Unveiling the Entropy Dynamics of Chain-of-Thought Reasoning

This paper investigates the entropy dynamics of Chain-of-Thought (CoT) and uncovers a consistent two-phase structure: an Uncertainty Region of exploration transitioning sharply to a Confidence Region of convergence. We demonstrate that the Confidence Region possesses two critical properties: 1) High Reliability -- answers in the confidence region become highly accurate and stable, and 2) High Redundancy -- models generate unnecessary tokens long after reaching the correct answer. These properties unlock more efficient and reliable inference strategies: 1) Early Exit leverages reliability and redundancy to terminate computation safely when returns diminish, and 2)Test-Time Scaling uses the Confidence Region signal to prioritize converged trajectories. To operationalize these insights, we formulate Confidence Region detection as a sequential change-point detection problem, being the first to apply classical change-point methods to monitor CoT reasoning. Using the Cumulative Sum (CUSUM) algorithm, a statistically optimal change-point detector, we develop a training-free framework for real-time inference control. Experiments show our approach establishes a superior Pareto-frontier for early exit. CUSUM achieves 63.06% accuracy with 11.1% token reduction, outperforming DEER and Dynasor by 3.28% and 4.36% in accuracy respectively. For test-time scaling, CUSUM-weighted voting consistently outperforms self-consistency.

Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification

Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However, existing works often struggle to verify the correctness of the generated optimization models, without checking the rationality of the constraints and variables or the validity of solutions to the generated models. This hampers the subsequent verification and correction steps, and thus it severely hurts the modeling accuracy. To address this challenge, we propose a novel LLM-based framework with Dual-side Verification (Opt-Verifier) from both structure and solution perspectives, thereby improving the modeling accuracy. The structure-side verification ensures that the modeling structure of the generated optimization models aligns with the original problem description, accurately capturing the problem's constraints and requirements. Meanwhile, the solution-side verification interprets and evaluates the solutions' validity, confirming that the optimization models are logically and mathematically sound. Experiments on popular benchmarks demonstrate that our approach achieves over 20\% improvement in accuracy.

The Rank and Gradient Lost in Non-stationarity: Sample Weight Decay for Mitigating Plasticity Loss in Reinforcement Learning

Deep reinforcement learning (RL) suffers from plasticity loss severely due to the nature of non-stationarity, which impairs the ability to adapt to new data and learn continually. Unfortunately, our understanding of how plasticity loss arises, dissipates, and can be dissolved remains limited to empirical findings, leaving the theoretical end underexplored.To address this gap, we study the plasticity loss problem from the theoretical perspective of network optimization. By formally characterizing the two culprit factors in online RL process: the non-stationarity of data distributions and the non-stationarity of targets induced by bootstrapping, our theory attributes the loss of plasticity to two mechanisms: the rank collapse of the Neural Tangent Kernel (NTK) Gram matrix and the $Θ(\frac{1}{k})$ decay of gradient magnitude. The first mechanism echoes prior empirical findings from the theoretical perspective and sheds light on the effects of existing methods, e.g., network reset, neuron recycle, and noise injection. Against this backdrop, we focus primarily on the second mechanism and aim to alleviate plasticity loss by addressing the gradient attenuation issue, which is orthogonal to existing methods. We propose Sample Weight Decay -- a lightweight method to restore gradient magnitude, as a general remedy to plasticity loss for deep RL methods based on experience replay. In experiments, we evaluate the efficacy of \methodName upon TD3, \myadded{Double DQN} and SAC with SimBa architecture in MuJoCo, \myadded{ALE} and DeepMind Control Suite tasks. The results demonstrate that \methodName effectively alleviates plasticity loss and consistently improves learning performance across various configurations of deep RL algorithms, UTD, network architectures, and environments, achieving SOTA performance on challenging DMC Humanoid tasks.

K^2-Agent: Co-Evolving Know-What and Know-How for Hierarchical Mobile Device Control

Existing mobile device control agents often perform poorly when solving complex tasks requiring long-horizon planning and precise operations, typically due to a lack of relevant task experience or unfamiliarity with skill execution. We propose K2-Agent, a hierarchical framework that models human-like cognition by separating and co-evolving declarative (knowing what) and procedural (knowing how) knowledge for planning and execution. K2-Agent's high level reasoner is bootstrapped from a single demonstration per task and runs a Summarize-Reflect-Locate-Revise (SRLR) loop to distill and iteratively refine task-level declarative knowledge through self-evolution. The low-level executor is trained with our curriculum-guided Group Relative Policy Optimization (C-GRPO), which (i) constructs a balanced sample pool using decoupled reward signals and (ii) employs dynamic demonstration injection to guide the model in autonomously generating successful trajectories for training. On the challenging AndroidWorld benchmark, K2-Agent achieves a 76.1% success rate using only raw screenshots and open-source backbones. Furthermore, K2-Agent shows powerful dual generalization: its high-level declarative knowledge transfers across diverse base models, while its low-level procedural skills achieve competitive performance on unseen tasks in ScreenSpot-v2 and Android-in-the-Wild (AitW).

Global Prior Meets Local Consistency: Dual-Memory Augmented Vision-Language-Action Model for Efficient Robotic Manipulation

Hierarchical Vision-Language-Action (VLA) models have rapidly become a dominant paradigm for robotic manipulation. It typically comprising a Vision-Language backbone for perception and understanding, together with a generative policy for action generation. However, its performance is increasingly bottlenecked by the action generation proceess. (i) Low inference efficiency. A pronounced distributional gap between isotropic noise priors and target action distributions, which increases denoising steps and the incidence of infeasible samples. (ii) Poor robustness. Existing policies condition solely on the current observation, neglecting the constraint of history sequence and thus lacking awareness of task progress and temporal consistency. To address these issues, we introduce OptimusVLA, a dual-memory VLA framework with Global Prior Memory (GPM) and Local Consistency Memory (LCM). GPM replaces Gaussian noise with task-level priors retrieved from semantically similar trajectories, thereby shortening the generative path and reducing the umber of function evaluations (NFE). LCM dynamically models executed action sequence to infer task progress and injects a learned consistency constraint that enforces temporal coherence and smoothness of trajectory. Across three simulation benchmarks, OptimusVLA consistently outperforms strong baselines: it achieves 98.6% average success rate on LIBERO, improves over pi_0 by 13.5% on CALVIN, and attains 38% average success rate on RoboTwin 2.0 Hard. In Real-World evaluation, OptimusVLA ranks best on Generalization and Long-horizon suites, surpassing pi_0 by 42.9% and 52.4%, respectively, while delivering 2.9x inference speedup.

ActionCodec: What Makes for Good Action Tokenizers

Vision-Language-Action (VLA) models leveraging the native autoregressive paradigm of Vision-Language Models (VLMs) have demonstrated superior instruction-following and training efficiency. Central to this paradigm is action tokenization, yet its design has primarily focused on reconstruction fidelity, failing to address its direct impact on VLA optimization. Consequently, the fundamental question of \textit{what makes for good action tokenizers} remains unanswered. In this paper, we bridge this gap by establishing design principles specifically from the perspective of VLA optimization. We identify a set of best practices based on information-theoretic insights, including maximized temporal token overlap, minimized vocabulary redundancy, enhanced multimodal mutual information, and token independence. Guided by these principles, we introduce \textbf{ActionCodec}, a high-performance action tokenizer that significantly enhances both training efficiency and VLA performance across diverse simulation and real-world benchmarks. Notably, on LIBERO, a SmolVLM2-2.2B fine-tuned with ActionCodec achieves a 95.5\% success rate without any robotics pre-training. With advanced architectural enhancements, this reaches 97.4\%, representing a new SOTA for VLA models without robotics pre-training. We believe our established design principles, alongside the released model, will provide a clear roadmap for the community to develop more effective action tokenizers.

Short Chains, Deep Thoughts: Balancing Reasoning Efficiency and Intra-Segment Capability via Split-Merge Optimization

While Large Reasoning Models (LRMs) have demonstrated impressive capabilities in solving complex tasks through the generation of long reasoning chains, this reliance on verbose generation results in significant latency and computational overhead. To address these challenges, we propose \textbf{CoSMo} (\textbf{Co}nsistency-Guided \textbf{S}plit-\textbf{M}erge \textbf{O}ptimization), a framework designed to eliminate structural redundancy rather than indiscriminately restricting token volume. Specifically, CoSMo utilizes a split-merge algorithm that dynamically refines reasoning chains by merging redundant segments and splitting logical gaps to ensure coherence. We then employ structure-aligned reinforcement learning with a novel segment-level budget to supervise the model in maintaining efficient reasoning structures throughout training. Extensive experiments across multiple benchmarks and backbones demonstrate that CoSMo achieves superior performance, improving accuracy by \textbf{3.3} points while reducing segment usage by \textbf{28.7\%} on average compared to reasoning efficiency baselines.

Why Attention Patterns Exist: A Unifying Temporal Perspective Analysis

Attention patterns play a crucial role in both training and inference of large language models (LLMs). Prior works have identified individual patterns such as retrieval heads, sink heads, and diagonal traces, yet these observations remain fragmented and lack a unifying explanation. To bridge this gap, we introduce \textbf{Temporal Attention Pattern Predictability Analysis (TAPPA), a unifying framework that explains diverse attention patterns by analyzing their underlying mathematical formulations} from a temporally continuous perspective. TAPPA both deepens the understanding of attention behavior and guides inference acceleration approaches. Specifically, TAPPA characterizes attention patterns as predictable patterns with clear regularities and unpredictable patterns that appear effectively random. Our analysis further reveals that this distinction can be explained by the degree of query self-similarity along the temporal dimension. Focusing on the predictable patterns, we further provide a detailed mathematical analysis of three representative cases through the joint effect of queries, keys, and Rotary Positional Embeddings (RoPE). We validate TAPPA by applying its insights to KV cache compression and LLM pruning tasks. Across these tasks, a simple metric motivated by TAPPA consistently improves performance over baseline methods. The code is available at https://github.com/MIRALab-USTC/LLM-TAPPA.

Ratio-Variance Regularized Policy Optimization for Efficient LLM Fine-tuning

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the \emph{variance (second central moment) of the policy ratio} provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose $R^2VPO$ (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate $R^2VPO$ on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that $R^2VPO$ consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.

Enhancing the Medical Context-Awareness Ability of LLMs via Multifaceted Self-Refinement Learning

Large language models (LLMs) have shown great promise in the medical domain, achieving strong performance on several benchmarks. However, they continue to underperform in real-world medical scenarios, which often demand stronger context-awareness, i.e., the ability to recognize missing or critical details (e.g., user identity, medical history, risk factors) and provide safe, helpful, and contextually appropriate responses. To address this issue, we propose Multifaceted Self-Refinement (MuSeR), a data-driven approach that enhances LLMs' context-awareness along three key facets (decision-making, communication, and safety) through self-evaluation and refinement. Specifically, we first design a attribute-conditioned query generator that simulates diverse real-world user contexts by varying attributes such as role, geographic region, intent, and degree of information ambiguity. An LLM then responds to these queries, self-evaluates its answers along three key facets, and refines its responses to better align with the requirements of each facet. Finally, the queries and refined responses are used for supervised fine-tuning to reinforce the model's context-awareness ability. Evaluation results on the latest HealthBench dataset demonstrate that our method significantly improves LLM performance across multiple aspects, with particularly notable gains in the context-awareness axis. Furthermore, by incorporating knowledge distillation with the proposed method, the performance of a smaller backbone LLM (e.g., Qwen3-32B) surpasses its teacher model, achieving a new SOTA across all open-source LLMs on HealthBench (63.8%) and its hard subset (43.1%). Code and dataset will be released at https://muser-llm.github.io.