Lianrui Li

Powei Chang, Jinpeng Zhang, Chaoqun Sun et al.

Reinforcement learning with verifiable rewards (RLVR) often adopts GRPO-style group-relative updates, sampling multiple rollouts per prompt to construct normalized learning signals. However, merely increasing the number of rollouts does not reliably strengthen learning: under GRPO-style group normalization, per-rollout policy-gradient features can concentrate into a low-rank, signed geometry, causing substantial cancellation during aggregation and weakening the effective update. We address this failure mode with SALT, a Subspace-Adaptive geometry pLug-in componenT that uses sample-wise gradient geometry to reweight the coefficients of group-relative updates. SALT estimates a dominant shared subspace from the mini-batch Gram geometry, decomposes group-relative coefficients into shared and residual channels, and adaptively amplifies the residual channel when signed cancellation is severe. Across diverse reasoning-oriented RLVR benchmarks and model scales, SALT improves effective update geometry and performance without modifying the reward model or the rollout sampling procedure

Lianrui Li, Dakuan Lu, Jiawei Shao et al.

We propose Self-correction Relative Policy Optimization (ScRPO), a novel reinforcement learning framework designed to enhance large language models on challenging mathematical problems by leveraging self-reflection and error correction. Our approach consists of two stages: (1) Trial-and-error learning stage: training the model with GRPO and collecting incorrect answers along with their corresponding questions in an error pool; (2) Self-correction learning stage: guiding the model to reflect on why its previous answers were wrong. Extensive experiments across multiple math reasoning benchmarks, including AIME, AMC, Olympiad, MATH-500, GSM8k, using Deepseek-Distill-Qwen-1.5B and Deepseek-Distill-Qwen-7B. The experimental results demonstrate that ScRPO consistently outperforms several post-training methods. These findings highlight ScRPO as a promising paradigm for enabling language models to self-improve on difficult tasks with limited external feedback, paving the way toward more reliable and capable AI systems.