On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation

• URL: http://arxiv.org/abs/2603.22117v1
• Date: Mon, 23 Mar 2026 15:42:24 GMT
• Title: On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation
• Abstract summary: We argue that the direction of updates is a more critical lens for understanding RLVR's effects.<n>Our work establishes the direction of change as a key principle for analyzing and improving RLVR.
• Score: 81.29776444949539
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the \textbf{magnitude} of these updates, largely overlooking their \textbf{direction}. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference $Δ\log p$ between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that $Δ\log p$ more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a \textit{test-time extrapolation} method that amplifies the policy along the learned $Δ\log p$ direction to improve reasoning accuracy without further training; (2) a \textit{training-time reweighting} method that focuses learning on low-probability (corresponding to higher $Δ\log p$) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

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