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First Return, Entropy-Eliciting Explore

Tianyu Zheng, Tianshun Xing, Qingshui Gu, Taoran Liang, Xingwei Qu, Xin Zhou, Yizhi Li, Zhoufutu Wen, Chenghua Lin, Wenhao Huang, Qian Liu, Ge Zhang, Zejun Ma

arXiv:2507.07017v1cs.AI

TL;DR

Sparse rewards make intermediate credit assignment and stable exploration challenging in LLM reasoning. FR3E targets high-uncertainty points with rollouts that construct intermediate feedback. The paper reports more stable training, longer reasoning chains, and increased yields of correct solutions.

  • Problem

    RLVR supports LLM reasoning, but sparse and delayed outcome rewards make it difficult to assign credit to intermediate steps and sustain effective exploration.

    Source: §1 · p. 1

  • Method

    FR3E locates high-uncertainty points in reasoning trajectories and launches targeted rollouts to construct intermediate feedback.

    Source: §1 · p. 2

  • Results

    FR3E produces more stable training dynamics, longer and more coherent reasoning chains, and a higher yield of correct solutions.

    Source: §6 · p. 12

  • Takeaways & Limitations

    FR3E provides a structured approach to improving LLM reasoning through more reliable exploration.

    Source: §6 · p. 12

    FR3E shows limited gains on Qwen2.5-Math-7B and performs comparably to GRPO++ across most benchmarks.

    Source: §5.2 · p. 9

Abstract

from arXiv · show

Reinforcement Learning from Verifiable Rewards (RLVR) improves the reasoning abilities of Large Language Models (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.

1 Introduction

FR3E targets uncertain reasoning decisions with structured rollouts that construct intermediate feedback, addressing sparse-reward credit assignment and exploration challenges. The paper reports more stable training and a higher proportion of fully correct trajectories.

1 Introduction

  • Sparse, delayed rewards make intermediate-step credit assignment difficult; uniform trajectory-level rewards can fail to distinguish pivotal reasoning from inconsequential actions.Critic-based and heuristic or process-reward alternatives also face instability, computational overhead, sampling variance, labeling costs, or granularity challenges.Source: §1 · pp. 1–2
  • FR3E identifies high-uncertainty decision points and launches targeted partial rollouts to construct localized, semantically grounded feedback without detailed step labels or a value model.The framework is presented as supporting more stable and data-efficient training without brittle reward shaping or complex critics.Source: §1 · p. 2
  • FR3E maintains stable, gradually increasing entropy during training and produces longer reasoning chains, with more All-Right and fewer All-Wrong trajectories across multiple rollouts per prompt.The paper says this prevents early entropy collapse and supports more reliable chains.Source: §1 · p. 2

2 Related Work

Related work addresses sparse-reward exploration, intermediate feedback, and credit assignment through structured search, hierarchical methods, critics, and value-model-free approaches. Adapting structured exploration to autoregressive LLM generation remains an active research area.

Reinforcement Learning: Challenges and Techniques

  • Go-Explore archives and revisits promising states, while hierarchical reinforcement learning uses subgoals and options to structure long-horizon tasks.PRMs and CALM are presented as approaches for intermediate rewards and subgoal-based credit attribution.Source: §2 · p. 2

Reinforcement Learning for Large Language Models

  • PPO’s value network is computationally costly and unstable for language generation, motivating value-model-free methods such as GRPO and RLOO.VinePPO uses rollouts from heuristic intermediate states, while PRIME derives implicit process rewards from final outcomes.Source: §2 · p. 3
  • Methods for granular credit assignment have advanced, but adapting structured exploration strategies such as Go-Explore to autoregressive LLM generation remains an active research area.The cited approaches include VinePPO, PRIME, GRPO, RLOO, and S-GRPO.Source: §2 · p. 3

3 Preliminary

The preliminaries frame autoregressive reasoning as sequential decision-making, then introduce rejection sampling, asymmetric clipping, and uncertainty-guided structured exploration as components of FR3E.

3.1 MDP Setup for Autoregressive Generation

  • Language reasoning tasks are modeled as MDPs with expected-return-maximizing policies, while rewards are typically sparse and arrive only after a complete rollout.Source: §3.1 · p. 3

3.2 Rejection Sampling

  • Prompts whose sampled rollouts all receive the same binary reward are rejected during entropy finding, preserving trajectories with informative reward variation.The degenerate prompts otherwise yield zero advantage estimates and can reduce effective batch size while increasing gradient-estimate variance.Source: §3.2 · p. 3

3.3 Clip-Higher

  • Clip-Higher uses asymmetric clipping bounds to permit larger probability increases for underexplored paths while limiting aggressive decreases.The paper reports that this design improves exploration efficiency and learning robustness.Source: §3.3 · pp. 3–4

3.4 Structured Exploration

  • FR3E adapts “First Return, Then Explore” by finding high-uncertainty states in promising trajectories and starting partial rollouts there to discover alternatives and generate feedback.High local entropy marks critical reasoning junctures for targeted exploration.Source: §3.4 · p. 4

4 FR3E: First Return, Entropy-Eliciting Explore

FR3E separates reasoning exploration into finding high-uncertainty points along base trajectories and exploring from those points with targeted rollouts. It uses sampled correctness feedback and adaptive advantage modulation to guide policy updates.

4 FR3E: First Return, Entropy-Eliciting Explore

  • FR3E identifies uncertain reasoning points in base trajectories, then explores from them with diverse rollouts that preserve semantic coherence.The framework incorporates entropy-based signals into path selection and policy updates.Source: §4 · p. 4

4.1.1 Base Trajectory Generation

  • A base reasoning trajectory is generated from each query using policy πθ.The trajectory represents step-by-step reasoning from the query to the final output.Source: §4.1.1 · pp. 4–5

4.1.2 Entropy Computation

  • Token-wise entropy measures uncertainty at each position, with higher entropy marking positions as candidates for structured exploration.The distribution is conditioned on the query and previously generated tokens.Source: §4.1.2 · p. 5

4.1.3 Entropy-Sensitive Position Selection

  • FR3E selects the top-K highest-entropy tokens across the trajectory as uncertain decision points and potential reasoning forks.This global selection identifies the most uncertain steps along the reasoning path.Source: §4.1.3 · p. 5

4.1.4 Semantic Block & State Construction

  • High-entropy positions segment trajectories into semantic blocks, and intermediate states represent the reasoning prefix through a block before the next selected position.This segmentation supports localized policy refinement and targeted credit propagation, particularly with sparse rewards and complex action spaces.Source: §4.1.4 · p. 6

4.2 Entropy-Eliciting Explore: Diversified Path Sampling from Anchors

  • From each intermediate state, FR3E samples multiple rollouts and scores each by answer correctness to estimate the state’s empirical value.These rollouts sample local alternatives while preserving semantic coherence with the base trajectory.Source: §4.2 · p. 6

4.3 Adaptive Advantage Modulation for Stable Learning

  • Advantage modulation scales learning signals by value change: it reduces influence when value improves and amplifies it when value stagnates or degrades.The batch average is exactly zero under the idealized equal-length assumption; trajectory-length variation can make the practical estimator only approximately unbiased.Source: §4.3 · p. 7

5 Experiments

Across mathematical reasoning benchmarks, FR3E is competitive with GRPO++ and often matches or slightly outperforms it, with stronger gains on general-purpose models. The experiments also report steadier training dynamics and more consistent reasoning trajectories, while highlighting distinct constraints in Qwen2.5-Math-7B.

5.1 Setup

  • Training combines low-difficulty DeepScaler data with difficulty-level 3–5 SimpleRL samples and evaluates across seven mathematical reasoning benchmarks.AIME24 uses avg@32; the other benchmarks use greedy sampling.Source: §5.1 · pp. 7–8

5.2 Main Results

  • FR3E’s advantage estimates fluctuate less than GRPO++’s and remain tightly centered around zero throughout training.The authors say this closely preserves the theoretical zero-mean advantage expectation.Source: §5.2 · p. 9, Figure 5 · p. 9
  • Across reasoning benchmarks, FR3E is competitive with and often matches or slightly outperforms GRPO++, particularly on general-purpose models.Table 1 is identified as the multi-benchmark accuracy comparison; the text reports the comparison qualitatively.Source: Table 1 · p. 9, §5.2 · p. 9
  • FR3E improves performance most on base Qwen2.5-7B and Qwen2.5-32B, while Qwen2.5-Math-7B performs comparably to GRPO++ across most benchmarks.The reported gains on the specialized model are limited; its AIME24 training trend is nevertheless described as more consistent under FR3E.Source: §5.2 · p. 9, §5.3.1 · p. 10

5.3.1 Training Dynamics of Qwen-Math-7B

  • On Qwen2.5-Math-7B, response length saturates early overall, but rises steadily with FR3E versus remaining flat with GRPO++; FR3E’s AIME24 trend is also more consistent.The authors suggest the model’s sequence-length limit may constrain longer reasoning paths.Source: §5.3.1 · p. 10, Figure 6 · p. 10, §5.3.2 · p. 11

5.3.2 Sources of Gains in FR3E

  • FR3E maintains higher or rising entropy later than GRPO++ on general-purpose models, while Qwen2.5-Math-7B reaches low entropy earlier despite comparable final AIME24 scores.The authors caution that entropy may not be the sole determinant of performance for domain-specialized models.Source: §5.3.2 · p. 10
  • FR3E increases All-Right trajectories and suppresses All-Wrong ones; Qwen2.5-32B shows the highest All-Right and lowest All-Wrong counts among the compared variants.Qwen2.5-7B improves faster and more consistently, while Qwen2.5-Math-7B still shows a moderate All-Right increase despite early entropy convergence.Source: §5.3.2 · p. 11, Figure 7 · p. 11, Figure 8 · p. 11
  • FR3E’s rollout-accuracy heatmap shows gradual transitions toward high accuracy and sustained performance after problems are learned, unlike GRPO++’s more variable progress.The authors associate this pattern with stable learning and reduced error propagation in long-chain reasoning.Source: §5.3.2 · p. 12, Figure 9 · p. 12

6 Conclusion

FR3E uses token-wise entropy to target uncertain points in reasoning trajectories, launches rollouts to explore alternatives, and constructs intermediate feedback with an adaptive advantage mechanism. The paper reports more stable training, longer and more coherent reasoning chains, and more correct solutions.

6 Conclusion

  • FR3E identifies high-uncertainty reasoning points with token-wise entropy and initiates targeted rollouts to explore alternative solution paths.The process constructs intermediate feedback to guide the model.Source: §6 · p. 12
  • An adaptive advantage mechanism is used to ensure stable policy updates.Source: §6 · p. 12
  • FR3E produces more stable training dynamics, longer and more coherent reasoning chains, and a higher yield of correct solutions.Source: §6 · p. 12

A Data Setting Claim

Preliminary experiments on the Qwen2.5 7B math base model found inferior performance with DAPO data compared with a DeepScaler–SimpleRL combination. The authors retained that data setting for subsequent training but caution that the finding may not transfer to other base models.

A Data Setting Claim

  • On the Qwen2.5 7B math base model, DAPO data yielded inferior performance to the DeepScaler and SimpleRL combination.Source: A Data Setting Claim · p. 17
  • The authors adopted the DeepScaler–SimpleRL data setting for their main experiments and kept it across subsequent model training.Source: A Data Setting Claim · p. 17
  • The data-setting conclusion is based on observations with Qwen2.5 7B math base and may not transfer to Qwen2.5 32B, which could have different data requirements.Source: A Data Setting Claim · p. 17

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