Beyond Alignment: Expanding Reasoning Capacity via Manifold-Reshaping Policy Optimization

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated remarkable success in enhancing the reasoning capabilities of Large Language Models (LLMs). However, recent studies question whether RL genuinely expands reasoning capacity or merely aligns existing latent capabilities, arguing that exploration remains confined within the pre-trained model's low-rank bias manifold. In this work, we challenge this accessibility boundary hypothesis by demonstrating that the latent reasoning space can be fundamentally expanded through targeted geometric interventions. We propose Manifold-Reshaping Policy Optimization (MRPO), a geometric framework designed to fundamentally restructure the inference space of LLMs. MRPO operates in two stages: first, we employ Spectral Orthogonal Exploration (SOE) to eject the policy initialization into the null space of the bias manifold; second, we integrate an Effective Rank regularization term into the policy optimization objective. This approach incentivizes the discovery and maintenance of high-dimensional reasoning trajectories against the entropy-reducing tendency of standard RL. Empirically, our 4B-parameter method achieves state-of-the-art performance on mathematical tasks, significantly outperforming larger models (e.g., Qwen3-32B) and expanding the capability boundary beyond standard GRPO. Our code is available at https://anonymous.4open.science/r/MRPO-D57B/

Reducing Cognitive Load in Multi-Agent Reinforcement Learning for Mathematical Problem Solving: Decoupling Reasoning and Code Generation

Current tool-integrated mathematical reasoning systems often adopt a single-agent paradigm, where one large language model handles problem reasoning, code generation, and code execution in an integrated workflow. While this design eases coordination, we hypothesize that it imposes cognitive load interference, as the agent must interleave long-horizon reasoning with precise program synthesis. We validate this hypothesis through a controlled comparison between a reasoning-only agent and a reasoning-plus-code agent, finding that the latter produces significantly fewer correct reasoning paths despite having tool-calling capabilities. To address this, we propose a dual-agent hybrid framework: a Reasoning Agent performs stepwise problem decomposition, and a Code Agent handles code generation and execution. Training combines imitation learning and reinforcement learning: the Code Agent receives strong rewards for matching intermediate ground-truth programs and weaker rewards for valid execution, while the Reasoning Agent is optimized chiefly via final-answer accuracy using advantage estimation to credit intermediate steps. This decoupled role design reduces cognitive interference and promotes stable reasoning-coding coordination.