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Analyze reinforcement learning with verifiable rewards using signed log-probability differences to identify reasoning-critical tokens. Reveals that RLVR updates concentrate on low-probability tokens, enabling test-time amplification and training-time reweighting techniques.
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| name | rlvr-update-direction-analysis |
| title | On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation |
| version | 0.0.3 |
| engine | skillxiv-v0.0.3-claude-opus-4.6 |
| license | MIT |
| url | https://arxiv.org/abs/2603.22117 |
| keywords | ["RLVR","LLM Reasoning","Directional Analysis","Token Importance","Interpretability"] |
| description | Analyze reinforcement learning with verifiable rewards using signed log-probability differences to identify reasoning-critical tokens. Reveals that RLVR updates concentrate on low-probability tokens, enabling test-time amplification and training-time reweighting techniques. |
How can directional analysis of parameter updates reveal which tokens are critical for reasoning improvements in RLVR-trained models, and how can this insight be exploited for inference and training?
Signed Log-Probability Differences (Δlog p) - Captures the direction and magnitude of probability shifts per token between base and RLVR models. More sensitive to reasoning-critical changes than magnitude-only metrics (entropy, KL divergence).
The paper shows that Δlog p exhibits "clear bimodal patterns" whereas magnitude-based metrics yield "nearly identical histograms for base and RLVR models."
1. Test-Time Extrapolation - Amplify the learned Δlog p direction at inference without retraining. Scale probability shifts by a factor α > 1 to enhance reasoning improvements. Improves accuracy without additional training cost.
2. Training-Time Reweighting - Upweight advantages (reward signals) for low-probability tokens during RLVR training. Concentrates gradient flow where it matters most, yielding consistent performance gains across benchmarks and models.
Both techniques translate the directional insight into actionable procedures for practitioners.
The directional analysis framework generalizes beyond RLVR:
