ICML 2026 Papers

Sparse Mixture-of-Experts architectures are essential for scaling model capacity efficiently, yet the standard Top-$k$ routing imposes a rigid sparsity pattern that ignores the intrinsic variance in token difficulty and layer-specific computational needs. Top-$p$ routing is more adaptive because it selects experts until their cumulative routing probability reaches a threshold, allowing confident tokens to use fewer experts and ambiguous tokens to recruit more. However, we demonstrate that existing naive Top-$p$ implementations with fixed global probability thresholds provide only marginal gains over Top-$k$, suffer from hyperparameter sensitivity, and result in uncontrolled computational costs. In this paper, we propose **DTop-$p$**, a sparsity-controllable dynamic routing mechanism that learns the Top-$p$ probability threshold with a Proportional-Integral controller and uses dynamic routing normalization to support layer-wise expert selection under a global sparsity constraint. Extensive experiments on Large Language Models and Diffusion Transformers demonstrate that **DTop-$p$** consistently outperforms both Top-$k$ and fixed Top-$p$ baselines while matching the average FLOPs of Top-$k$ MoE. Our analysis confirms that **DTop-$p$** exhibits strong scaling properties across expert granularity, total expert capacity, model size, and dataset size, offering a robust and efficient MoE framework for foundation model pre-training.

Foundation models show great promise in achieving zero-shot or few-shot forecasting for ODE-based chaotic systems via large-scale pretraining. However, existing architectures often fail to capture the multi-scale temporal structures and distinct spectral characteristics of chaotic dynamics. To address this, we introduce ChaosNexus, a foundation model for chaotic system forecasting underpinned by the proposed ScaleFormer architecture. By processing temporal contexts across hierarchically varying patch sizes, ChaosNexus effectively captures long-range dependencies and preserves high-frequency fluctuations. To address heterogeneity across distinct systems, we integrate Mixture-of-Experts (MoE) layers into each ScaleFormer block and explicitly condition the final forecasts on a learned frequency fingerprint, providing the model with a global spectral view of the system. Extensive evaluations on over 9,000 synthetic systems demonstrate that ChaosNexus achieves superior fidelity in long-term attractor statistics while maintaining competitive point-wise accuracy. Furthermore, in real-world applications, it achieves a remarkable zero-shot mean error below 1°C for 5-day station-based weather forecasting. Code is available at https://github.com/tsinghua-fib-lab/ChaosNexus.

Recent advances in image and video generation raise hopes that these models possess world modeling capabilities—the ability to generate realistic, physically plausible videos. This could revolutionize applications in robotics, autonomous driving, and scientific simulation. However, before treating these models as world models, we must ask: Do they adhere to physical laws? Current evaluation methods rely on subjective judgments or trajectory matching, limiting their usage for physical reasoning estimation, where many generations could be physically plausible. Thus, we introduce **Morpheus**, one of the first physics-informed evaluation frameworks for measuring the ability of video generation models to comprehend Newtonian dynamics. **Morpheus** features 130 real-world videos capturing physical phenomena, guided by conservation laws. Using those as conditioning for video generation, we assess physical plausibility leveraging interpretable metrics evaluated with respect to infallible conservation laws known per physical setting, leveraging advances in physics-informed neural networks and vision-language foundation models. Importantly, **Morpheus** targets controlled Newtonian rigid-body settings to enable quantitative checks. Our findings reveal that even with advanced prompting and video conditioning, contemporary models struggle to encode physical principles despite generating aesthetically pleasing videos. Code and data available [here](https://github.com/physics-from-video/Morpheus).

Tabular Language Models (TLMs) have been claimed to achieve strong generalization for tabular prediction. We conduct a systematic re-evaluation of Tabula-8B as a representative TLM, utilizing 165 datasets from the UniPredict benchmark. Our investigation reveals three findings. First, binary and categorical classification achieve near-zero median lift over majority-class baselines and strong aggregate performance is driven entirely by quartile classification tasks. Second, top-performing datasets exhibit pervasive contamination, including complete train-test overlap and task-level leakage that evades standard deduplication. Third, instruction-tuning without tabular exposure recovers 92.2% of standard classification performance and on quartile classification, format familiarity closes 71.3% of the gap with the residual attributable to contaminated datasets. These findings suggest claimed generalization likely reflects evaluation artifacts rather than learned tabular reasoning. We conclude with recommendations for strengthening TLM evaluation.

While the shift toward unified foundation models has revolutionized many deep learning domains, sleep medicine remains largely restricted to task-specific models that focus on localized micro-structure features. These approaches often neglect the rich, multi-modal context of Polysomnography (PSG) and fail to capture the global macro-structure of a full night's sleep. To address this, we introduce SleepMaMi, a Sleep Foundation Model engineered to master both hour-long sleep architectures and fine-grained signal morphologies. Our framework utilizes a hierarchical dual-encoder design: a Macro-Encoder to model full-night temporal dependencies and a Micro-Encoder to capture short-term characteristics from biosignals. Macro-Encoder is trained via Demographic-Guided Contrastive Learning, which aligns overnight sleep patterns with objective subject metadata, such as age and sex, to refine global representations. Micro-Encoder is optimized via a hybrid Masked Autoencoder (MAE) and multi-modal contrastive objective. Pre-trained on a massive corpus of >20,000 PSG recordings (158K hours), SleepMaMi outperforms or matches existing foundation models across a diverse suite of downstream tasks, demonstrating superior generalizability and label-efficient adaptation for clinical sleep analysis.

While Large Vision-Language Models (VLMs) excel at interpolation, they suffer catastrophic failures in systematic generalization, most notably in visual counting beyond training distributions. In this work, we investigate this extrapolation bottleneck by deconstructing visual counting into three cognitive stages: object individuation, abstract magnitude representation, and symbolic decoding. Using a controlled environment of synthetic Go game boards, we isolate the specific mechanism of failure. Contrary to the hypothesis that models suffer from perceptual errors, we demonstrate via linear probing that visual backbones maintain robust, linearly separable representations of quantity well into the extrapolation regime. Furthermore, models retain latent magnitude awareness, successfully performing comparative reasoning on quantities they fail to enumerate. We pinpoint the collapse to the Symbolic Decoding stage, where the model fails to project valid visual magnitudes onto discrete tokens. Our findings support a Fractured Magnitude Hypothesis: VLMs fail to acquire a Universal Number Space, instead learning disjoint, modality-specific statistical manifolds that prevent cross-modal grounding for unseen pairings. We validate our findings on the state-of-the-art foundation model, suggesting that bridging the extrapolation gap requires inductive priors that enforce unified magnitude representations rather than simply scaling training data.

Group fairness can ensure equitable performance across different demographic subgroups for medical image analysis. However, the current fine-tuned foundation models (FMs) exhibit significant subgroup disparity. One-shot federated learning (OFL) can potentially mitigate this by leveraging cross-institutional data diversity within a single communication round. However, heterogeneous distributions across medical institutions may cause OFL local models to diverge severely, resulting in parameter conflicts that amplify disparity upon aggregation. To address these challenges, we propose Fair-FedMOE, a group-fair OFL framework for medical FMs. During local training, Fairness-aware Expert Routing leverages learnable prototypes to route samples to group-specific experts, enabling subgroup-specialized learning to capture group-specific features without inter-group interference. During model aggregation, Prototype-guided Differential Aggregation computes personalized weights based on prototype similarity and applies differentiated aggregation strategies to filter conflicting updates. We propose RES-AUC, a Rawlsian justice-inspired metric based on worst-group performance that remains stable as groups increase. Extensive experiments on retinal and chest X-ray datasets with multiple FMs demonstrate consistent fairness gains without sacrificing accuracy.

We propose a modular, data-driven framework for jointly learning unknown functional mappings and discovering the underlying one-parameter symmetry subgroup governing the data. Unlike conventional geometric deep learning methods that assume known symmetries, our approach identifies the relevant continuous subgroup directly from data. Our framework focuses on three primary geometric components of one-parameter subgroup actions: elliptic, hyperbolic, and parabolic regimes. For the given regime, our framework instantiates a corresponding symmetry discovery architecture with invariant and equivariant representation layers structured according to the Lie algebra of the subgroup, and learns the exact generator parameters end-to-end from data. This yields models whose invariance or equivariance is guaranteed by construction and admits formal proofs, enabling symmetry to be explicitly traced to identifiable components of the architecture. The approach is applicable to one-parameter subgroups of a wide range of matrix Lie groups, including $SO(n)$, $SL(n)$, and the Lorentz group. Experiments on synthetic and real-world systems, including moment of inertia prediction, double-pendulum dynamics, and high-energy \textit{Top Quark Tagging}, demonstrate accurate subgroup recovery and strong predictive performance across both compact and non-compact regimes.

Diffusion language models (DLMs) can match or surpass similarly sized autoregressive language models on language understanding and reasoning. However, their mask-and-denoise pretraining relies on heuristic random masking, which fails to target the most informative tokens. Consequently, the model spends significant computational effort on redundant or trivial tokens. To address this, we propose InfoDLM, an adaptive DLM pretraining framework that reformulates mask selection as an active, feedback-driven process. InfoDLM targets tokens that offer the highest measurable information gain during mask selection. Specifically, we: (1) introduce a Trainable Information-Gain (TIG) signal to quantify information gain of each masking configuration; (2) develop a feedback mechanism that adapts the masking policy to the model’s evolving state with a maturity indicator; and (3) jointly optimize the DLM and masking policy through an interleaved training flow with minimal computational overhead. Across reasoning-oriented benchmarks, InfoDLM achieves up to 13\% improvement in reasoning accuracy over a small variant of LLaDA under comparable pretraining budgets.

Bridging high-level semantic understanding with low-level physical control remains a persistent challenge in embodied intelligence, stemming from the fundamental spatiotemporal scale mismatch between cognition and action. Existing generative VLA policies typically adopt a "Generation-from-Noise" paradigm, which disregards this disparity, leading to representation inefficiency and weak condition alignment during optimization. In this work, we propose ResVLA, an architecture that shifts the paradigm to "Refinement-from-Intent." Recognizing that robotic motion naturally decomposes into global intent and local dynamics, ResVLA utilizes spectral analysis to decouple control into a deterministic low-frequency anchor and a stochastic high-frequency residual. By anchoring the generative process on the predicted intent, our model focuses strictly on refining local dynamics via a residual diffusion bridge. Extensive simulation experiments show that ResVLA achieves competitive performance, strong robustness to language and robot embodiment perturbations, and faster convergence than standard generative baselines. ResVLA also demonstrates strong performance in real-world robot experiments.

Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address this problem through selection-conditioned risk control, aiming to ensure that an accepted prediction has an error probability no larger than a user-specified risk level. To this end, we propose LEC, a principled framework that reframes selective prediction as a decision problem governed by a *linear expectation constraint* over selection and error indicators. This formulation directly controls the ratio between the expected number of accepted errors and the expected number of accepted predictions, which corresponds to the marginal error probability conditioned on selection. Under exchangeability, we derive a *finite-sample sufficient condition* that relies only on a held-out calibration set, enabling the computation of a risk-constrained, retention-maximizing threshold. Furthermore, we extend LEC to two-model routing systems: if the primary model's uncertainty exceeds its calibrated threshold, the input is delegated to a subsequent model, while maintaining system-level selection-conditioned error control. Experiments on both closed-ended and open-ended question answering (QA) and vision question answering (VQA) demonstrate that LEC maintains the prescribed risk level in accepted predictions and substantially improves sample retention compared to baselines.

Large Vision-Language Models (LVLMs) have achieved remarkable progress in multimodal reasoning tasks; however, their learning remains constrained by the limitations of human-annotated supervision. Recent self-rewarding approaches attempt to overcome this constraint by allowing models to act as their own critics or reward providers. Yet, purely text-based self-evaluation struggles to verify complex visual reasoning steps and often suffers from evaluation hallucinations. To address these challenges, inspired by recent advances in tool-integrated reasoning, we propose Agent0-VL, a self-evolving vision-language agent that achieves continual improvement with tool-integrated reasoning. Agent0-VL incorporates tool usage not only into reasoning but also into self-evaluation and self-repair, enabling the model to introspect, verify, and refine its reasoning through evidence-grounded analysis. It unifies two synergistic roles within a single LVLM: a Solver that performs multi-turn tool-integrated reasoning, and a Verifier that generates structured feedback and fine-grained self-rewards through tool-grounded critique. These roles interact through a Self-Evolving Reasoning Cycle, where tool-based verification and reinforcement learning jointly align the reasoning and evaluation distributions for stable self-improvement. Through this zero-external-reward evolution, Agent0-VL aligns its reasoning and verification behaviors without any human annotation or external reward models, achieving continual self-improvement. Experiments on chart reasoning, geometric problem solving, and visual scientific analysis show that Agent0-VL achieves an 12.5% improvement over the Qwen-VL base model.

Data-efficient learning aims to eliminate redundancy in large training datasets by training models on smaller subsets of the most informative examples. While data selection has been extensively explored for vision models and large language models (LLMs), it remains underexplored for Large Vision-Language Models (LVLMs). Notably, none of existing methods can outperform random selection at different subset sizes. In this work, we propose the first principled method for data-efficient instruction tuning of LVLMs. We prove that examples with similar cross-modal attention matrices during instruction tuning have similar gradients. Thus, they influence model parameters in a similar manner and convey the same information to the model during training. Building on this insight, we propose XMAS, which clusters examples based on the trajectories of the top singular values of their attention matrices obtained from fine-tuning a small proxy LVLM. By sampling a balanced subset from these clusters, XMAS effectively removes redundancy in large-scale LVLM training data. Extensive experiments across 4 target models, 2 proxy models, and 2 datasets show that XMAS consistently outperforms 10 baseline methods. Moreover, XMAS can discard 50% of the LLaVA-665k dataset and 85% of the Vision-Flan dataset while fully preserving performance of LLaVA-1.5-7B on 10 downstream benchmarks and speeding up its training by 1.2×. This is 30% more data reduction compared to the best baseline for LLaVA-665k. The project’s website can be found at https://bigml-cs-ucla.github.io/XMAS-project-page/.

Despite rapid progress, multimodal reasoning still lacks a systematic approach to synthesize large-scale vision-centric datasets beyond visual math. We introduce a framework able to synthesize vision-centric problems spanning diverse levels of complexity, and the resulting dataset with over 1M high-quality problems including: reasoning traces, preference data, and instruction prompts supporting SFT, offline and online RL. Our vision-centric synthesis framework uses a two-stage process focusing on: (1) generating diverse verifiable questions from existing images at scale, and (2) creating complex compositional visual problems by merging simpler questions. Remarkably, finetuning Qwen2.5-VL-7B on our data outperforms existing open-data baselines across evaluated vision-centric benchmarks, and our best configurations match or surpass strong closed-data models such as MiMo-VL-7B-RL on V*Bench, CV-Bench and MMStar-V. Notably, despite being entirely vision-centric, our data transfers positively to text-only reasoning (MMLU-Pro, +3.7%) and audio reasoning (MMAU, +1.32%), demonstrating its effectiveness. Similarly, despite containing no embodied visual data, we observe notable gains (NiEH, +8.8%) when evaluating open-ended embodied QA. Lastly, we use our data to comprehensively analyze at scale (1M+) the entire VLM post-training pipeline showing that (i) SFT on high-quality data with cognitive behaviours on reasoning traces is essential to scale online RL, (ii) offline RL could match online RL’s performance while disaggregating compute demands, and, (iii) SFT on high quality data also improve out-of-domain, cross-modality transfer.

Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and Neural ODEs often require complex training pipelines and substantial machine learning expertise, or they depend strongly on system-specific prior knowledge. We propose FIM-ODE, a pretrained Foundation Inference Model that *amortises* ODE inference by predicting the vector field directly from noisy trajectory data *in a single forward pass*. We pretrain FIM-ODE on a prior distribution over ODEs with low-degree polynomial vector fields and represent the target field with neural operators. FIM-ODE achieves strong *zero-shot* performance, matching and often improving upon ODEFormer, a recent pretrained symbolic baseline, across a range of regimes despite using a simpler training prior. Pretraining also provides a strong initialisation for finetuning, enabling fast and stable adaptation that outperforms modern neural and GP baselines without requiring machine learning expertise. Our pretrained model, code repository, and tutorials are available online.

Large language models (LLMs) often fail in systematic, model-specific ways under meaning-preserving question rewrites (paraphrases, format changes, benign distractors). In this work, we address this instability by identifying where the model's reasoning process diverges across semantically-equivalent inputs. For each target LLM, we sample multiple solution traces under rewrites and aggregate them into a graph of recurring intermediate steps, which pinpoints where incorrect traces diverge from correct ones. We then generate a small set of semantics-preserving examples that mirror the rewrite patterns most responsible for these divergences, and use them to steer the model (\emph{targeted alternation training}), either via fine-tuning or via in-context learning. Across MMLU-Pro, Big-MATH, and DROP, this yields consistent gains and cross-dataset generalization. On Humanity’s Last Exam, using 200 in-context examples, it improves GPT-5.2 (xhigh) from 35.4\% to 38.1\%, demonstrating that targeted alternation training can materially improve a frontier, API-accessible closed model under realistic access constraints.

Tabular foundation models (TFMs) increasingly rival tree ensembles, but their performance is often compute-inefficient: with standard affine scalar tokenization, each feature injects value variation through an essentially one-dimensional channel, and feature IDs/positional signals cannot increase within-feature value degrees of freedom, yielding weak early-layer value sensitivity and redundant hidden states. We present a unified tokenize-and-route framework for strong TFMs: RaBEL expands each scalar into compact localized RBF features (optionally exponent-gated) to improve conditioning and shallow-layer effective rank, while a reordered bidirectional block $\textbf{S$\rightarrow$N$\rightarrow$F}$ aligns computation with the readout by aggregating cross-sample context before feature mixing and using attention pooling. Together, these changes yield $\textbf{LimiX-2M}$, a 2M-parameter model that outperforms larger TabPFN-v2 and TabICL baselines on widely used tabular benchmarks while reducing training and inference costs. These results highlight value-aware tokenization and readout-aligned routing as key levers for improving the accuracy--efficiency trade-off in TFMs. Model checkpoints and inference code are available at https://github.com/limix-ldm-ai/LimiX.

Large Vision-Language Models (LVLMs) have shown remarkable performance on a wide range of vision-language tasks. Despite this progress, they are still prone to hallucination, generating responses that are inconsistent with visual content. In this work, we find that LVLMs tend to hallucinate when they pay insufficient attention to the correct visual evidence and gradually forget it during the generation process. We empirically find that although LVLMs overall attend insufficiently to visual evidence, they exhibit sensitivity to the correct visual evidence in specific layers, with notable inter-layer discrepancy. Motivated by this observation, we propose a novel hallucination mitigation method that enhances visual evidence based on **I**nter-**L**ayer **V**isual **A**ttention **D**iscrepancy (**ILVAD**). Specifically, we obtain the attention weights from early generated tokens to visual tokens across layers and identify the tokens that are repeatedly activated as visual evidence, forming a saliency map. We then enhance attention to visual evidence during generation through the saliency map to reduce visual forgetting. In addition, we leverage the saliency map to obtain attention scores of generated text to visual evidence, in order to select and emphasize text tokens that are strongly grounded in visual evidence. Our method is training-free and plug-and-play. Multiple benchmark evaluations conducted on five recently released models show that our method can consistently mitigate hallucinations in different LVLMs over various architectures. Code is available at https://github.com/ytx-ML/ILVAD.

Test-time compute (TTC) strategies have emerged as a lightweight approach to boost reasoning in large language models, but their applicability to vision-language models (VLMs) remains unclear. We present a systematic study of TTC for visual reasoning across seven open-source VLMs and six benchmarks, revisiting two paradigms: (i) feature-based scoring of chain-of-thought (CoT) traces and (ii) confidence-based aggregation via majority voting (MV). In the single-model setting, feature cues (e.g., length, pivot words) fail to improve accuracy, while MV yields only modest, CoT-dependent gains. To explain this limitation, we theoretically show that the voting method’s effectiveness depends on prediction diversity: when outputs are highly correlated, the benefit of voting vanishes. In contrast, multi-model ensembles introduce stronger diversity through architectural differences, training data, and scale, making them both more realistic and more promising for TTC. However, MV treats all models equally, leaving it vulnerable to correlated errors from weaker models. To address this, we propose Entropy-based TTC, which selects the most confident prediction based on predictive entropy. Our method reduces to MV in the single-model case but, in ensembles, leverages confidence disparities to prioritize stronger models. We prove that our method theoretically outperforms MV under mild dependence assumptions, and empirically show that it consistently surpasses both MV and the best individual model across diverse visual reasoning benchmarks. This demonstrates that smaller models can enhance, rather than hinder, larger ones when combined appropriately, unlocking ensemble gains not achievable with existing TTC strategies.