First Return, Entropy-Eliciting Explore (2507.07017v1)

Abstract: Reinforcement Learning from Verifiable Rewards (RLVR) improves the reasoning abilities of LLMs but it struggles with unstable exploration. We propose FR3E (First Return, Entropy-Eliciting Explore), a structured exploration framework that identifies high-uncertainty decision points in reasoning trajectories and performs targeted rollouts to construct semantically grounded intermediate feedback. Our method provides targeted guidance without relying on dense supervision. Empirical results on mathematical reasoning benchmarks(AIME24) show that FR3E promotes more stable training, produces longer and more coherent responses, and increases the proportion of fully correct trajectories. These results highlight the framework's effectiveness in improving LLM reasoning through more robust and structured exploration.

• The paper introduces a two-stage exploration framework that identifies high-uncertainty states using token-wise entropy for improved reinforcement learning in LLMs.
• It employs targeted partial rollouts and adaptive advantage modulation to replace uniform reward propagation, ensuring precise credit assignment.
• Empirical results show enhanced training stability and up to 6% accuracy gains on mathematical benchmarks compared to traditional RLVR methods.

Structured Exploration for LLM Reasoning: An Analysis of FR3E

The paper "First Return, Entropy-Eliciting Explore" (FR3E) (2507.07017) presents a structured exploration framework for reinforcement learning from verifiable rewards (RLVR) in LLMs, with a focus on mathematical reasoning tasks. The work addresses the persistent challenge of unstable and inefficient exploration in RLVR, particularly the difficulty of assigning credit to intermediate steps in long reasoning trajectories where rewards are sparse and delayed.

Motivation and Context

Existing RLVR approaches, such as Group Relative Policy Optimization (GRPO), typically propagate final outcome rewards uniformly across all intermediate steps. This uniform credit assignment is misaligned with the actual contribution of each step, leading to suboptimal learning and phenomena such as "overthinking." Value-model-based methods (e.g., PPO, VAPO) introduce a critic to estimate intermediate values, but suffer from instability and computational overhead due to the vast state space of LLMs. Heuristic and sampling-based methods (e.g., VinePPO, PRMs, PRIME) attempt to provide intermediate feedback but are limited by sampling variance, labeling costs, and the brittleness of heuristics.

FR3E: Methodological Contributions

FR3E introduces a two-stage, value-model-free exploration paradigm inspired by the "First Return, Then Explore" principle from Go-Explore, adapted for the autoregressive generation process of LLMs:

1. First Return (Uncertainty Localization):
   • For each generated reasoning trajectory, FR3E computes token-wise entropy to identify high-uncertainty positions—tokens where the model's output distribution is most diffuse.
   • The top-K entropy positions are selected as critical decision points, segmenting the trajectory into semantically meaningful blocks.
2. Entropy-Eliciting Explore (Targeted Rollouts):
   • From each identified high-entropy state, the model performs multiple partial rollouts, generating alternative continuations.
   • Each rollout is evaluated for correctness, and the empirical value of each state is estimated as the average reward over its rollouts.
   • This process yields localized, semantically grounded feedback, enabling more precise credit assignment and policy updates.
3. Adaptive Advantage Modulation:
   • The advantage function is dynamically scaled based on the marginal improvement in empirical value between consecutive states, stabilizing learning and preventing premature convergence.
   • This modulation ensures that the policy gradient remains approximately unbiased, even with variable trajectory lengths.
4. Auxiliary Mechanisms:
   • Rejection Sampling: Prompts yielding only all-correct or all-incorrect rollouts are excluded from entropy analysis, maintaining informative gradient signals.
   • Clip-Higher: Asymmetric clipping in PPO updates encourages exploration by allowing greater increases in the probability of underexplored actions, mitigating entropy collapse.

Empirical Evaluation

FR3E is evaluated on a suite of mathematical reasoning benchmarks (AIME24, GSM8K, Math500, Minerva Math, Gaokao2023en, OlympiadBench, College Math, AMC23) using Qwen2.5 model variants (7B, Math-7B, 32B). Key findings include:

• Training Stability and Exploration:
  • FR3E maintains higher entropy during training, especially in general-purpose models, indicating sustained exploration and avoidance of early policy collapse.
  • The method produces longer and more coherent reasoning chains, as evidenced by increased average response lengths.
• Performance Gains:
  • On generalist models (Qwen2.5-7B, 32B), FR3E outperforms GRPO++ by 2–6% on several benchmarks, with the largest gains observed in larger models.
  • On the domain-specialized Qwen2.5-Math-7B, improvements are marginal, suggesting that RLVR strategies may interfere with highly specialized prior knowledge.
• Trajectory Consistency:
  • FR3E increases the proportion of "All-Right" (fully correct) trajectories while reducing "All-Wrong" ones, indicating more reliable and consistent policy updates.
  • Heatmap analyses of rollout accuracy show that FR3E achieves stable, incremental improvements, with learned solutions persisting across training epochs.
• Advantage Estimation:
  • The advantage values under FR3E remain tightly centered around zero, reflecting minimal distributional shift and stable policy optimization.

Numerical Highlights

• On AIME24, FR3E achieves 25.2% accuracy on Qwen2.5-7B (+2.5% over GRPO++), and 40.2% on Qwen2.5-32B (+6.1%).
• On GSM8K, FR3E reaches 92.8% (7B, +1.6%) and 96.1% (32B, +0.3%).
• Average accuracy improvements across all benchmarks are +1.8% (Math-7B), +3.0% (7B), and +3.1% (32B).

Theoretical and Practical Implications

FR3E demonstrates that uncertainty-driven, structured exploration can address the credit assignment problem in RL for LLMs without the need for dense supervision or complex value models. By localizing exploration to high-entropy decision points, the method achieves more data-efficient learning and robust policy improvement, particularly in tasks characterized by sparse rewards and long reasoning chains.

Practical implications include:

• Improved RLVR Training Pipelines: FR3E can be integrated into existing RLHF/RLVR frameworks to enhance exploration and stability, especially for generalist LLMs.
• Resource Efficiency: The partial rollout mechanism reduces computational cost compared to full trajectory sampling, making large-scale RLVR more tractable.
• Model Specialization Considerations: The limited gains on domain-specialized models highlight the need for tailored RL strategies that respect existing knowledge priors.

Limitations and Future Directions

• Domain Specialization: The method's effectiveness diminishes on highly specialized models, suggesting a need for adaptive exploration strategies that account for prior task-specific knowledge.
• Hyperparameter Sensitivity: The selection of entropy thresholds, number of rollouts, and block segmentation parameters may require tuning for different tasks and model architectures.
• Scalability: While partial rollouts are more efficient, the approach still incurs additional inference cost compared to standard RLVR, particularly as model and dataset sizes grow.

Potential future developments:

• Automated Block Selection: Leveraging learned or adaptive criteria for identifying exploration anchors could further improve efficiency and generalization.
• Integration with Process Reward Models: Combining FR3E with automated process supervision may yield even finer-grained credit assignment.
• Extension to Multi-Turn and Agentic Tasks: The structured exploration paradigm could be adapted for multi-turn dialogue, tool use, or agentic planning tasks in LLMs.

Conclusion

FR3E advances the state of RL for LLM reasoning by introducing a principled, uncertainty-driven exploration framework that enables more stable, efficient, and effective policy optimization. Its empirical results substantiate the claim that structured, entropy-based exploration can yield more reliable and scalable improvements in complex reasoning tasks, particularly for generalist models. The approach provides a foundation for further research into adaptive exploration and credit assignment in large-scale LLM training.