GraphPO: Graph-based Policy Optimization for Reasoning Models

Reinforcement Learning with Verifiable Rewards (RLVR) has become a standard paradigm for enhancing the capability of large reasoning models. RLVR typically samples responses independently and optimizes the policy using from final answers. This paradigm has two limitations. First, independently responses often contain similar intermediate reasoning steps, causing redundant exploration and wasted computation. Second, sparse final-answer rewards make it hard to identify useful steps. Tree-based methods partly address this problem by sharing prefixes and comparing branches from the same prefix to provide fine-grained signals. However, tree branches are still expanded independently. When different branches reach similar reasoning states, they cannot share information and repeat similar exploration. Moreover, tree-based methods ignore such dispersion and only perform local comparisons within separate branches, which can lead to higher variance in advantage estimation. To address this challenge, we propose GraphPO (Graph-based Policy Optimization), a novel RL framework that represents rollouts as a directed acyclic graph, with reasoning steps as edges and semantic states summarized from the reasoning paths as nodes. GraphPO merges semantically equivalent reasoning paths into equivalence classes, allowing them to share suffixes and reallocating budget away from redundant expansions to diverse exploration. Furthermore, we assign efficiency advantages to incoming edges and correctness advantages to outgoing edges, thereby improving inference efficiency while deriving process supervision from outcome. Theory shows that GraphPO reduces advantage-estimation variance and enhances reasoning efficiency. Experiments on three LLMs across reasoning and agentic search benchmarks show that GraphPO consistently outperforms chain- and tree-based baselines with the same token budgets or response budgets.

CloDS: Visual-Only Unsupervised Cloth Dynamics Learning in Unknown Conditions

Deep learning has demonstrated remarkable capabilities in simulating complex dynamic systems. However, existing methods require known physical properties as supervision or inputs, limiting their applicability under unknown conditions. To explore this challenge, we introduce Cloth Dynamics Grounding (CDG), a novel scenario for unsupervised learning of cloth dynamics from multi-view visual observations. We further propose Cloth Dynamics Splatting (CloDS), an unsupervised dynamic learning framework designed for CDG. CloDS adopts a three-stage pipeline that first performs video-to-geometry grounding and then trains a dynamics model on the grounded meshes. To cope with large non-linear deformations and severe self-occlusions during grounding, we introduce a dual-position opacity modulation that supports bidirectional mapping between 2D observations and 3D geometry via mesh-based Gaussian splatting in video-to-geometry grounding stage. It jointly considers the absolute and relative position of Gaussian components. Comprehensive experimental evaluations demonstrate that CloDS effectively learns cloth dynamics from visual data while maintaining strong generalization capabilities for unseen configurations. Our code is available at https://github.com/whynot-zyl/CloDS. Visualization results are available at https://github.com/whynot-zyl/CloDS_video}.%\footnote{As in this example.

Rethinking Sample Polarity in Reinforcement Learning with Verifiable Rewards

Large reasoning models (LRMs) are typically trained using reinforcement learning with verifiable reward (RLVR) to enhance their reasoning abilities. In this paradigm, policies are updated using both positive and negative self-generated rollouts, which correspond to distinct sample polarities. In this paper, we provide a systematic investigation into how these sample polarities affect RLVR training dynamics and behaviors. We find that positive samples sharpen existing correct reasoning patterns, while negative samples encourage exploration of new reasoning paths. We further explore how adjusting the advantage values of positive and negative samples at both the sample level and the token level affects RLVR training. Based on these insights, we propose an Adaptive and Asymmetric token-level Advantage shaping method for Policy Optimization, namely A3PO, that more precisely allocates advantage signals to key tokens across different polarities. Experiments across five reasoning benchmarks demonstrate the effectiveness of our approach.