Know What You Know: Metacognitive Entropy Calibration for Verifiable RL Reasoning

TL;DR

This paper introduces EGPO, a framework that incorporates model uncertainty into reinforcement learning for reasoning tasks, leading to improved reasoning accuracy by calibrating entropy and addressing the uncertainty-reward mismatch.

Contribution

EGPO is a novel entropy calibration method that explicitly integrates intrinsic uncertainty into RLVR, enhancing reasoning performance without modifying the verifier or reward structure.

Findings

EGPO improves reasoning accuracy across multiple benchmarks.

Uncertainty calibration stabilizes policy optimization in reasoning tasks.

The method effectively distinguishes high- and low-uncertainty solutions.

Abstract

Large reasoning models (LRMs) have emerged as a powerful paradigm for solving complex real-world tasks. In practice, these models are predominantly trained via Reinforcement Learning with Verifiable Rewards (RLVR), yet most existing outcome-only RLVR pipelines rely almost exclusively on a binary correctness signal and largely ignore the model's intrinsic uncertainty. We term this discrepancy the uncertainty-reward mismatch, under which high- and low-uncertainty solutions are treated equivalently, preventing the policy from "Know What You Know" and impeding the shift from optimizing for correct answers to optimizing effective reasoning paths. This limitation is especially critical in reasoning-centric tasks such as mathematics and question answering, where performance hinges on the quality of the model's internal reasoning process rather than mere memorization of final answers. To address this, we propose EGPO, a metacognitive entropy calibration framework that explicitly integrates intrinsic uncertainty into RLVR for enhancing LRMs. EGPO estimates per-sample uncertainty using a zero-overhead entropy proxy derived from token-level likelihoods and aligns it with extrinsic correctness through an asymmetric calibration mechanism that preserves correct reasoning while selectively regulating overconfident failures, thereby enabling stable and uncertainty-aware policy optimization. Moreover, EGPO recovers informative learning signals from otherwise degenerate group-based rollouts without modifying the verifier or reward definition. Extensive experiments across multiple benchmarks demonstrate that the proposed EGPO leads to substantial and consistent improvements in reasoning performance, establishing a principled path for advancing LRMs through metacognitive entropy calibration.