ICLR 2026 论文列表

While test-time scaling with verification has shown promise in improving the performance of large language models (LLMs), role of the verifier and its imperfections remain underexplored. The effect of verification manifests through interactions of three quantities: (i) the generator’s *coverage*, (ii) the verifier’s *region of convergence* (ROC), and (iii) the sampling algorithm’s *sub-optimality*. Though recent studies capture subsets of these factors, a unified framework quantifying the geometry of their interplay is missing. We frame verifiable test-time scaling as a transport problem. This characterizes the interaction of coverage, ROC, and sub-optimality, and uncovers that the sub-optimality–coverage curve exhibits three regimes. A *transport regime* -- where sub-optimality increases with coverage, a *policy improvement regime* -- where sub-optimality may decrease with coverage, depending on the verifier’s ROC, and a *saturation regime* -- where sub-optimality plateaus, unaffected by coverage. We further propose and analyze two classes of sampling algorithms -- *sequential* and *batched*, and examine how their computational complexities shape these trade-offs. Empirical results with \texttt{Qwen}, \texttt{Llama}, and \texttt{Gemma} models corroborate our theoretical findings.

The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral decomposition, offering a natural framework for comparison. We propose a novel approach representing each system as a distribution of its joint operator eigenvalues and spectral projectors and defining a metric between systems leveraging optimal transport. The proposed metric is invariant to the sampling frequency of trajectories. It is also computationally efficient, supported by finite-sample convergence guarantees, and enables the computation of Fréchet means, providing interpolation between dynamical systems. Experiments on simulated and real-world datasets show that our approach consistently outperforms standard operator-based distances in machine learning applications, including dimensionality reduction and classification, and provides meaningful interpolation between dynamical systems.

With the growing demand for high-quality image generation on resource-constrained devices, efficient diffusion models have received increasing attention. However, such models suffer from approximation errors introduced by efficiency techniques, which significantly degrade generation quality. Once deployed, these errors are difficult to correct, as modifying the model is typically infeasible in deployment environments. Through an analysis of error propagation across diffusion timesteps, we reveal that these approximation errors can accumulate exponentially, severely impairing output quality. Motivated by this insight, we propose Iterative Error Correction (IEC), a novel test-time method that mitigates inference-time errors by iteratively refining the model’s output. IEC is theoretically proven to reduce error propagation from exponential to linear growth, without requiring any retraining or architectural changes. IEC can seamlessly integrate into the inference process of existing diffusion models, enabling a flexible trade-off between performance and efficiency. Extensive experiments show that IEC consistently improves generation quality across various datasets, efficiency techniques, and model architectures, establishing it as a practical and generalizable solution for test-time enhancement of efficient diffusion models. The code is available at https://github.com/zysxmu/IEC.

Language models demonstrate remarkable abilities when pre-trained on large text corpora and fine-tuned for specific tasks, but how and why pre-training shapes the success of the final model remains poorly understood. Notably, although pre-training success is often quantified by cross entropy loss, cross entropy can be poorly predictive of downstream performance. Instead, we provide a theoretical perspective on this relationship through the lens of coverage, which quantifies the probability mass the pre-trained model places on high-quality responses and which is necessary and sufficient for post-training and test-time scaling methods like Best-of-N to succeed. Our main results develop an understanding of the coverage principle, a phenomenon whereby next-token prediction implicitly optimizes toward a model with good coverage. In particular, we uncover a mechanism that explains the power of coverage in predicting downstream performance: coverage generalizes faster than cross entropy, avoiding spurious dependence on problem dependent parameters such as the sequence length. We also study practical algorithmic interventions with provable benefits for improving coverage, including (i) model/checkpoint selection procedures, (ii) gradient normalization schemes, and (iii) test-time decoding strategies.

Optimizing the timing and frequency of advertisements (ads) is a central problem in digital advertising, with significant economic consequences. Existing scheduling policies rely on simple heuristics, such as uniform spacing and frequency caps, that overlook long-term user interest. However, it is well-known that users' long-term interest and engagement result from the interplay of several psychological effects (Curmei, Haupt, Recht, and Hadfield-Menell, ACM CRS, 2022). In this work, we model change in user interest upon showing ads based on three key psychological principles: mere exposure, hedonic adaptation, and operant conditioning. The first two effects are modeled using a concave function of user interest with repeated exposure, while the third effect is modeled using a temporal decay function, which explains the decline in user interest due to overexposure. Under our psychological behavior model, we ask the following question: Given a continuous time interval $T$, how many ads should be shown, and at what times, to maximize the user interest towards the ads? Towards answering this question, we first show that, if the number of displayed ads is fixed to $n$, then the optimal ad-schedule only depends on the operant conditioning function. Our main result is a quasi-linear time algorithm that, given the number of ads $n$, outputs a near-optimal ad-schedule, i.e., the difference in the performance of our schedule and the optimal schedule is exponentially small. Our algorithm leads to significant insights about optimal ad placement and shows that simple heuristics such as uniform spacing are sub-optimal under many natural settings. The optimal number of ads to display, which also depends on the mere exposure and hedonistic adaptation functions, can be found through a simple linear search given the above algorithm. We further support our findings with experimental results, demonstrating that our strategy outperforms various baselines.

Process reward models (PRMs) have demonstrated significant efficacy in enhancing the mathematical reasoning capabilities of large language models (LLMs) by leveraging test-time scaling (TTS). However, while most PRMs exhibit substantial gains in mathematical domains, the scarcity of domain-specific training data and knowledge-based learning patterns limits their generalization ability when faced with other domains. To address this limitation, we shift the learning objective from verifying domain-specific knowledge to modeling domain-agnostic logical flow. Centering on \textit{contextual coherence} between chain-of-thought (CoT) steps, our approach is realized through a novel data annotation and training framework, which enhances the model's generalization capabilities across diverse domains. For instance, our resulting model, \textbf{ContextPRM}, achieves a notable 6.5\% average accuracy improvement over the majority voting baseline via weighted majority voting across nine non-mathematical domains in MMLU-Pro, including law, history, and philosophy, significantly surpassing the 2.2\% improvement from VersaPRM and 0.5\% gains from other mathematics-focused PRMs, demonstrating consistent performance across both mathematical and non-mathematical domains.

Modeling neural population dynamics is crucial for foundational neuroscientific research and various clinical applications. Conventional latent variable methods typically model continuous brain dynamics through discretizing time with recurrent architecture, which necessarily results in compounded cumulative prediction errors and failure of capturing instantaneous, nonlinear characteristics of EEGs. We propose ODEBrain, a Neural ODE latent dynamic forecasting framework to overcome these challenges by integrating spatio-temporal-frequency features into spectral graph nodes, followed by a Neural ODE modeling the continuous latent dynamics. Our design ensures that the latent representations can capture stochastic variations of complex brain state at any given time point. Extensive experiments verifies that ODEBrain can improve significantly over existing methods in forecasting EEG dynamics with enhanced robustness and generalization capabilities.

Watermarking provides an effective means for data governance. However, conventional post-editing graph watermarking approaches degrade the graph quality and involve NP-hard subroutines. Alternatively, recent approaches advocate for embedding watermarking patterns in the noisy latent during data generation from diffusion models, but remain uncharted for graph models due to the hardness of inverting the graph diffusion process. In this work, we propose CheckWate: the first watermarking framework for graph diffusion models embedding checkerboard watermark and providing polynomial time verification. To address NP-completeness due to graph isomorphism, CheckWate embeds the watermark into the latent eigenvalues, which are isomorphism-invariant. To detect the watermark through reversing the graph diffusion process, CheckWate leverages the graph eigenvectors to approximately dequantizes the discrete graph back to the continuous latent, with theoretical guarantees on the detectability and dequantization error. We further introduce a latent sparsification mechanism to enhance the robustness of CheckWate against graph modifications. We evaluate CheckWate on four datasets and four graph modification attacks, against three generation time watermark schemes. CheckWate achieves remarkable generation quality while being detectable under strong attacks such as isomorphism, whereas the baselines are unable to detect the watermark. Code available at: https://anonymous.4open.science/r/checkwate.

Recently, large time series models (LTSM) have become popular and important because they exhibit characteristics similar to large language models, such as flexible context length, scalability, and task generality, outperforming the advanced task-specific models in the domain. However, existing research indicates that the pre-trained LTSM can show a poor non-convex loss landscape (indicating poor trainability). Hence, directly fine-tuning pre-trained LTSM shows overfitting, which leads to poor fine-tuning performance, even worse than training from scratch on the downstream datasets. This severely diminishes the value of the pre-trained LTSM. To address this, we propose a new fine-tuning method called Smoothed Full Fine-tuning (SFF). Specifically, before fine-tuning, we first construct an auxiliary LTSM with a smooth loss landscape (indicating good trainability) through random initialization. Second, we utilize it to smooth the loss landscape of the pre-trained LTSM through linear interpolation between their weights. As a result, the smoothed LTSM acquires good trainability while retaining good pre-training knowledge, thereby achieving better performance when fine-tuned on the downstream dataset. We also explain why SFF is effective from the perspective of optimization theory: interpolation perturbs sharp minima without obviously harming originally flat regions, thereby aiding sharp minima escape to better and smoother basins. Extensive experiments on popular datasets show that our method indeed improves the performance of eight popular LTSMs, e.g., Timer, TimesFM, MOMENT, UniTS, MOIRAI, Chronos, TTMs, and Sundial, in different downstream tasks.

Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing bespoke architectures for each group of symmetries, limiting scalability and preventing knowledge transfer across related symmetries. In the case of the space groups—symmetries critical to modeling crystalline solids in materials science and condensed matter physics—this challenge is particularly salient as there are 230 such groups in three dimensions. In this work we present a new approach to such crystallographic symmetries by developing a single machine learning architecture that is capable of adapting its weights automatically to enforce invariance to any input space group. Our approach is based on constructing symmetry-adapted Fourier bases through an explicit characterization of constraints that group operations impose on Fourier coefficients. Encoding these constraints into a neural network layer enables weight sharing across different space groups, allowing the model to leverage structural similarities between groups and overcome data sparsity when limited measurements are available for specific groups. We demonstrate the effectiveness of this approach in achieving competitive performance on material property prediction tasks and performing zero-shot learning to generalize to unseen groups.

Universal Test-Time Adaptation (UTTA) tackles the challenge of handling both class and domain shifts in unsupervised settings with stream testing data. Currently, most UTTA methods can only deal with minor shifts and heavily rely on heuristic approaches. To advance UTTA under dual shifts, we propose a novel Active Universal Test-Time Adaptation (AUTTA) framework, Exposing Mixture and Annotating Confusion (EMAC), which incorporates active human annotation into the UTTA setting. To select appropriate samples for annotation in AUTTA, we first identify the mixed regions of target domain samples under dual shifts, highlighting potential candidate samples. We then design a reward-guided active selection strategy to prioritize annotating the most representative samples within this set, maximizing annotation effectiveness. Additionally, to balance the use of pseudo-labels with the limited number of annotations, we propose an adaptation objective designed to address the adaptation imbalance caused by annotation scarcity. Extensive experiments show that the proposed AUTTA approach significantly improves performance and achieves state-of-the-art.

We propose a post-hoc adaptive conformal anomaly detection method for monitoring time series that leverages predictions from pre-trained foundation models without requiring additional fine-tuning. Our method yields an interpretable anomaly score directly interpretable as a false alarm rate (p-value), facilitating transparent and actionable decision-making. It employs weighted quantile conformal prediction bounds and adaptively learns optimal weighting parameters from past predictions, enabling calibration under distribution shifts and stable false alarm control, while preserving out-of-sample guarantees. As a model-agnostic solution, it integrates seamlessly with foundation models and supports rapid deployment in resource-constrained environments. This approach addresses key industrial challenges such as limited data availability, lack of training expertise, and the need for immediate inference, while taking advantage of the growing accessibility of time series foundation models. Experiments on both synthetic and real-world datasets show that the proposed approach delivers strong performance, combining simplicity, interpretability, robustness, and adaptivity.

Unsupervised Multimodal anomaly detection (MAD) — identifying defects by jointly analyzing RGB images and 3D data — is crucial for quality control in manufacturing. However, existing MAD methods struggle when only a few normal samples are available. Cross-modal alignment models fail to learn stable correspondences with scarce training data, and memory-based approaches misclassify any unseen normal variation as anomalous.To addresses the few-shot challenge, we introduce PIRN (Prototypical-based Intra-modal Reconstruction with Normality Communication for Multi-modal Anomaly Detection.), a prototype-based intra-modal reconstruction framework with explicit cross-modal knowledge transfer. PRINC features three key innovations: (1) Balanced Prototype Assignment (BPA) formulates token‑to‑prototype routing as a balanced optimal‑transport problem, guaranteeing uniform utilisation of all prototypes and preventing codebook collapse.(2) Adaptive Prototype Refinement (APR) treats prototypes as adaptive memory and updates them on‑the‑fly with gated GRU cells driven by optimally‑matched image context, expanding coverage to unseen yet normal variations while suppressing anomalies. (3) Multi‑modal Normality Communication (MNC) exchanges complementary normal cues across modalities via gated cross‑attention. MNC enables one modality to reconstruct its feature map not only from its own prototypes, but also with high-level normal patterns provided by the other modality.Extensive experiments on standard benchmarks demonstrate that PIRN significantly outperforms prior methods, achieving new state-of-the-art results, especially in challenging few-shot scenarios.

Anomaly detection in time series is essential for applications from industrial monitoring to financial risk management. Recent methods --- including forecasting error models, representation learning, augmentation, and weak-label learning --- have achieved strong results for specific anomaly types such as sudden point or gradual collective anomalies. While many prior works report window-level metrics that may mask errors, several recent methods evaluate at the point level as well. Our goal is to use a stricter point-wise protocol to make masking effects explicit. We introduce FOLD (Point-wise Anomaly Detection via fold-bifurcation), a framework that reframes detection as tracking a system’s proximity to a critical transition. FOLD extracts stress signals from a forecasting model and integrates them with a fold-bifurcation inspired ODE to produce the risk state, flagging anomalies once it crosses a threshold calibrated on normal data. This requires no anomaly labels and no additional detector training, enabling a parameter-free and efficient detection process. By modeling anomalies as stress accumulation toward a tipping point, FOLD naturally aligns with point-wise detection, providing a unifying and interpretable perspective that complements type-specific methods. Experiments on 40 benchmarks against 34 state-of-the-art baselines show that FOLD achieves competitive or superior performance, with particular strength under strict point-wise evaluation.

Asynchronous stochastic gradient methods are central to scalable distributed optimization, particularly when devices differ in computational capabilities. Such settings arise naturally in federated learning, where training takes place on smartphones and other heterogeneous edge devices. In addition to varying computation speeds, these devices often hold data from different distributions. However, existing asynchronous SGD methods struggle in such heterogeneous settings and face two key limitations. First, many rely on unrealistic assumptions of similarity across workers' data distributions. Second, methods that relax this assumption still fail to achieve theoretically optimal performance under heterogeneous computation times. We introduce Ringleader ASGD, the first asynchronous SGD algorithm that attains the theoretical lower bounds for parallel first-order stochastic methods in the smooth nonconvex regime, thereby achieving optimal time complexity under data heterogeneity and without restrictive similarity assumptions. Our analysis further establishes that Ringleader ASGD remains optimal under arbitrary and even time-varying worker computation speeds, closing a fundamental gap in the theory of asynchronous optimization.

Time series foundation models (TSFMs) are a potential class of powerful, general-purpose tools for forecasting and related temporal tasks, but their behavior is strongly shaped by subtle inductive biases in their design. Rather than developing a new model and claiming that it is better than existing TSFMs, e.g., by winning on existing benchmarks, our objective is to understand how the various "knobs" of the training process affect model quality. Using a mix of theory and controlled empirical evaluation, we identify and show how various design choices (e.g., patch size, embedding choice, training objective, etc.) lead to implicit biases in fundamental model properties (e.g., temporal behavior, geometric structure, how aggressively or not the model regresses to the mean, etc.), and how these biases can be intuitive or counterintuitive, depending on properties of the model and data. We illustrate in a case study on outlier handling how multiple biases interact in complex ways.

The scientific reasoning ability of large language models (LLMs) has recently attracted significant attention. Time series, as a fundamental modality in scientific data, presents unique challenges that are often overlooked in current multimodal LLMs, which either encode numerical sequences as text or convert them into images. Such approaches may be insufficient for comprehensive scientific time series understanding and generation. Existing unified time series models typically specialise in either forecasting or analysis, and their effectiveness on non-periodic, heterogeneous scientific signals remains unclear. To address these gaps, we introduce SciTS, a benchmark spanning 12 scientific domains and 43 tasks, with over 50k+ instances, both univariate and multivariate signals ranging from $10^0$ to $10^7$ in length and up to 10~MHz in frequency. We benchmark 17 models, including text-only LLMs, multimodal LLMs, and unified time series models, and find that general-purpose LLMs exhibit stronger generalisability than specialised time series models, while representing time series as text or images limits their performance due to excessively long sequences and loss of numerical precision, respectively. We then introduce TimeOmni, a working example to explore insights into how LLMs can be extended to handle scientific time series while remaining compatible with general-purpose LLM training. This work fills a gap in both dedicated benchmarks and illustrative frameworks for scientific time series, paving the way for LLMs to understand and generate complex temporal scientific data.

Learning from multi-variate time-series with heterogeneous channel configurations remains a fundamental challenge for deep neural networks, particularly in clinical domains such as intracranial electroencephalography (iEEG), where channel setups vary widely across subjects. In this work, we introduce multi-variate parallel attention (MVPA), a novel self-attention mechanism that disentangles content, temporal, and spatial attention, enabling flexible, generalizable, and efficient modeling of time-series data with varying channel counts and configurations. We use MVPA to build MVPFormer, a generative foundation model for human electrophysiology, trained to predict the evolution of iEEG signals across diverse subjects. To support this and future efforts by the community, we release the Long-term iEEG dataset, the largest publicly available iEEG dataset to date, comprising nearly 10,000 hours of recordings from heterogeneous clinical sources. MVPFormer leverages MVPA to achieve strong generalization across subjects, demonstrating expert-level performance in several iEEG tasks. MVPFormer surpasses state-of-the-art (SOTA) Transformer baselines in seizure detection across the Long-term, the MAYO, and the FNUSA datasets, while also achieving SOTA performance on four Brain TreeBank iEEG decoding tasks (volume, pitch, onset, and speech). We further validate MVPA on standard time-series forecasting and classification tasks, where it matches or exceeds the performance of existing attention-based models. Together, our contributions establish MVPA as a general-purpose attention mechanism for heterogeneous time-series and MVPFormer as the first open-source, open-weights, and open-data iEEG foundation model with SOTA clinical performance.

ICU (Intensive Care Unit) records comprise heterogeneous multivariate time series sampled at irregular intervals with pervasive missingness, yet clinical applications demand predictive models that are both accurate and interpretable. We present our Graph Attention-based Relational Learning for Intensive Care (GARLIC) model, a novel neural network architecture that imputes missing data through a learnable exponential-decay encoder, captures inter-sensor dependencies through time-lagged summary graphs, and fuses global patterns with cross-dimensional sequential attention. All attention weights and graph edges are learned end-to-end to serve as built-in observation-, signal-, and edge-level explanations. To reconcile auxiliary reconstruction and primary classification objectives, we develop an alternating decoupled optimization scheme that stabilizes training. On three ICU benchmarks (PhysioNet 2012 \& 2019, MIMIC-III) for outcome prediction, GARLIC sets the new state of the art, significantly improving AUROC and AUPRC over best-performing baselines at comparable computational cost. Ablation studies confirm each module’s contribution, and feature-removal trials validate importance attribution fidelity through a monotonic performance drop (full > top 50\% > random 50\% > bottom 50\%). Additionally, we also demonstrate GARLIC's superiority in data imputation and classification on various datasets beyond the ICU domain, showing its generalizability and applicability to broader tasks and datasets. Finally, real-time case studies demonstrate actionable risk warnings with transparent explanations, marking a significant advancement toward accurate, explainable deep learning for irregularly sampled ICU time series data.