Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), has advanced LLM reasoning. However, GRPO suffers from three credit assignment failures: uniform token-level granularity that ignores heterogeneous informational value, uniform polarity that penalizes correct steps and rewards incorrect ones, and zero-variance collapse that erases outcome-driven gradients. We systematically quantify these failures, revealing highly non-uniform token informativeness, widespread step-level polarity misalignment, and substantial training waste. To address these limitations, we propose Entropy-Progress Aligned GRPO (EP-GRPO), a framework that mines the model's intrinsic information flow for dense, self-supervised guidance. EP-GRPO integrates entropy-gated modulation to prioritize high entropy decision pivots, implicit process signals from policy divergence anchored to outcome advantages for directional token-level feedback without external reward models, and cumulative entropy mapping that enables progress-aligned advantage normalization, naturally maintaining gradient flow under zero reward variance. Extensive experiments on mathematical reasoning benchmarks demonstrate that EP-GRPO achieves superior accuracy and efficiency compared to GRPO and its variants. The code will be available.
Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capabilities of Large Language Models (LLMs) by leveraging direct outcome verification instead of learned reward models. Building on this paradigm, Group Relative Policy Optimization (GRPO) eliminates the need for critic models but suffers from indiscriminate credit assignment for intermediate steps, which limits its ability to identify effective reasoning strategies and incurs overthinking. In this work, we introduce a model-free and verifiable process supervision via probing the model's belief in the correct answer throughout its reasoning trajectory. By segmenting the generation into discrete steps and tracking the conditional probability of the correct answer appended at each segment boundary, we efficiently compute interpretable segment-wise progress measurements to refine GRPO's trajectory-level feedback. This approach enables more targeted and sample-efficient policy updates, while avoiding the need for intermediate supervision derived from costly Monte Carlo rollouts or auxiliary models. Experiments on mathematical and general-domain benchmarks show consistent gains over GRPO across diverse models: up to 2.6-point accuracy improvements and 13.7% reasoning-length reductions on math tasks, and up to 2.4 points and 4% on general-domain tasks, demonstrating strong generalization.
Group Relative Policy Optimization (GRPO) has emerged as a promising approach for improving the reasoning capabilities of large language models. However, it struggles to effectively balance the tradeoff between exploration and exploitation during training, often resulting in suboptimal performance. Motivated by the theoretical insight that changes in entropy are governed by the covariance between token probabilities and their corresponding advantages, we propose a hyperparameter-free, covariance-weighted optimization method that dynamically down-weights extreme token-level updates via a Gaussian kernel. This approach automatically reduces the instability caused by exploration-exploitation trade-off while preserving informative learning signals. Extensive empirical evaluations show that our approach improves downstream performance across reasoning benchmarks compared with GRPO, and effectively stablizes entropy as training progresses.
Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models (LLMs). However, GRPO is prone to advantage collapse, a failure mode where homogeneous rewards within a group (e.g., all correct or all incorrect answers) yield near-zero advantages and vanishing gradients. To address this, we introduce the Advantage Collapse Rate (ACR), the first diagnostic metric quantifying the proportion of training batches with ineffective gradients. Across models from 0.5B to 14B parameters on mathematical reasoning benchmarks, we show that ACR strongly predicts training stagnation and final performance. We then propose Adaptive Virtual Sample Policy Optimization (AVSPO), a lightweight extension of GRPO that injects virtual reward samples, guided by real-time ACR monitoring, to enable learning from homogeneous groups without additional model rollouts. AVSPO reduces advantage collapse by 58-63% relative to GRPO and yields consistent accuracy gains of 4-6 percentage points across all model scales, while maintaining generalization on the evaluated out-of-domain task. Code and datasets are available at https://github.com/hexixiang/Advantage-Collapse-Rate.