GUPO: Gradient Uncertainty-aware Policy Optimization for Post-Training Large Language Models

Group Relative Policy Optimization (GRPO) has become a widely used approach for post-training Large Language Models (LLMs) for reasoning. In GRPO, the group gradients induced by different queries within the same mini-batch are directly averaged to form the policy update. However, these group gradients can point in conflicting directions. Our empirical analysis suggests that group-gradient conflicts tend to be associated with less effective policy updates, motivating the need for a reliable aggregated update direction under such conflicts. Standard GRPO aggregation treats the realized group gradients as deterministic contributions and does not account for differences in their reliability during aggregation. To address this issue, we propose Gradient Uncertainty-Aware Policy Optimization (GUPO), which models each group gradient as a random variable under a Bayesian formulation and estimates its probability distribution. GUPO then derives gradient uncertainty using a Dirichlet-based formulation and uses it to calibrate the contribution of each group gradient during aggregation. Extensive experiments on multiple benchmarks demonstrate the effectiveness of GUPO.

Temporal GRPO: Beyond Trajectory-Level Credit in Vision-Language-Action Reinforcement Learning

Outcome-driven reinforcement learning offers a scalable way to post-train vision-language-action (VLA) policies from sparse task-success feedback. In common GRPO-based VLA post-training, one rollout-level advantage is applied to every action in the trajectory. A rollout that completes several valid stages but fails later can therefore penalize the actions that produced its earlier progress. We call this trajectory-level credit aliasing. Temporal GRPO addresses this problem by constructing detectable task stages, aligning each rollout with stage-specific action intervals, and comparing only rollouts that have entered the same stage. The resulting stage advantages are applied to their corresponding intervals in a single policy update. On RoboTwin 2.0, Temporal GRPO improves task success and sample efficiency, with consistent gains across task horizons. Controlled updates on LIBERO-Long preserve shared prerequisite stages and concentrate improvement at the first stage where rollout outcomes diverge.

Ground-Truth Neighborhood Regularization for Reinforcement Learning Post-Training of Time Series Foundation Models

Time series forecasting (TSF) plays an important role in a wide range of real-world applications. Recently, time series foundation models (TSFMs), pretrained on large-scale datasets, have demonstrated strong generalization capabilities and emerged as an important paradigm for TSF. Reinforcement learning (RL) post-training has consequently attracted growing attention as a means of further improving their performance on downstream tasks. However, we find that, in certain forecast regions, RL post-training may gradually shift the output distributions of TSFMs away from the ground truth, thereby limiting their performance. We refer to this phenomenon as \textbf{suboptimal collapse}. Our analysis suggests that difficulty in initially sampling high-quality trajectories near the ground truth is an important contributing factor to suboptimal collapse. To address this issue, we propose Ground-Truth Neighborhood Regularization (GTN-R) for RL post-training of TSFMs. GTN-R uses the ground truth as a reference for locating high-quality regions and guides the model's probability mass toward the ground-truth neighborhood. This increases the probability of sampling high-quality trajectories, mitigates suboptimal collapse, and improves performance. Moreover, GTN-R can be flexibly integrated into various RL methods for TSFMs. Extensive experiments show its effectiveness.

Dirichlet-Guided Group Forecasting for Alleviating Over-smoothing in Time Series Forecasting

Time series forecasting often suffers from over-smoothing, especially when future dynamics are multi-modal. Forecasts may follow the coarse trend of the observed future, but fail to preserve sharp changes, oscillations, turning points, and regime transitions that define plausible dynamic evolution. In this work, we revisit over-smoothing from the perspective of latent dynamical mode compression: under partial observation and single-realization supervision, multiple plausible future modes can be weakened, merged, or averaged during forecasting. Based on this view, we propose Dirichlet-Guided Group Forecasting (DGF), a mode-preserving forecasting framework that explicitly models multiple mode-conditioned predictive distributions and uncertainty over their selection probabilities. DGF uses a Dirichlet-guided hierarchical sampling mechanism and reward-based optimization to encourage forecasts that are accurate, dynamically consistent, and mode-distinct. Extensive experiments on real-world forecasting benchmarks show that DGF reduces over-smoothing while improving forecasting accuracy, diversity, and dynamical consistency.

Generalizing Graph Foundation Models via Hyperbolic Retrieval-Augmented Generation

Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference. However, the parameterized knowledge encoded within these models is insufficient to cope with distribution shifts, limiting their generalization ability. To mitigate this issue, retrieval-augmented generation (RAG) has been introduced to incorporate external knowledge at inference time. Nevertheless, existing RAG frameworks operating in Euclidean space suffer from a fundamental geometric limitation: the polynomial volume growth of Euclidean space is inherently mismatched with the tree-structured external knowledge bases. This mismatch leads to the loss of semantic granularity in retrieval and gives rise to the hubness phenomenon.To address this limitation, we propose a Hyperbolic Retrieval-Augmented Generation (HyRAG) framework designed to enhance the generalization capabilities of GFMs. Specifically, the introduced Hyperbolic Knowledge Indexing module retains the tree-like hierarchies of the external knowledge base by modeling them within hyperbolic space. The Multi-granularity Retrieval module then provides GFMs with the global semantic anchors and local semantic nuances through coarse-grained and fine-grained knowledge retrieval, respectively. Finally, the Dual-path Fusion module achieves effective knowledge integration for graph tasks at both the feature and structural levels. Experiments on multiple graph benchmarks demonstrate significant improvements in the zero-shot setting, highlighting the generalization of our method for robust GFMs inference.

PAPO-VLA: Planning-Aware Policy Optimization for Vision-Language-Action Models

Vision-Language-Action (VLA) models show promising ability in language-guided robotic tasks. However, making VLA policies reliable remains challenging, because a manipulation task is completed through closed-loop interaction, where each action affects subsequent execution. To analyze this problem, we revisit VLA policy during execution and argue that a VLA policy acts both as a planner, which makes task-oriented decisions that change the direction of execution, and as an executor, which realizes these decisions through dense continuous actions. This view suggests that improving VLA reliability requires particular attention to planning actions. Existing optimization methods can imitate actions or improve complete trajectories, but they usually do not explicitly identify planning actions or measure their importance for task success. To address this issue, we propose Planning-Aware Policy Optimization for VLA models (PAPO-VLA). PAPO-VLA first identifies planning actions by jointly considering action variation and trajectory outcome, then estimates their importance through causal sufficiency and causal necessity, and finally incorporates this importance into GRPO advantage estimation. In this way, more important planning actions receive stronger optimization emphasis, while the whole trajectory is still optimized by trajectory-level feedback. Experiments on multiple benchmarks demonstrate the effectiveness of PAPO-VLA.

TIDE-Bench: Task-Aware and Diagnostic Evaluation of Tool-Integrated Reasoning

Tool-integrated reasoning has emerged as a promising paradigm for enhancing large language models with external computation, retrieval, and execution capabilities. However, the field still lacks a high-quality and unified evaluation benchmark, and existing TIR evaluations remain limited in dataset quality, task diversity, diagnostic comprehensiveness, and evaluation efficiency. In this work, we introduce TIDE-Bench, a holistic and efficient benchmark for evaluating TIR methods, featuring three key advantages. First, it provides diverse task settings, combining widely used mathematical reasoning and knowledge-intensive QA tasks with two newly designed tasks, namely the tool-grounded experimental design task and the dynamic interactive task, to probe models' abilities in complex tool invocation and multi-tool coordination. Second, TIDE-Bench adopts a comprehensive yet task-aware evaluation protocol, jointly measuring final answer quality, process reliability, tool-use efficiency, and inference cost across heterogeneous task settings. Third, TIDE-Bench constructs high-quality and discriminative evaluation sets by filtering low-discrimination instances from existing datasets, substantially reducing evaluation cost while focusing on more challenging samples. Extensive experiments on multiple foundation models and TIR methods reveal persistent bottlenecks in tool grounding, offering insights for future TIR research.

CAMD: Coverage-Aware Multimodal Decoding for Efficient Reasoning of Multimodal Large Language Models

Recent advances in Multimodal Large Language Models (MLLMs) have shown impressive reasoning capabilities across vision-language tasks, yet still face the challenge of compute-difficulty mismatch. Through empirical analyses, we identify that existing decoding methods may waste compute on easy cases while underserving hard ones, affecting both model effectiveness and efficiency. To address this issue, we first develop a theoretical framework that links sampling coverage, instance difficulty, and residual risk. Our analysis reveals that multimodal reasoning exhibits a heavy-tailed difficulty distribution; a small subset of hard or ambiguous samples dominates the residual failure probability. Based on this insight, we propose Coverage-Aware Multimodal Decoding (CAMD), an adaptive inference mechanism that dynamically allocates computation according to estimated uncertainty. CAMD integrates evidence-weighted scoring, posterior coverage estimation, and sequential Bayesian updating to balance efficiency and reliability under a limited token budget. Experiments on various benchmark datasets and baselines demonstrate the effectiveness and advantages of our approach.

Closing the Loop: A Control-Theoretic Framework for Provably Stable Time Series Forecasting with LLMs

Large Language Models (LLMs) have recently shown exceptional potential in time series forecasting, leveraging their inherent sequential reasoning capabilities to model complex temporal dynamics. However, existing approaches typically employ a naive autoregressive generation strategy. We identify a critical theoretical flaw in this paradigm: during inference, the model operates in an open-loop manner, consuming its own generated outputs recursively. This leads to inevitable error accumulation (exposure bias), where minor early deviations cascade into significant trajectory drift over long horizons. In this paper, we reformulate autoregressive forecasting through the lens of control theory, proposing \textbf{F-LLM} (Feedback-driven LLM), a novel closed-loop framework. Unlike standard methods that passively propagate errors, F-LLM actively stabilizes the trajectory via a learnable residual estimator (Observer) and a feedback controller. Furthermore, we provide a theoretical guarantee that our closed-loop mechanism ensures uniformly bounded error, provided the base model satisfies a local Lipschitz constraint. Extensive experiments demonstrate that F-LLM significantly mitigates error propagation, achieving good performance on time series benchmarks.

Adaptive Uncertainty-Aware Tree Search for Robust Reasoning

Inference-time reasoning scaling has significantly advanced the capabilities of Large Language Models (LLMs) in complex problem-solving. A prevalent approach involves external search guided by Process Reward Models (PRMs). However, a fundamental limitation of this framework is the epistemic uncertainty of PRMs when evaluating reasoning paths that deviate from their training distribution. In this work, we conduct a systematic analysis of this challenge. We first provide empirical evidence that PRMs exhibit high uncertainty and unreliable scoring on out-of-distribution (OOD) samples. We then establish a theoretical framework proving that while standard search incurs linear regret accumulation, an uncertainty-aware strategy can achieve sublinear regret. Motivated by these findings, we propose Uncertainty-Aware Tree Search (UATS), a unified method that estimates uncertainty via Monte Carlo Dropout and dynamically allocates compute budget using a reinforcement learning-based controller. Extensive experiments demonstrate that our approach effectively mitigates the impact of OOD errors.