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 presents FR3E, an RL framework that uses token-level entropy to pinpoint high-uncertainty decisions for effective exploration.
• It introduces a two-phase approach—‘First Return’ and entropy-eliciting exploration—to generate semantically meaningful intermediate rewards and enhance policy updates.
• Empirical results across multiple math benchmarks show FR3E boosts training stability, trajectory coherence, and accuracy, particularly in large general-purpose models.

Structured Exploration for LLM Reasoning: An Analysis of FR3E

The paper "First Return, Entropy-Eliciting Explore" (FR3E) (2507.07017) presents a novel reinforcement learning (RL) framework for LLMs that addresses the persistent challenge of unstable and inefficient exploration in reasoning-intensive tasks, particularly mathematical problem solving. The authors propose a structured, uncertainty-driven exploration paradigm that departs from both value-model-based and trajectory-level reward assignment approaches, offering a more robust mechanism for credit assignment and policy improvement in LLMs.

Motivation and Context

Existing RL methods for LLMs, such as PPO, VAPO, and GRPO, are hampered by either the instability and computational overhead of value model training or the imprecision of trajectory-level reward assignment. These limitations are especially pronounced in tasks with sparse and delayed rewards, where uniform credit assignment across reasoning steps fails to distinguish between pivotal and inconsequential actions. Heuristic or sampling-based intermediate reward estimation, as in VinePPO and process reward models (PRMs), introduces further complexity, variance, and labeling costs.

FR3E is motivated by the need for a scalable, value-model-free exploration strategy that can provide semantically meaningful intermediate feedback without dense supervision or brittle heuristics. The framework draws inspiration from the "First Return, Then Explore" paradigm in Go-Explore, adapting it to the sequential, autoregressive nature of LLM generation.

Methodology

FR3E decomposes the RL process into two complementary phases:

1. First Return: The model generates a base trajectory for a given prompt and computes token-wise entropy to identify high-uncertainty decision points. These points, corresponding to local maxima in entropy, are selected as anchors for further exploration.
2. Entropy-Eliciting Explore: From each identified anchor (intermediate state), the model performs multiple partial rollouts, generating alternative continuations. The correctness of each rollout is evaluated, and the empirical value of the anchor state is estimated as the average reward across rollouts.

This approach enables the construction of semantically grounded, localized feedback signals that guide policy updates. The framework introduces an adaptive advantage modulation mechanism, scaling the learning signal based on the marginal improvement in value between consecutive anchor states. This dynamic adjustment prevents premature convergence and maintains exploration diversity.

Key implementation details include:

• Rejection Sampling: Prompts yielding degenerate (all-correct or all-incorrect) rollouts are excluded from entropy analysis, ensuring informative exploration.
• Clip-Higher Objective: Asymmetric clipping in the PPO objective encourages probability growth for low-confidence tokens, mitigating entropy collapse and supporting exploration.
• Block-wise Segmentation: Trajectories are segmented at high-entropy positions, enabling fine-grained credit assignment and targeted policy refinement.

Empirical Results

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). The main findings are:

• Training Stability: FR3E maintains higher and more stable entropy during training, particularly in general-purpose models, indicating healthier exploration and reduced risk of premature exploitation.
• Performance Gains: On AIME24, FR3E achieves a 2.5% and 6.1% absolute accuracy improvement over GRPO++ for Qwen2.5-7B and Qwen2.5-32B, respectively. Average accuracy improvements across benchmarks are 3.0% (7B) and 3.1% (32B).
• Trajectory Consistency: The number of "All-Right" (fully correct) trajectories increases while "All-Wrong" trajectories decrease under FR3E, reflecting more reliable and consistent reasoning.
• Response Length and Coherence: FR3E produces longer and more coherent reasoning chains, especially in generalist models, suggesting improved capacity for complex, multi-step reasoning.
• Domain-Specific Models: Gains on Qwen2.5-Math-7B are limited, indicating that RL strategies may require adaptation for models with strong domain priors.

Implications and Theoretical Considerations

FR3E demonstrates that structured, entropy-driven exploration can significantly enhance the reasoning capabilities of LLMs in RL settings. By localizing exploration to high-uncertainty decision points and leveraging partial rollouts, the framework achieves more precise credit assignment and efficient policy improvement without the instability of value models or the cost of dense supervision.

The adaptive advantage modulation mechanism ensures that learning signals are dynamically scaled, preserving exploration in regions of the reasoning space where the model is uncertain or underperforming. This contributes to stable, incremental learning and mitigates the risk of error propagation in long-chain reasoning.

The empirical results suggest that the benefits of FR3E are most pronounced in general-purpose and large-scale models, where exploration capacity and trajectory diversity are critical. For domain-specialized models, further research is needed to reconcile the tension between strong priors and the flexibility required for RL-based improvement.

Future Directions

Several avenues for future research emerge from this work:

• Generalization to Other Domains: Extending FR3E to code generation, multi-turn dialogue, and other complex reasoning tasks could validate its generality.
• Integration with Process Reward Models: Combining entropy-driven exploration with automated or implicit process reward estimation may yield further gains in credit assignment.
• Scalability and Efficiency: Optimizing the computational footprint of partial rollouts and entropy computation will be important for large-scale deployment.
• Adaptive Exploration Strategies: Investigating alternative uncertainty metrics or dynamic anchor selection could enhance exploration efficiency.

Conclusion

FR3E introduces a principled, structured exploration framework for RL in LLMs, grounded in entropy-based uncertainty signals and partial trajectory rollouts. The approach yields measurable improvements in training stability, reasoning coherence, and accuracy on challenging mathematical benchmarks, particularly for generalist and large-scale models. The framework's value-model-free design and adaptive learning dynamics position it as a robust alternative to existing RL methods for LLM reasoning, with significant implications for the development of more reliable and capable language agents.