Shaofan Liu

Jiazheng Zhang, Ziche Fu, Junrui Shen et al.

Policy entropy has emerged as a fundamental measure for understanding and controlling exploration in reinforcement learning with verifiable rewards (RLVR) for LLMs. However, existing entropy-aware methods mainly regulate entropy through global objectives, while the token-level mechanism by which sampled policy updates reshape policy entropy remains underexplored. In this work, we develop a theoretical framework of entropy mechanics in RLVR. Our analysis yields a first-order approximation of the entropy change, giving rise to entropy polarity, a signed token-level quantity that predicts how much a sampled update expands or contracts entropy. This analysis further reveals a structural asymmetry: reinforcing frequent high-probability tokens triggers contraction tendencies, whereas expansive tendencies typically require lower-probability samples or stronger distributional correction. Empirically, we show that entropy polarity reliably predicts entropy changes, and that positive and negative polarity branches play complementary roles in preserving exploration while strengthening exploitation. Building on these insights, we propose Polarity-Aware Policy Optimization (PAPO), which preserves both polarity branches and implements entropy control through advantage reweighting. With the empirical entropy trajectory as an online phase signal, PAPO adaptively reallocates optimization pressure between entropy-expanding and entropy-contracting updates. Experiments on mathematical reasoning and agentic benchmarks show that PAPO consistently outperforms competitive baselines, while delivering superior training efficiency and substantial reward improvements.

Shaofan Liu, Junbo Chen, Jianke Zhu

Incremental scene reconstruction is essential to the navigation in robotics. Most of the conventional methods typically make use of either TSDF (truncated signed distance functions) volume or neural networks to implicitly represent the surface. Due to the voxel representation or involving with time-consuming sampling, they have difficulty in balancing speed, memory storage, and surface quality. In this paper, we propose a novel hybrid voxel-octree approach to effectively fuse octree with voxel structures so that we can take advantage of both implicit surface and explicit triangular mesh representation. Such sparse structure preserves triangular faces in the leaf nodes and produces partial meshes sequentially for incremental reconstruction. This storage scheme allows us to naturally optimize the mesh in explicit 3D space to achieve higher surface quality. We iteratively deform the mesh towards the target and recovers vertex colors by optimizing a shading model. Experimental results on several datasets show that our proposed approach is capable of quickly and accurately reconstructing a scene with realistic colors.

Di Wu, Liu Liu, Anran Huang et al.

Articulated objects are pervasive in daily environments, such as drawers and refrigerators. Towards their part-level surface reconstruction and joint parameter estimation, REArtGS introduces a category-agnostic approach using multi-view RGB images at two different states. However, we observe that REArtGS still struggles with screw-joint or multi-part objects and lacks geometric constraints for unseen states. In this paper, we propose REArtGS++, a novel method towards generalizable articulated object reconstruction with temporal geometry constraint and planar Gaussian splatting. We first model a decoupled screw motion for each joint without type prior, and jointly optimize part-aware Gaussians with joint parameters through part motion blending. To introduce time-continuous geometric constraint for articulated modeling, we encourage Gaussians to be planar and propose a temporally consistent regularization between planar normal and depth through Taylor first-order expansion. Extensive experiments on both synthetic and real-world articulated objects demonstrate our superiority in generalizable part-level surface reconstruction and joint parameter estimation, compared to existing approaches. Project Site: https://sites.google.com/view/reartgs2/home.