ICML 2026 Papers

Inference time optimization techniques, such as repeated sampling, have significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, the critical role of model uncertainty remains largely underexplored in these optimization strategies. In this paper, we investigate the dynamics of confidence along reasoning trajectories and for first time reveal a surprising and unique pattern: correct answer traces tend to exhibit confidence improvement over time (positive confidence gain), while incorrect traces show attenuated or declining confidence as reasoning proceeds. Based on this observation, we propose Confidence Dynamic Gain (CDG) based voting, which incorporates how the confidence trajectory of the response evolves along the reasoning chain. Experiments across four open-source architectures (DeepSeek-R1, gpt-oss, Gemma-3, Qwen-QwQ) on the AIME24/25, HMMT25, and BRUMO25 benchmarks demonstrate that CDG yields a significant performance boost over baselines. These results demonstrate that our method provides a robust discriminative signal for improving answer selection in LLM reasoning. We also provide theoretical insights for this phenomenon. Code will be released at https://github.com/Accenture/CDG.git.

Graph-based attention deficit hyperactivity disorder (ADHD) detection methods have been extensively studied, but comparatively less attention has been paid to short-term brain functional reorganization. In this paper, we propose an ADHD disease detection model based on short- and long-term brain function encoding and memory graph network. We first exploit a novel brain map sequence construction method based on short-term windows to extract short-term brain function features. Then, we design a short-term state and temporal dependency encoder to characterize short-term sequence patterns of brain function. Furthermore, a brain function memory is introduced to capture the association of brain activity patterns and historical sequence patterns. Concurrently, GNN-based long-term brain function feature extraction network is used to extract brain structure features, which are fused with short-term features for ADHD detection. Experimental validation on the publicly available neuroimaging datasets ADHD-200 and OpenNeuro-ds002424 demonstrates the superior performance of our model in brain disorder detection.

Irregular time series arise ubiquitously in real-world systems, where observations are sparse, asynchronous, and governed by underlying continuous-time dynamics. Existing continuous–discrete state-space models typically rely on path-based variational inference, which is computationally expensive or constrained by restrictive posterior assumptions. We propose SDEVI, a novel framework that performs variational inference directly on the joint distribution over discrete-time observations, while guaranteeing consistency with an underlying continuous process governed by a Stochastic Differential Equation(SDE). SDEVI employs a variational posterior induced by linear time-varying SDEs as a scalable inference backbone. To enable intricate dynamics modeling for real-world data, we introduce non-linear-SDE-induced variational inference and generalize our framework to the complex domain. Extensive experiments across healthcare, physics, climate, and IoT benchmarks demonstrate state-of-the-art performance on interpolation, extrapolation, regression, and classification tasks.

Although causal discovery from multivariate time series is widely used, it remains challenging under noise. Convergent cross mapping (CCM) infers causality by reconstructing shadow manifolds via time-delay embedding (TDE) and evaluating cross-map skill between manifolds. Despite Takens’ theorem guarantees in ideal settings, TDE effectively attempts to recover system state from a single noisy view, often yielding geometrically degraded manifolds and unreliable distance-based neighborhoods, which in turn weakens causal identification. We propose TopoDistill, a topology-informed knowledge distillation framework that improves univariate shadow-manifold reconstruction by aligning local neighborhood structure to a multivariate system representation. A global embedder trained on multivariate observations captures a global attractor representation, while a delay embedder is distilled to produce embeddings whose neighborhood distributions match the global topology. This cross-view alignment yields smoother and more reliable neighborhoods, improving cross mapping under noise while maintaining specificity against spurious correlations. Theoretical analysis and experimental results demonstrate that our method enables effective causal discovery.

Battery lifetime early prediction is crucial for safety assessment and decision planning, yet early-stage degradation signals are extremely weak and difficult to distinguish from stochastic noise. Existing methods primarily rely on denoising or signal decomposition, which may lose critical degradation cues. In nature, most organisms exhibit the binaural effect, exploiting discrepancies between left and right auditory inputs to enhance perceptual reliability. Inspired by this, we propose DITING, a weak degradation listener for battery lifetime early prediction. We first employ optimal-transport-based selective matching to extract a robust health template from initial cycles, and further design a tri-coupled degradation manifestation mechanism to distinguish degradation signals from noise. By exploiting the randomness of noise, matched responses under symmetric coupling suppress stochastic fluctuations, while degradation-driven cumulative deviations propagate through the coupling process to form stable bilateral discrepancies, thereby amplifying weak early-stage cues for lifetime prediction. Experiments on various datasets demonstrate that DITING achieves state-of-the-art performance and provides more reliable early support for full-lifecycle battery management.

Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven Multivariate Time Series (MTS) models, or (ii) map IMTS onto regular temporal grids through interpolation, which may distort temporal dynamics by introducing artificial values. To address these limitations, we propose a new input-embedding-based approach. We identify that the key bottleneck lies not in the backbone architecture, but in conventional embedding layers that assume uniform sampling. In this work, we introduce QuITE (Query-Based Irregular Time Series Embedding), a simple yet effective plug-and-play embedding module for IMTS. QuITE employs learnable query tokens to aggregate irregular observations through a single self-attention layer, directly producing backbone-compatible latent representations without artificial value generation or architectural modification. Extensive experiments on real-world benchmarks show that QuITE consistently improves MTS models, yielding average relative gains of up to 54.7% in forecasting and 15.8% in classification across diverse datasets and backbone architectures.

Conformal prediction is challenging for time series with time-varying conditional distributions. Existing sequential conformal methods can yield volatile, non-nested prediction intervals due to noisy tail conditional quantile estimation and quantile crossing issue. To overcome these challenges, we construct prediction intervals for time series via a novel method called Conditional Quantile Adjusted Conformal Prediction (CQACP), which stabilizes sequential conformal calibration by modeling the conditional quantile curve of nonconformity score. At each time step, CQACP evaluates a base conditional quantile learner on a grid of quantile levels and fits a Cornish--Fisher approximation parameterized by conditional moments of nonconformity score with monotonicity constraints. Asymptotically, we prove the conditional validity of the prediction interval under serial dependence and show improved conditional quantile estimation accuracy. Experiments on multiple real-world datasets demonstrate that CQACP maintains accurate coverage and produces smooth, narrow, and nested prediction intervals across different significance levels and prediction models.

Autoregressive generative models for irregularly sampled clinical time-series data are increasingly used for zero-shot risk forecasting. Prior work typically adopts a single fine-grained discretization of time, where tokens are generated at one fixed, predetermined temporal resolution. We demonstrate that the zero-shot accuracy of individual generative forecasters varies with temporal resolution: performance can degrade when the model resolution is poorly matched to the temporal dynamics of the endpoint being evaluated. We then propose MoRGen (Mixture-of-Resolutions Generation), which fuses forecasts from generative experts trained at multiple temporal resolutions using a low-capacity task-specific mixture, improving performance across tasks with different temporal dynamics. Across multiple horizons and outcomes on three independent clinical datasets, MoRGen achieves lower binary cross-entropy (BCE) and statistically significant AUROC gains over autoregressive generative models that forecast tokens at a fixed temporal resolution.

Modeling dynamic dependencies from irregularly sampled event sequences is a fundamental challenge in modern machine learning. In many real-world systems, individual-level states evolve continuously over time while being simultaneously influenced by population-level dynamics. However, existing methods typically model these processes in isolation or rely on discrete-time approximations that fail to capture long-range temporal irregularities and sparse observations. This paper studies the problem of learning coupled continuous-time latent dynamics from irregular events, where individual event sequences and global distributional processes evolve asynchronously and interact over time. We propose a Coupled Continuous-Time Latent Dynamics (CoCLD) framework that jointly models individual latent dynamics and population-level distributional shifts, and aligns them in a continuous-time latent space. CoCLD integrates a Diffusion-based Latent Interpolator with neural ordinary differential equations, enabling principled interpolation, generation, and alignment of latent states across arbitrary time points. We show that the proposed coupling mechanism yields a consistent estimator of continuous-time latent dynamics under sparse and irregular observations. Empirical evaluations show CoCLD effectively captures dynamic dependencies and generalizes across tasks like next-event prediction, mobility trajectory generation, and sequential behavior modeling, indicating that learning coupled continuous-time latent dynamics is a powerful paradigm for irregular event sequence modeling.

Transformers have been established as the most popular backbones in sequence modeling, mainly due to their effectiveness in in-context retrieval tasks and the ability to learn at scale. Their quadratic memory and time complexity, however, bound their applicability in longer sequences and so has motivated researchers to explore effective alternative architectures such as modern recurrent neural networks (a.k.a long-term recurrent memory module). Despite their recent success in diverse downstream tasks, they struggle in tasks that requires long context understanding and extrapolation to longer sequences. We observe that these shortcomings come from three disjoint aspects in their design: (1) limited memory capacity that is bounded by the architecture of memory and feature mapping of the input; (2) online nature of update, i.e., optimizing the memory only with respect to the last input; and (3) less expressive management of their fixed-size memory. To enhance all these three aspects, we present Atlas, a long-term memory module with high capacity that learns to memorize the context by optimizing the memory based on the current and past tokens, overcoming the online nature of long-term memory models. Our experimental results on language modeling, common-sense reasoning, recall-intensive, and long-context understanding tasks support the effectiveness of Atlas compared to other modern recurrent neural networks.

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.

Tokenization is a key component of autoregressive (AR) generative models, converting raw data into more manageable units for modeling. Commonly, tokens describe local information, such as regions of pixels in images or word pieces in text, and AR generation predicts these tokens in a fixed order. A worthwhile question is whether token structures affect the ability to steer the generation through test-time search, where multiple candidate generations are explored and evaluated by a verifier. Using image generation as our testbed, we hypothesize that recent 1D ordered tokenizers with coarse-to-fine structure can be more amenable to search than classical 2D grid structures. This is rooted in the fact that the intermediate states in coarse-to-fine sequences carry semantic meaning that verifiers can reliably evaluate, enabling effective steering during generation. Through controlled experiments, we find that AR models trained on coarse-to-fine ordered tokens exhibit improved test-time scaling behavior compared to grid-based counterparts. Moreover, we demonstrate that, thanks to the ordered structure, pure test-time search over token sequences (i.e., without training an AR model) can perform training-free text-to-image generation when guided by an image-text verifier. Beyond this, we systematically study how classical search algorithms (best-of-$N$, beam search, lookahead search) interact with different token structures, as well as the role of different verifiers and AR priors.

Graph prompt tuning has shown great potential in graph learning by introducing trainable prompts to enhance the model performance in conventional single-domain scenarios. Recent research has extended graph prompts to improve Graph Foundation Models (GFMs) by few-shot tuning auxiliary prompts. Despite their progress, most existing methods embed source-domain information into prompts, which serve either as input to GFMs or encoded during model pre-training. Such prompt entanglement with specific source domains and GFM pre-training strategy restricts their generalisability to other domains and different GFMs. Furthermore, existing GFM prompts merely rely on few-shot tuning for adaptation, neglecting the rich information in unlabelled target domain test data. Motivated by these insights, this paper aims to empower GFMs with pre-training-agnostic test-time graph prompt tuning, named GFMate. GFMate introduces centroid and layer prompts applied after pre-training on target domains, avoiding entanglement with specific source domains and model pre-training. In addition, a test-time complementary learning objective is devised to exploit both labelled and unlabelled target domain data for effective test-time prompt tuning. Extensive experiments on 12 benchmark datasets demonstrate the superior performance and efficiency of GFMate, achieving improvements of up to 30.63%. Code is available at https://github.com/YanJiangJerry/GFMate.

Irregular multivariate time series (IMTS) forecasting is challenging due to non-uniform sampling and variable asynchronicity. These irregularities violate the equidistant assumptions of standard models, hindering local temporal modeling and rendering classical frequency-domain methods ineffective for capturing global periodic structures. To address this challenge, we propose TFMixer, a joint time–frequency modeling framework for IMTS forecasting. Specifically, TFMixer incorporates a Global Frequency Module that employs a learnable Non-Uniform Discrete Fourier Transform (NUDFT) to directly extract spectral representations from irregular timestamps. In parallel, the Local Time Module introduces a query-based patch attention mechanism to adaptively aggregate informative temporal segments and alleviate information density imbalance. Finally, TFMixer fuses the time-domain and frequency-domain representations to generate forecasts and further leverages inverse NUDFT for explicit seasonal extrapolation. Extensive experiments on real-world IMTS benchmarks demonstrate the effectiveness and robustness of TFMixer under irregular sampling and missing data.

Probabilistic forecasting with exogenous variables is vital for decision-making but remains underexplored compared to deterministic methods. We propose KITE, a knowledge-guided probabilistic modeling framework designed to bridge this gap by addressing two key bottlenecks: (1) topological disparity in sampling initialization and (2) spurious covariate correlations during the iterative conditional generation process. KITE introduces a *History-Conditional Manifold* to construct an informative source distribution from historical dynamics, effectively anchoring the starting point closer to the target space. Additionally, a *Knowledge-Guided Conditioning* module is developed to regularize variable interactions using statistical priors, suppressing spurious correlations and enhancing the robustness of covariate conditioning. Extensive experiments demonstrate that KITE outperforms state-of-the-art methods in both deterministic and probabilistic forecasting.

Time series imputation benefits from leveraging cross-feature correlations, yet existing attention-based methods re-discover feature relationships at each layer, lacking persistent anchors to maintain consistent representations. To address this, we propose HELIX, which assigns each feature a learnable feature identity, a persistent embedding that captures intrinsic semantic properties throughout the network. Unlike graph-based methods that rely on predefined topology and assume homogeneous spatial relationships, HELIX learns arbitrary feature dependencies end-to-end from temporal co-variation, naturally handling datasets where features mix spatial locations with semantic variables. Integrated with hybrid temporal-feature attention, HELIX achieves the state-of-the-art performance, surpassing all 16 baselines on 5 public datasets across 21 experimental settings in our evaluation. Furthermore, our mechanistic analysis reveals that HELIX aligns learned feature identities and dependencies with latent physical and semantic structure progressively across layers, demonstrating that it more effectively translates cross-feature structure into imputation accuracy.

Large Language Models have shown strong capabilities in interpreting multimodal data but remain limited in handling time-series data. Addressing this gap could help to translate longitudinal and wearable data into actionable insights and patient-facing digital health applications. We propose OpenTSLM, an open-source family of Time Series Language Models integrating time-series as a native modality into pretrained LLMs, enabling natural-language prompting and reasoning over multiple time-series via either soft prompting (OpenTSLM-SoftPrompt) or cross-attention (OpenTSLM-Flamingo). To enable training models for time-series reasoning, we introduce three datasets: HAR-CoT (human activity recognition), Sleep-CoT (sleep staging), and ECG-QA-CoT (electrocardiogram question answering). Across tasks, OpenTSLM models outperform baselines, reaching F1 scores of 69.88% in sleep staging and 67.64% in HAR; OpenTSLM-Flamingo also scales more efficiently in memory as the number and length of time series increase. Expert evaluations with cardiologists show that OpenTSLMs exhibit strong reasoning capabilities on raw ECG data.

Time series foundation models rely on large-scale pretraining over diverse datasets across domains, yet their heterogeneity in temporal patterns could hinder the effectiveness of training and learning transferable time series representations. Inspired a fundamental concept, normalized power spectral density (PSD) in signal processing, we assume harmonizing datasets via PSDs in the spectral domain could reduce mismatches and enhance pretraining. We then go beyond the direct intractable minimization optimization and innovatively reformulate it as a principled harmonization approach. Specifically, we propose Harmonizer, a module that reshapes spectral structures and implicitly harmonizing PSDs across datasets, which theoretically corresponds to a shared reparameterization of second-order temporal correlations. Our theoretical analysis further reveals token interactions with Harmonizer can be efficiently mediated by a compact set of resonators, motivating a HarmonicAttention design that performs self-attention in a low-dimensional interaction space. Then, we propose Olivia, a novel time series foundation model built upon these harmonization mechanisms. Extensive experiments on several large-scale benchmarks (TSLib, GIFT-Eval, and GluonTS), demonstrate Olivia consistently achieves state-of-the-art performance under zero-shot, few-shot, and full-shot forecasting scenarios. Our code is at \url{https://github.com/TSTS13/Olivia}.

Federated Learning (FL) enables privacy-preserving collaboration among distributed clients in open-world environments, but its performance often degrades under data heterogeneity and unpredictable distribution shifts. Test-Time Adaptation (TTA) has recently been introduced into FL to leverage unlabeled data from unseen clients for online adaptation. However, most existing federated TTA methods employ local feature statistics, which can be brittle under diverse and severe distribution shifts. In this work, we observe that despite significant variations in feature distributions, the relational structure among class prototypes—termed *prototype affinity topology*—remains remarkably stable across heterogeneous clients. Building on this insight, we propose FedPAT, a **Fed**erated TTA framework that leverages **P**rototype **A**ffinity **T**opology as a cross-client structural prior. FedPAT learns a global PAT by aggregating class prototypes from source clients, capturing consensus inter-class relationships that are robust to local distribution variations. For unseen target clients, we design a topology-aware mechanism that enhances predictions via diffusion of the global PAT, fuses them with parametric outputs, and performs lightweight optimization for robust test-time adaptation. Extensive experiments demonstrate that FedPAT consistently outperforms advanced federated TTA and classical TTA methods across various distribution shifts.