mode when averaging perturbed attribution maps on dynamic physical fields: stochastic input perturbations do not induce stationary amplitude noise in attribution maps, but instead cause a geometric displacement of the attributions. Consequently, pointwise averaging blurs these spatially misaligned features. To tackle this issue, we introduce WassersteinGrad, which extracts a geometric consensus of perturbed attribution maps by computing their entropic Wasserstein barycenter. The results, obtained on regional weather data and a meteorologist-validated neural model, demonstrate promising explainability properties of WassersteinGrad over gradient-based baselines across both single-step and autoregressive forecasting settings.

In time-series forecasting, rollout errors are not merely one-step fitting discrepancies: once fed back into the evolving state, they can perturb future predictions. We formalize this effect through local rollout consistency, which compares the next prediction produced under teacher forcing with that produced under free running. In principle, this consistency can be enforced directly by tracking the residual-induced perturbation of the next state. In practice, however, the residual-to-state alignment operator is often difficult to design when the input state and output block have different dimensions, heterogeneous components, or architecture-dependent layouts. We therefore use a first-order local surrogate that penalizes the Jacobian-vector product of the predictor along the actual feedback perturbation, suppressing precisely the directions through which self-generated errors remain visible to future predictions. We further give the same loss a geometric interpretation near a predictive manifold: by controlling residual-induced directions that probe the normal bundle, the objective yields theoretical conditions under which free-running trajectories remain inside a stability tube around the manifold. Experiments on time series forecasting tasks support this view, showing that the proposed regularization improves predictive accuracy. More broadly, our results suggest a training principle for time-series forecasters and sequential predictors: a model should not only make small one-step errors, but also learn not to let its own errors echo into the future.

Earth Observation (EO) forecasting aims to predict future Earth surface dynamics from satellite observations under changing meteorological conditions. In this paper, we view this task as a partially observed, weather-driven world modeling problem, in which weather acts as a conditioning signal, while forecasting remains uncertain due to sparse observations and unobserved land-surface states. However, existing methods do not fully capture this setting: deterministic models collapse uncertainty into a single future prediction, while diffusion-based methods typically treat weather variables as undifferentiated conditioning signals, and existing benchmarks focus mainly on reconstruction accuracy rather than whether forecasts respond correctly to changed weather forcing. We introduce EO-WM, a video diffusion transformer for multispectral EO forecasting. EO-WM incorporates a physically informed conditioning framework that represents meteorological forcing through a climatological baseline, weather anomalies, and cumulative physical stress signals. Specifically, it separates baseline and anomaly through distinct conditioning pathways, and accumulates anomalous forcing over time to capture sustained heat and drought stress. To evaluate weather-response behavior beyond standard metrics, we introduce two diagnostic benchmarks: an Extreme Summer Benchmark for severity-aware prediction of vegetation degradation under extreme weather, and a Seasonal Matched-Pair Benchmark for testing response fidelity under changed weather forcing. Experiments show that EO-WM reduces the error in predicted Normalized Difference Vegetation Index (NDVI) decline amplitude by a relative 5.63\% and improves directional hit rate by a relative 7.80\%, while remaining competitive on standard pixel-level metrics.

The quadratic attention cost of Vision Transformers (ViTs) forces a sharp compromise between discretization and rollout horizon, and binds tightest in the fine-scale PDE regime where shocks, reaction fronts, and material interfaces occupy a small, time-varying fraction of the domain. Further, conventional neural surrogates do not adapt to localized features dynamically. We propose WAMRViT, a ViT that tokenizes its input as a balanced quadtree under a wavelet-inspired refinement criterion, encodes position and refinement level jointly via a 3D rotary positional embedding with a soft level axis, and regrids in cell space at inference to remain stable over long rollouts. A multi-scale variant additionally keeps each leaf at its native source resolution and defers the per-level resolution differential to the model. Unlike prior adaptive-tokenization work, the tokenizer imposes no a priori token count; we evaluate under fully adaptive topology over long autoregressive rollouts; and WAMRViT is the first machine-learning surrogate to natively tokenize multi-level Adaptive Mesh Refinement (AMR) data. We demonstrate that on uniform-grid datasets, WAMRViT exceeds a finest-patch uniform backbone on the region of interest while using a fraction of the tokens, with a structural interpolation cost on the global metric that the multi-scale variant closes at the initial rollout steps. On a complex AMR combustion problem whose extremely fine scale features uniform-grid baselines cannot represent natively and must project onto a coarser grid, WAMRViT operates directly on the adaptive cells and substantially reduces finest-level error at matched parameters. Code: https://anonymous.4open.science/r/wamrvit-review-74E1

Quantifying uncertainty in time series forecasting is particularly demanding because sequential data exhibit temporal dependence and are prone to distributional changes. Conformal inference has emerged as a powerful uncertainty quantification approach through the construction of prediction sets. Recent advances have introduced online conformal methods that adaptively adjust prediction thresholds through feedback mechanisms. However, the existing feedback mechanism typically relies solely on miscoverage indicators (actual feedback)—whether the true label falls within the interval at each time step—while overlooking the empirical prediction threshold (estimated feedback) that is derived from the oracle conformal method. In this paper, we propose $\textit{Dynamic Dual-feedback Conformal Inference}$ (DDCI), which incorporates a dual-feedback mechanism consisting of $\textit{actual feedback}$ and $\textit{estimated feedback}$. The former drives the primary adjustment of the intervals based on true observations, while the latter dampens excessive expansions or contractions by leveraging empirical thresholds from conformal inference during updates. By balancing these two signals, DDCI achieves more stable and narrower prediction intervals in sequential settings while adhering to the target coverage rate in practice.

Long-horizon forecasting of dynamical time series remains a fundamental challenge in machine learning, as accurate predictions require learning the underlying dynamics. While recent time-series foundation models leveraging in-context learning (ICL) have shown promise, we show that they fail to genuinely capture the governing dynamics. By rewriting the context of a time series as a collection of lagged input-output pairs, we frame dynamical time-series forecasting as a posterior inference problem over the space of structural causal models (SCMs), arguing that the underlying dynamic structure is a natural inductive bias. We propose DynaPFN, which uses pretrained tabular Prior-Fitted Networks (PFNs) to approximate this posterior through ICL, augmented with a library of dynamical features that permit simpler representations of complex systems. Even though the pretrained models have never seen time series data, DynaPFN outperforms existing zero-shot forecasting baselines on established benchmarks of chaotic time series and real-world datasets, demonstrating that incorporating structural priors over system dynamics is a valid approach for robust long-horizon forecasting.

Diffusion models have become a widely used framework for probabilistic time series forecasting, modeling the distribution of future values given an observed history. In time series forecasting, however, the future continues the observed history, creating an asymmetry the standard diffusion process leaves unaddressed, with slowly-varying content largely determined by the observed continuity while higher-frequency dynamics carry most of the residual uncertainty. Existing diffusion-based forecasters decouple this asymmetry through an external rule before generation, leaving the corruption trajectory blind to which parts of the target the history can already anchor. We propose \textsc{DiffDiff}, a diffusion framework that embeds this predictability asymmetry into the diffusion trajectory itself, so that a single end-to-end diffusion process becomes aware of which parts of the target the history can already anchor. \textsc{DiffDiff} makes the forward operator step-dependent so that the noisy intermediate state progressively shifts from the target itself toward its second-order differenced structure, while a conditioning pathway supplies the denoiser with both value-domain and differential history information balanced by a stage-adaptive gate at each diffusion step. The terminal distribution approaches a standard Gaussian, preserving compatibility with existing samplers. On seven benchmarks across four prediction horizons, \textsc{DiffDiff} outperforms six diffusion baselines, and our analysis confirms that \textsc{DiffDiff} concentrates the diffusion's generative effort on the most uncertain components of the target while relieving it from rebuilding the history-anchored content.

Probabilistic time series forecasting requires modeling and predicting complex and time-varying distributions. Recently, Denoising Diffusion Probabilistic Model~(DDPM)-based approaches have shown promise by equipping the diffusion process with pretrained mean and variance estimators to accommodate distributional shift. However, these methods typically follow the standard DDPM framework and consider only partial components of the evidence lower bound (ELBO), treating the training of estimators as designed regression tasks separate from the variational inference framework. To address this, we rethink the ELBO under the Location-Scale Noise Model (LSNM) and find that it naturally induces a Gaussian negative log likelihood objective for the estimators and inherently defines a joint training objective that unifies recent the diffusion paradigms for probabilistic forecasting. Building on this principled ELBO reformulation, we propose DiffPTS, a general framework that enables end-to-end optimization of all components within the ELBO. Across multiple benchmarks, DiffPTS consistently outperforms recent models, achieving state-of-the-art performance with an average CRPS/MSE reduction of over 14.53\%/16.55\% compared to existing diffusion-based methods. The code is provided at \url{https://anonymous.4open.science/r/DiffPTS}.

Long-horizon time series forecasting requires a careful balance between predictive accuracy and computational cost. Segmented temporal modeling has therefore become a practical strategy for reducing the burden of long-range prediction. However, real-world time series often contain superposed multi-periodic components, whose spectral structures vary across time, variables, and samples. Such variability limits fixed aggregation or frequency-modeling mechanisms, making them less adaptive to non-stationary periodic patterns and potentially causing informative components to be attenuated over long forecasting horizons. To address this limitation, we propose DSR-TSF, a spectrum-driven dynamic routing framework for long-horizon forecasting. DSR-TSF adaptively selects and combines multiple period-specific branches conditioned on the spectral characteristics of the input sequence, thereby improving the model's ability to capture non-stationary periodic structures. It further learns period-aware dynamic weights to modulate the contributions of multi-periodic patterns while retaining the segmented prediction structure. Without complex resampling or explicit period alignment, DSR-TSF provides a compact mechanism for modeling spectral heterogeneity and achieves competitive performance across seven datasets with diverse dimensionalities and temporal characteristics.

Real-world time series typically exhibit non-uniform information density across temporal positions, frequency structures, and forecasting horizons: critical dynamics are concentrated in local segments, different frequency components carry different structural information, and different horizons require different modeling complexity. However, most existing methods still allocate computation approximately uniformly across these dimensions, leading to redundant computation in low-information regions and insufficient modeling of key patterns. To address this, we propose BucpTSF, an information-density-driven structured framework for time series forecasting. Specifically, BucpTSF reorganizes raw sequences into hierarchically heterogeneous multi-level token representations through information-density-aware temporal representation reorganization, captures key cross-token dependencies with low overhead via frequency-selective structured token interaction, and further introduces horizon-conditioned structured extrapolation to adaptively balance dynamic modeling and structural extrapolation bias for different horizons, thereby improving the accuracy and stability of long-term forecasting. Extensive experiments on real-world datasets show that BucpTSF consistently outperforms strong baselines under various forecasting settings, validating the effectiveness of information-density-driven non-uniform computation allocation for time series forecasting.

AI weather models are fast and skillful, yet their errors are strongly conditional because the best member changes with lead time, variable, initialization state, and atmospheric regime. Operational deterministic multi-model forecasting therefore requires more than averaging strong forecasters. It requires anticipating which member deserves trust before future analyses exist. BlendCast turns this anticipation problem into a vision-language forecasting task. Given meteorological maps and structured ensemble diagnostics, the model reads the current weather situation, reasons about prospective member reliability, and converts that judgment into deterministic per-variable ensemble weights. To teach this behavior, BlendCast first gives the model demonstrations of what member-skill reasoning and weight decisions should look like, then refines the resulting policy with multi-variable reinforcement learning so that its own analyses are rewarded when they lead to better, physically consistent forecasts. On held-out 2025 forecasts, BlendCast reduces WRMSE by 2.6\% over equal weighting and by 2.0% over conventional ensemble post-processing, closing 63.2% of the gap to oracle blending. These results show that, with multimodal weather evidence and reward-aligned training, VLMs can act as real-time forecasters of forecasters for deterministic AI weather ensembles. Project and demo:https://anonymous.4open.science/status/BlendCast-2567

Current multivariate time series forecasting methods mainly rely on static linear decoders, but these often suffer from severe representational bottlenecks. In this paper, we propose a novel architecture called DecodeTS (\textbf{\underline{D}}ynamic \textbf{\underline{E}}xpert-\textbf{\underline{C}}oupled \textbf{\underline{O}}ptimal \textbf{\underline{DE}}coder for Time Series Forecasting), which replaces the conventional static prediction head with a heterogeneous expert library. DecoderTS adopts a divide-and-conquer strategy to disentangle complex temporal dynamics, such as long-term trends and abrupt changes. Crucially, we introduce an optimal transport (OT)-based dynamic routing mechanism that can adaptively assign customized combinations of experts to different variables. By imposing OT marginal constraints, DecoderTS is theoretically proven to achieve collaborative load balancing among experts and effectively eliminate representation collapse. Extensive experiments on more than \textbf{15} datasets and about \textbf{30} baselines demonstrate that DecoderTS achieves state-of-the-art forecasting accuracy, which delivers a \textbf{17.06\%} performance gain while attaining up to about \textbf{41×} inference time speedup and up to \textbf{3.61×} reduction in memory footprint.

Cyber-physical system (CPS) forecasting models depend on sensor streams with noisy, biased, missing, or temporally misaligned readings, yet standard forecasting evaluation often selects models by nominal error without showing whether they remain robust under such faults. We introduce SensorFault-Bench, a shared CPS-grounded sensor-fault stress-test protocol for evaluating forecasting architectures and robustness-improvement methods, together with an operational taxonomy that organizes the method comparison. Across four real-world datasets and eight scored scenarios governed by a standardized severity model, it reports worst-scenario degradation, clean mean squared error (MSE), and worst-scenario fault-time MSE, separating relative robustness from absolute error. A disjoint fault-transfer split lets explicit fault-training methods train on adjacent fault families while reported scores use separate benchmark scenarios. Empirically, forecasting architectures favored by clean MSE can degrade sharply under faults, and clean-MSE rankings can disagree with worst-scenario fault-time error rankings. Chronos-2, the evaluated zero-shot foundation-model representative, matches or trails the last-value naive forecaster in clean MSE on the two single-target datasets and has the largest worst-scenario degradation on ETTh1 and Traffic, where all channels are forecast targets. For the evaluated robustness-improvement method set, paired deltas show selective degradation reductions: projected gradient descent adversarial training and randomized training lead where value faults dominate observed degradation, while fault augmentation leads where availability faults dominate. SensorFault-Bench provides open-source code, documented data access, and reproduction and extension guides, so new datasets, architectures, and robustness-improvement methods can be evaluated under the same CPS sensor-fault robustness protocol.

Multivariate weather time series are a central modality for forecasting and decision support, and the surrounding language increasingly mediates how numerical weather is consumed by users and downstream models. However, existing pipelines depend on closed-source language model ensembles with expert quality control or on retrieving human-curated text, while prior caption-RL rewards optimize cycle similarity or downstream-task utility, neither of which can tell a captioner that a confidently asserted phenomenon is contradicted by the data, so the absence of an executable, station-observable, and refutation-aware reward signal has blocked the application of self-play RL to this scientific modality. To address this, we propose AtmoZero, a post-training framework that trains a weather-time-series captioner without a single human-written caption, by aligning a language model with a library of seven station-observable scientific verifiers, pairing them with an explicit refutation channel that penalizes caption claims the data contradicts, and combining them with auxiliary reconstruction and forecaster-utility rewards under group-relative policy optimization. Extensive empirical results on a twelve-year ERA5 reanalysis corpus and real-world surface observations show that AtmoZero attains the lowest unsupported-claim rate and forecasting error at every horizon, outperforming closed-source captioners, dense-reward RL, and far-larger foundation models, with extensive analyses confirming that these gains arise from multiple complementary signals and are robust under distribution shift.

Accurate real-time forecasting of atmospheric pollutants is essential for reducing exposure risks and improving public health. Traditional numerical forecasting systems suffer from incomplete parameterizations, uncertain inputs, and high computational cost. Existing deep learning approaches improve efficiency, but often entangle meteorological and pollutant variables within unified forecasting frameworks, limiting flexibility and pollutant-specific representation learning. To address these challenges, we propose AirMPA, a decoupled autoregressive framework for meteorology-to-pollution forecasting. AirMPA predicts 13 atmospheric pollutants at 0.4$^\circ$ spatial resolution and 12-h temporal resolution using meteorological fields, emission priors, and historical pollutant concentrations. The model is built on an improved Swin-Transformer architecture with zonal release attention and dual-branch fusion, enabling more effective modeling of global transport continuity and heterogeneous pollutant dynamics. During training, AirMPA uses ERA5 reanalysis as meteorological forcing, while during inference it directly ingests forecast fields from external meteorological models, enabling stable autoregressive prediction up to 5 days ahead. Experiments show that AirMPA consistently outperforms Aurora and surpasses CAMS in approximately 90\% of pollutant--lead-time evaluation cases over the 5-day forecast horizon, while outperforming CAMS on all variables beyond 48 h. These results demonstrate the potential of decoupled meteorology-to-pollution forecasting for global air quality prediction.

Spatial-temporal (ST) forecasting underpins many real-world systems such as traffic, climate, and energy networks. While existing methods implicitly assume strong spatiotemporal coupling, we observe that real-world ST data exhibits distinct coupling regimes, ranging from temporal-dominated and spatial-dominated to strongly coupled patterns. This mismatch causes current models to suffer from spurious dependencies and degraded performance when one correlation dominates. To overcome this limitation, we aim to dynamically modulate spatial and temporal modeling based on the data's inherent coupling structure. However, three key challenges exist: unknown coupling structure, heterogeneous coupling dynamics, and suboptimal spatial modeling. We propose AdaST, an adaptive ST forecasting framework that tackles these challenges through a decompose-recompose paradigm. AdaST factorizes inputs into components capturing different coupling patterns using heterogeneity-aware experts. Each component is processed by role-aligned modules, and a correlation-informed adaptive recomposer integrates them for final prediction. Extensive experiments confirm that AdaST significantly outperforms state-of-the-art baselines, validating the necessity of an adaptive approach.

Neural surrogate benchmarks for spatiotemporal PDEs are dominated by idealized test beds with periodic boundaries and synthetic dynamics. Architecture rankings established on these benchmarks do not transfer to real atmospheric chemistry, and standard regression metrics conceal the failure modes that determine operational utility. AQBench evaluates ten architectures across five model families on high-resolution WRF-Chem simulations of $PM_2.5$, $NO_2$, and $CO$ over the Indian subcontinent, against five operationally-grounded objectives: long-horizon stability, exceedance detection, extreme-episode bias, advection-diffusion residuals, and multi-pollutant forecasting. Three findings emerge. Spectral neural operators, the strongest family on canonical PDE benchmarks, rank in the bottom four on 168 hour RMSE here. Models that lead on aggregate regression underestimate during extreme pollution episodes and miss the majority of true exceedance events. Joint training on $PM_2.5$, $NO_2$, and $CO$ improves $PM_2.5$ accuracy across most architectures with no parameter increase, with Transolver gaining 21\% at 168th hour. The dataset, evaluation framework, and trained baselines are released.