ICLR 2026 Papers

In this work, we contribute the first approach to solve infinite-horizon discounted general-utility Markov decision processes (GUMDPs) in the single-trial regime, i.e., when the agent's performance is evaluated based on a single trajectory. First, we provide some fundamental results regarding policy optimization in the single-trial regime, investigating which class of policies suffices for optimality, casting our problem as a particular MDP that is equivalent to our original problem, as well as studying the computational hardness of policy optimization in the single-trial regime. Second, we show how we can leverage online planning techniques, in particular a Monte-Carlo tree search algorithm, to solve GUMDPs in the single-trial regime. Third, we provide experimental results showcasing the superior performance of our approach in comparison to relevant baselines.

Large language models (LLMs), despite possessing latent safety understanding from their vast pretraining data, remain vulnerable to generating harmful content and exhibit issues such as over-refusal and utility degradation after safety alignment. Current safety alignment methods often result in superficial refusal shortcuts or rely on intensive supervision for reasoning-based approaches, failing to fully leverage the model's intrinsic safety self-awareness. We propose \textbf{AlphaAlign}, a simple yet effective pure reinforcement learning (RL) framework with verifiable safety reward designed to incentivize this latent safety awareness through proactive safety reasoning. AlphaAlign employs a dual-reward system: a verifiable safety reward encourages correctly formatted and explicitly justified refusals for harmful queries while penalizing over-refusals, and a normalized helpfulness reward guides high-quality responses to benign inputs. This allows the model to develop proactive safety reasoning capabilities without depending on supervised safety-specific reasoning data. AlphaAlign demonstrates three key advantages: (1) Simplicity and efficiency, requiring only binary prompt safety labels and minimal RL steps for substantial improvements. (2) Breaking the safety-utility trade-off, by enhancing refusal of harmful content and reducing over-refusals, while simultaneously maintaining or even improving general task performance and robustness to unseen jailbreaks. (3) Deep alignment, fostering proactive safety reasoning that generates explicit safety rationales rather than relying on shallow refusal patterns. Our codes are available at \url{https://anonymous.4open.science/r/AlphaAlign-D5B0}

Mixture-of-Experts (MoE) enables efficient scaling of large language models (LLMs) with sparsely activated experts during inference. To effectively deploy large MoE models on memory-constrained devices, many systems introduce expert offloading which caches a subset of experts in fast memory, leaving others on slow memory to run on CPU or load on demand. While some research has exploited the locality of expert activations, where consecutive tokens activate similar experts, the degree of this **local routing consistency** varies across models and remains understudied. In this paper, we propose two metrics to measure local routing consistency of MoE models: (1) **Segment Routing best Performance (SRP)**, which evaluates how well a fixed group of experts can cover the needs of a segment of tokens, and (2) **Segment Cache best Hit rate (SCH)**, which measures the hit rate of an expert cache utilizing a length of future information under a cache limit. We analyze 20 MoE LLMs with diverse sizes and architectures and use toy models to verify key factors related to local routing consistency. We find a strong trade-off between local routing consistency and *local* load balance, while showing that *global* load balance can coexist with local routing consistency. Meanwhile, settings like shared experts that decrease expert combination space can lead to low local routing consistency. We further reveal that domain-specialized experts contribute more to routing consistency than vocabulary-specialized ones, and that most models balance between cache effectiveness and efficiency with cache sizes approximately twice the active experts. These findings pave the way for memory-efficient MoE design and deployment without compromising inference speed.

Modeling realistic pedestrian trajectories requires accounting for both social interactions and environmental context, yet most existing approaches largely emphasize social dynamics. We propose EnvSocial-Diff: a diffusion-based crowd simulation model informed by social physics and augmented with environmental conditioning and individual-group interaction. Our structured environmental conditioning module explicitly encodes obstacles, objects of interest, and lighting levels, providing interpretable signals that capture scene constraints and attractors. In parallel, the individual-group interaction module goes beyond individual-level modeling by capturing both fine-grained interpersonal relations and group-level conformity through a graph-based design. Experiments on multiple benchmark datasets demonstrate that EnvSocial-Diff outperforms the latest state-of-the-art methods, underscoring the importance of explicit environmental conditioning and multi-level social interaction for realistic crowd simulation.

While most reinforcement learning methods today flatten the distribution of future returns to a single scalar value, distributional RL methods exploit the return distribution to provide stronger learning signals and to enable applications in exploration and safe RL. While the predominant method for estimating the return distribution is by modeling it as a categorical distribution over discrete bins or estimating a finite number of quantiles, such approaches leave unanswered questions about the fine-grained structure of the return distribution and about how to distinguish states with high return uncertainty for decision-making. The key idea in this paper is to use modern, flexible flow-based models to estimate the full future return distributions and identify those states with high return variance. We do so by formulating a new flow-matching objective that generates probability density paths satisfying the distributional Bellman equation. Building upon the learned flow models, we estimate the return uncertainty of distinct states using a new flow derivative ODE. We additionally use this uncertainty information to prioritize learning a more accurate return estimation on certain transitions. We compare our method (Value Flows) with prior methods in the offline and online-to-online settings. Experiments on $37$ state-based and $25$ image-based benchmark tasks demonstrate that Value Flows achieves a $1.3\times$ improvement on average in success rates.

Univariate time series (UTS), where each timestamp records a single variable, serve as crucial indicators in web systems and cloud servers. Anomaly detection in UTS plays an essential role in both data mining and system reliability management. However, existing reconstruction-based and prediction-based methods struggle to capture certain subtle anomalies, particularly small point anomalies and slowly rising anomalies. To address these challenges, we propose a novel prediction-based framework named Contextual and Seasonal LSTMs (CS-LSTMs). CS-LSTMs are built upon a noise decomposition strategy and jointly leverage contextual dependencies and seasonal patterns, thereby strengthening the detection of subtle anomalies. By integrating both time-domain and frequency-domain representations, CS-LSTMs achieve more accurate modeling of periodic trends and anomaly localization. Extensive evaluations on public benchmark datasets demonstrate that CS-LSTMs consistently outperform state-of-the-art methods, highlighting their effectiveness and practical value in robust time series anomaly detection.

3D part amodal segmentation--decomposing a 3D shape into complete, semantically meaningful parts, even when occluded--is a challenging but crucial task for 3D content creation and understanding. Existing 3D part segmentation methods only identify visible surface patches, limiting their utility. Inspired by 2D amodal segmentation, we introduce this novel task to the 3D domain and propose a practical, two-stage approach, addressing the key challenges of inferring occluded 3D geometry, maintaining global shape consistency, and handling diverse shapes with limited training data. First, we leverage existing 3D part segmentation to obtain initial, incomplete part segments. Second, we introduce HoloPart, a novel diffusion-based model, to complete these segments into full 3D parts. HoloPart utilizes a specialized architecture with local attention to capture fine-grained part geometry and global shape context attention to ensure overall shape consistency. We introduce new benchmarks based on the ABO and PartObjaverse-Tiny datasets and demonstrate that HoloPart significantly outperforms state-of-the-art shape completion methods. By incorporating HoloPart with existing segmentation techniques, we achieve promising results on 3D part amodal segmentation, opening new avenues for applications in geometry editing, animation, and material assignment.

Large language models (LLMs) exhibit advancing capabilities in complex tasks, such as reasoning and graduate-level question answering, yet their resilience against misuse, particularly involving scientifically sophisticated risks, remains underexplored. Existing safety benchmarks typically focus either on instructions requiring minimal knowledge comprehension (e.g., ``tell me how to build a bomb") or utilize prompts that are relatively low-risk (e.g., multiple-choice or classification tasks about hazardous content). Consequently, they fail to adequately assess model safety when handling knowledge-intensive, hazardous scenarios. To address this critical gap, we introduce SOSBench, a regulation-grounded, hazard-focused benchmark encompassing six high-risk scientific domains: chemistry, biology, medicine, pharmacology, physics, and psychology. The benchmark comprises 3,000 prompts derived from real-world regulations and laws, systematically expanded via an LLM-assisted evolutionary pipeline that introduces diverse, realistic misuse scenarios (e.g., detailed explosive synthesis instructions involving advanced chemical formulas). We evaluate frontier models within a unified evaluation framework using our SOSBench. Despite their alignment claims, advanced models consistently disclose policy-violating content across all domains, demonstrating alarmingly high rates of harmful responses (e.g., 84.9% for Deepseek-R1 and 50.3% for GPT-4.1). These results highlight significant safety alignment deficiencies and underscore urgent concerns regarding the responsible deployment of powerful LLMs.

We propose RAdaGD, a novel family of adaptive gradient descent methods on general Riemannian manifolds. RAdaGD adapts the step size parameter without line search, and includes instances that achieve a non-ergodic convergence guarantee, $f(x_k) - f(x_\star) \le \mathcal{O}(1/k)$, under local geodesic smoothness and generalized geodesic convexity. A core application of RAdaGD is Gaussian Variational Inference, where our method provides the first convergence guarantee in the absence of $L$-smoothness of the target log-density, under additional technical assumptions. We also investigate the empirical performance of RAdaGD in numerical simulations and demonstrate its competitiveness in comparison to existing algorithms.

Learning dynamical systems that respect physical symmetries and constraints remains a fundamental challenge in data-driven modeling. Integrating physical laws with graph neural networks facilitates principled modeling of complex N-body dynamics and yields accurate and permutation-invariant models. However, training graph neural networks with iterative, gradient-descent-based optimization algorithms (e.g., Adam, RMSProp, LBFGS) often leads to slow training, especially for large, complex systems. In comparison to 15 different optimizers, we demonstrate that Hamiltonian Graph Networks (HGN) can be trained 150-600× faster - but with comparable accuracy - by replacing iterative optimization with random feature-based parameter construction. We show robust performance in diverse simulations, including N-body mass-spring and molecular dynamics systems in up to $3$ dimensions and 10,000 particles with different geometries, while retaining essential physical invariances with respect to permutation, rotation, and translation. Our proposed approach is benchmarked using a NeurIPS 2022 Datasets and Benchmarks Track publication to further demonstrate its versatility. We reveal that even when trained on minimal 8-node systems, the model can generalize in a zero-shot manner to systems as large as 4096 nodes without retraining. Our work challenges the dominance of iterative gradient-descent-based optimization algorithms for training neural network models for physical systems.

Cooperative multi-agent reinforcement learning (MARL) commonly adopts centralized training with decentralized execution, where value-factorization methods enforce the individual-global-maximum (IGM) principle so that decentralized greedy actions recover the team-optimal joint action. However, the reliability of this recipe in real-world settings remains uncertain due to environmental uncertainties arising from the sim-to-real gap, model mismatch, system noise. We address this gap by introducing Distributionally robust IGM (DrIGM), a principle that requires each agent's robust greedy action to align with the robust team-optimal joint action. We show that DrIGM holds for a novel definition of robust individual action values, which is compatible with decentralized greedy execution and yields a provable robustness guarantee for the whole system. Building on this foundation, we derive DrIGM-compliant robust variants of existing value-factorization architectures (e.g., VDN/QMIX/QTRAN) that (i) train on robust Q-targets, (ii) preserve scalability, and (iii) integrate seamlessly with existing codebases without bespoke per-agent reward shaping. Empirically, on high-fidelity SustainGym simulators and a StarCraft game environment, our methods consistently improve out-of-distribution performances.

Data-driven models are increasingly adopted in critical scientific fields like weather forecasting and fluid dynamics. These methods can fail on out-of-distribution (OOD) data, but detecting such failures in regression tasks is an open challenge. We propose a new OOD detection method based on estimating joint likelihoods using a score-based diffusion model. This approach considers not just the input but also the regression model's prediction, providing a task-aware reliability score. Across numerous scientific datasets, including PDE datasets, satellite imagery and brain tumor segmentation, we show that this likelihood strongly correlates with prediction error. Our work provides a foundational step towards building a verifiable 'certificate of trust', thereby offering a practical tool for assessing the trustworthiness of AI-based scientific predictions.

Proprioceptive information is critical for precise servo control by providing real-time robotic states. Its collaboration with vision is highly expected to enhance performances of the manipulation policy in complex tasks. However, recent studies have reported inconsistent observations on the generalization of vision-proprioception policies. In this work, we investigate this by conducting temporally controlled experiments. We found that during task sub-phases that robot's motion transitions, which require target localization, the vision modality of the vision-proprioception policy plays a limited role. Further analysis reveals that the policy naturally gravitates toward concise proprioceptive signals that offer faster loss reduction when training, thereby dominating the optimization and suppressing the learning of the visual modality during motion-transition phases. To alleviate this, we propose the Gradient Adjustment with Phase-guidance (GAP) algorithm that adaptively modulates the optimization of proprioception, enabling dynamic collaboration within the vision-proprioception policy. Specifically, we leverage proprioception to capture robotic states and estimate the probability of each timestep in the trajectory belonging to motion-transition phases. During policy learning, we apply fine-grained adjustment that reduces the magnitude of proprioception's gradient based on estimated probabilities, leading to robust and generalizable vision-proprioception policies. The comprehensive experiments demonstrate GAP is applicable in both simulated and real-world environments, across one-arm and dual-arm setups, and compatible with both conventional and Vision-Language-Action models. We believe this work can offer valuable insights into the development of vision-proprioception policies in robotic manipulation. Videos and code are available at https://gewu-lab.github.io/GAP/.

We introduce Kolmogorov–Arnold Neural Operator (KANO), a dual‑domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the pure-spectral bottleneck of Fourier Neural Operator (FNO): KANO remains expressive over a generic position-dependent dynamics for any physical input, whereas FNO stays practical only to spectrally sparse operators and strictly imposes fast-decaying input Fourier tail. We verify our claims empirically on position-dependent differential operators, for which KANO robustly generalizes but FNO fails to. In the quantum Hamiltonian learning benchmark, KANO reconstructs ground‑truth Hamiltonians in closed-form symbolic representations accurate to the fourth decimal place in coefficients and attains $\approx6\times10^{-6}$ state infidelity from projective measurement data, substantially outperforming that of the FNO trained with ideal full wave function data, $\approx1.5\times10^{-2}$, by orders of magnitude.

In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model $f(\boldsymbol{x})=g(\boldsymbol{U}\boldsymbol{x})$ with hidden subspace $\boldsymbol{U}\in \mathbb{R}^{r\times d}$, which is the canonical setup to study representation learning. We prove that under generic non-degenerate assumptions on the link function, a standard two-layer neural network trained via layer-wise gradient descent can agnostically learn the target with $o_d(1)$ test error using $\widetilde{\mathcal{O}}(d)$ samples and $\widetilde{\mathcal{O}}(d^2)$ time. The sample and time complexity both align with the information-theoretic limit up to leading order and are therefore optimal. During the first stage of gradient descent learning, the proof proceeds via showing that the inner weights can perform a power-iteration process. This process implicitly mimics a spectral start for the whole span of the hidden subspace and eventually eliminates finite-sample noise and recovers this span. It surprisingly indicates that optimal results can only be achieved if the first layer is trained for more than $\mathcal{O}(1)$ steps. This work demonstrates the ability of neural networks to effectively learn hierarchical functions with respect to both sample and time efficiency.

Multi-task learning often suffers from gradient conflicts, leading to unfair optimization and degraded overall performance. To address this, we present SVFair, a Shapley value-based framework for fair gradient aggregation. We propose two scalable geometric conflict metrics: VolDet, a gram determinant volume metric, and VolDetPro, its sign-aware extension distinguishing antagonistic gradients. By integrating these metrics into Shapley value computation, SVFair quantifies each task’s deviation from the overall gradient and rebalances updates toward fairness. In parallel, our Shapley value computation admits controllable complexity. Extensive experiments show that SVFair achieves state-of-the-art results across diverse supervised and reinforcement learning benchmarks, and further improves existing methods when integrated as a fairness-enhancing module.

Reasoning models often exhibit overthinking, characterized by redundant reasoning steps. We identify \emph{internal bias} elicited by the input question as a key trigger of such behavior. Upon encountering a problem, the model immediately forms a preliminary guess about the answer, which we term an internal bias since it may not be explicitly generated, and it arises without systematic reasoning. When this guess conflicts with its subsequent reasoning, the model tends to engage in excessive reflection, resulting in wasted computation. We validate the association between internal bias and overthinking across multiple models and diverse reasoning tasks. To demonstrate the causal relationship more rigorously, we conduct two counterfactual interventions, showing that removing the input question after the model reduces the redundant reasoning across various complex reasoning tasks, and manually injecting bias affects overthinking accordingly. Further interpretability experiments suggest that excessive attention to the input question serves as a key mechanism through which internal bias influences subsequent reasoning trajectories. Finally, we evaluated several methods aimed at mitigating overthinking, yet the influence of internal bias persisted under all conditions.

Selective prediction aims to endow predictors with a reject option, to avoid low confidence predictions. However, existing literature has primarily focused on closed-set tasks, such as visual question answering with predefined options or fixed-category classification. This paper considers selective prediction for visual language foundation models, addressing a taxonomy of tasks ranging from closed to open set and from finite to unbounded vocabularies, as in image captioning. We seek training-free approaches of low-complexity, applicable to any foundation model and consider methods based on external vision-language model (VLM) embeddings, like CLIP. This is denoted as $\textit{Plug-and-Play Selective Prediction} (\textbf{\texttt{PaPSP}})$. We identify two key challenges: (1) $\textit{instability of the visual-language representations}$, leading to high variance in image-text embeddings, and (2) $\textit{poor calibration of similarity scores}$. To address these issues, we propose a $\textit{memory augmented}$ $\textbf{\texttt{PaPSP}}$ ($\textbf{\texttt{MA-PaPSP}}$) model, which augments $\textbf{\texttt{PaPSP}}$ with a retrieval dataset of image-text pairs. This is leveraged to reduce embedding variance by averaging retrieved nearest-neighbor pairs and is complemented by the use of contrastive normalization to improve score calibration. Through extensive experiments on multiple datasets, we show that $\textbf{\texttt{MA-PaPSP}}$ outperforms $\textbf{\texttt{PaPSP}}$ and other selective prediction baselines for selective captioning, image-text matching, and fine-grained classification. Source code will be made public.

While reinforcement learning (RL) demonstrated remarkable success in enhancing the reasoning capabilities of language models, the training dynamics of RL in LLMs remain unclear. In this work, we provide an explanation of the RL training process through empirical analysis and rigorous theoretical modeling. First, through systematic reasoning-pattern-level and token-level analysis across the RL training process, we show that while different reasoning patterns exhibit relatively stable success rates during training, RL primarily optimizes a sparse subset of critical tokens, thereby reshaping reasoning pattern distributions to affect model performance. Building on these empirical insights, we develop a theoretical framework to understand the training dynamics of RL with two typical rewards: verifiable reward (RLVR) and model's internal feedback (RLIF). For RLVR, we analyze the training dynamics under two special cases: one where models readily converge to optimal reasoning strategies, and another where optimization becomes challenging, revealing that the base model's reasoning quality is crucial for determining convergence behavior. For RLIF, we examine how internal rewards initially improve model performance but can potentially lead to degradation with continued training. Extensive experiments validate our findings, advancing both theoretical understanding and practical applications of RL in language model enhancement.