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Explore with Memory, Learn without It: In-Context Exploration and Self-Distillation for LLM Reasoning

Yutong Chen, Zhichao Xu, Rui Liu, Kunpeng Liu

arXiv:2610.17734v1cs.LGcs.AI

TL;DR

RLVR commonly estimates rewards through independent sampling, which can repeat wrong answers. LEAF carries each problem’s latest response, reward, and feedback into later rollouts, then uses self-distillation; it reaches Random Sampling’s final pass rate with about four times fewer verifier calls and improves unseen-test accuracy over the strongest baseline on both models.

  • Problem

    Independent sampling can reproduce earlier wrong answers, while group-based advantage estimation trades rollout efficiency for larger response groups.

    Source: §1 · p. 1

  • Method

    LEAF carries each problem’s previous response, reward, and feedback into its next rollout, then uses a successful-context teacher to distill into a context-free student.

    Source: §1 · p. 2

  • Results

    LEAF reaches Random Sampling’s final pass rate with about four times fewer verifier calls and exceeds the strongest baseline on unseen test sets by 1.59 pp (Qwen3-8B) and 1.83 pp (Olmo-3-7B-Instruct).

    Source: §1 · p. 2

  • Takeaways & Limitations

    In the reported experiments, LEAF improves both exploration efficiency and unseen-test accuracy.

    Source: §1 · p. 2, §5 · p. 8

    Richer-feedback effects are tested only on code tasks; how memory affects exploration still needs further research.

    Source: Limitations · p. 9

Abstract

from arXiv · show

Exploration bounds learning efficiency in reinforcement learning with verifiable rewards (RLVR). Current methods explore mostly through independent sampling, without fully using the information gathered along the way, such as known wrong answers and environment feedback. We propose LEAF, which injects a dynamic, problem-specific memory into the context before every rollout. The memory contains the most recent response, its reward, and other environment feedback. It is updated after every verifier call. We decouple policy updates from rollouts and update the policy through self-distillation. On four benchmarks and two open models, LEAF accelerates exploration by about 4x compared with a random sampling baseline. On unseen test sets, it improves accuracy over the strongest baseline by 1.59 and 1.83 percentage points on the two models, while using less compute than any RL baseline. These results highlight the potential of LEAF in improving both exploration and learning efficiency. Code is available at: https://github.com/on1262/LEAF

1 Introduction

LEAF addresses inefficient exploration by carrying problem-specific feedback into later attempts and transferring what those attempts learn through self-distillation. It reaches Random Sampling’s final pass rate with fewer verifier calls and improves unseen-test accuracy over the strongest baseline.

1 Introduction

  • RLVR commonly estimates rewards by independently sampling several responses; larger groups improve advantage estimates but reduce rollout efficiency, while PPO requires a critic.Source: §1 · p. 1
  • Prior work studies feedback-guided refinement and transfers feedback into parameters, while LEAF also adapts each rollout’s context to earlier attempts.LEAF combines rich feedback, inference adaptation, and one verified answer per problem per step.Source: §1 · p. 1
  • On MATH-500, LCB, and MBPP+ across both models, adding feedback when the prior answer is shown reduced repeated wrong answers from 62.8% to 35.9% on average.Source: §1 · p. 2
  • For each problem, LEAF feeds the previous response, reward, and environment feedback into the next rollout, then distills from a successful context into the context-free policy.The memory is updated after each attempt.Source: §1 · p. 2
  • On unseen test sets, LEAF exceeds the strongest baseline by 1.59 pp (Qwen3-8B) and 1.83 pp (Olmo-3-7B-Instruct).The reported comparisons are against the strongest baseline for each model.Source: §1 · p. 2
  • LEAF reaches Random Sampling’s final pass rate with about four times fewer verifier calls.Source: §1 · p. 2

2 Method

LEAF explores by conditioning each rollout on problem-specific memory, then transfers successful rollout contexts into policy parameters through a separate self-distillation update.

2.1 Preliminary

  • Each problem receives K verifier calls that return a binary reward and feedback; pass@k tracks correctness, which can differ from observed reward when code tests include hidden cases.Source: §2.1 · p. 2

2.2 Explore with memory

  • Each attempt uses the problem, previous response, verdict, feedback, and revision instruction as context; its verifier call updates the memory for the next attempt.Source: §2.2 · p. 3
  • To limit degradation from long prior answers, LEAF stores a compressed version of the previous response, whose final result, code, or conclusion usually appears at the end.Source: §2.2 · p. 3
  • Every M = 5 steps, LEAF resets memory and obtains a fresh draft revised once with a blind self-check, sending only that revision to the verifier.Source: §2.2 · p. 3

2.3 From memory to parameters

  • After rollouts finish, LEAF collects contexts preceding correct answers and distills their teacher token distributions into plain-prompt student outputs.Source: §2.3 · p. 3

3 Experiments

Experiments compare LEAF with sampling and RL baselines on exploration and held-out generalization, then test its memory, response-length, update, trace, and divergence choices. LEAF improves exploration efficiency and held-out accuracy, while ablations identify trade-offs across its components.

3.1.1 Settings

  • Exploration uses four benchmarks and two models, with 24 verifier calls per problem and at most five GPU hours per benchmark; generalization trains on disjoint sets and evaluates matching benchmarks using avg@4.The main exploration and generalization results are averaged over three random seeds; other ablations use a single seed.Source: §3.1.1 · p. 4, §3.2.1 · p. 5

3.1.2 Results

  • 80.84% (Qwen3-8B) and 84.50% (Olmo-3-7B) pass rates exceed SCoRe by 2.19 pp and 1.77 pp; exploration is 3.70× faster than the best baseline.Figure 3 compares cumulative pass rate against verifier calls, compute, and GPU time; Table 1 reports pass rate averaged over four benchmarks and summed exploration cost.Source: Table 1 · p. 5, §3.1.2 · p. 5

3.2.2 Results

  • LEAF reaches 64.69% and 63.01% avg@4 on unseen test sets, beating the strongest baselines by 1.59 pp and 1.83 pp while using about 1.9× less compute than SEED.SFT scores 58.16% and 58.21% avg@4, respectively 6.53 pp and 4.80 pp below LEAF; the authors attribute LEAF's gain to distillation rather than correct answers alone.Source: §3.2.2 · pp. 5–6, Table 2 · p. 6

3.3.1 Effect of restart, last response, feedback and history length during exploration

  • Removing the last response lowers pass rates on both models; feedback removal also hurts, while restart frequency trades final pass rate against mean accuracy and GPU time.Keeping three dialogue rounds instead of one lowers averaged final pass rate from 82.71% to 82.67% and raises GPU time from 3.89 to 4.29 hours.Source: Figure 4 · p. 6, §3.3.1 · p. 6

3.3.2 Effect of response length

  • LEAF's exploration responses are 1.17 times as long as Random Sampling and gain 4.88 pp; after policy update, its responses are 1.60 times as long as Base and gain 4.20 pp.SCoRe's 1.27-times-longer exploration responses gain 2.89 pp; response length and accuracy gain are reported as highly related across generalization methods.Source: Table 3 · p. 7, §3.3.2 · p. 7

3.3.3 Effect of interleaved updates during exploration

  • Interleaved updates do not consistently improve final pass rate and raise GPU time by 2.3–3.8× on Qwen3-8B and 1.5–2.2× on Olmo-3-7B-Instruct.On Qwen3-8B, all tested update intervals finish slightly below no update; on Olmo-3-7B-Instruct, only updates every step finish higher.Source: Table 4 · p. 7, §3.3.3 · p. 7

3.3.4 Effect of rollout traces in policy update

  • Successful rollout traces yield the highest teacher accuracy across three training sets and both models: 85.69% and 78.37% on average.Failure traces reduce the averages to 55.73% and 58.12%, while random traces yield 79.33% and 76.60%.Source: Table 5 · p. 7, §3.3.4 · p. 7

3.3.5 Effect of the divergence in the policy update

  • Reverse KL reaches 64.92% and 62.71% overall test avg@4, exceeding Forward KL and JSD on the respective models.Forward KL reaches 63.80% and 60.93%; JSD reaches 59.69% and 62.04%.Source: Table 6 · p. 8, §3.3.5 · p. 8

4 Related Work

Prior RLVR exploration often samples independently, so failed attempts cannot inform subsequent responses. LEAF instead conditions each rollout on earlier attempts and updates parameters by self-distillation on single trajectories.

4 Related Work

  • Independent sampling leaves failed attempts unable to inform subsequent responses, while larger groups trade rollout efficiency for more extensive exploration.Group-based methods use independent responses for advantage estimates; single-rollout PPO instead requires a critic.Source: §4 · p. 8
  • Prior refinement work uses earlier attempts through prompting, multi-turn reinforcement learning, or training models to use feedback more effectively.Examples include verbal reflection, self-refinement, textual critiques, explicit reflection, and retrospective credit assignment.Source: §4 · p. 8
  • Unlike multi-turn reinforcement learning and weighted fine-tuning approaches, LEAF generates one rollout per problem per step and self-distills on single trajectories.Its updates do not use reward objectives on groups of answers.Source: §4 · p. 8
  • Self-distillation often transfers privileged context into an unconditioned student, including feedback, trajectory information, revisions, memories, or skills.Other approaches combine distillation with supervised fine-tuning, preference optimization, or reinforcement learning.Source: §4 · p. 8

5 Conclusion

LEAF uses dynamic memory to make independent rollouts more informative and updates the policy through self-distillation. It reaches Random Sampling’s final pass rate with about four times fewer verifier calls, while using less compute than RL baselines without policy updates.

5 Conclusion

  • About four times fewer verifier calls let LEAF reach Random Sampling’s final pass rate, and it ended above all RL baselines at lower compute without policy update.Self-distillation further gave the best overall test accuracy.Source: §5 · pp. 8–9
  • LEAF keeps a dynamic memory for each rollout trace and updates the policy through self-distillation to improve learning efficiency.The conclusion identifies independent rollouts as making exploration less efficient.Source: §5 · p. 8
  • Ablations on key designs highlight LEAF as a framework for better exploration efficiency.The conclusion also reports that self-distillation gave the best overall test accuracy.Source: §5 · pp. 8–9

Limitations

Feedback richness differs by benchmark, constraining where its effect is tested. The authors state that how memory affects exploration needs further research.

Limitations

  • Richer-feedback effects are tested only on code tasks, because math and science benchmarks provide correctness verdicts alone.LiveCodeBench and MBPP+ include execution results such as errors and failed tests; MATH-500 and SciKnowEval do not.Source: Limitations · p. 9
  • How memory affects exploration still needs further research.The paper reports ablations on key components but identifies this question as unresolved.Source: Limitations · p. 9

Ethical Considerations

The study uses public datasets and open-weight models, without collecting personal data or involving human participants. The authors also flag risks from model bias and verifier errors, and note that benchmark gains do not establish deployment safety.

Ethical Considerations

  • The study uses public datasets and open-weight models without collecting new personal data or involving human participants.It relies on original dataset curation without additional screening for personal information or offensive content.Source: Ethical Considerations · p. 9
  • LEAF may inherit model biases and propagate verifier-feedback errors, including judgments from an LLM judge.Benchmark gains do not establish deployment safety; scientific answers require independent verification and generated code requires security review.Source: Ethical Considerations · p. 9

A Repeated wrong answers under independent sampling

The section measures repeated wrong answers under independent sampling and compares how LEAF’s memory components affect repeat and fix rates. LEAF carries the previous answer and verifier feedback between attempts, with periodic blind-revision restarts.

A Repeated wrong answers under independent sampling

  • A wrong answer counts as a repeat when its error signature matches an earlier wrong answer to the same problem; signatures use normalized final answers for MATH-500 and public-test feedback for coding.Responses without an extracted answer count as non-repeats; coding correctness is judged on public tests in this analysis.Source: A Repeated wrong answers under… · pp. 11–12, Table 7 · p. 11
  • The paired memory comparisons isolate feedback and the previous response: LEAF includes both, while each ablation removes one component.LEAF w/o feedback substitutes a blind correction instruction; LEAF w/o last response includes feedback without the previous answer.Source: A Repeated wrong answers under… · p. 12, §B.1 · p. 13
  • LEAF has lower repeat rates and higher fix rates than LEAF w/o feedback in all six paired comparisons; its repeat rate is lower by about 27 pp on average.Against LEAF w/o last response, LEAF has a higher repeat rate in five of six pairs and a lower fix rate on MATH-500 for both models.Source: A Repeated wrong answers under… · pp. 12–13, Table 8 · p. 12
  • LEAF’s repeat-to-base-frequency ratio is lower than LEAF w/o feedback in all six pairs, but falls below 1 only for Olmo-3-7B-Instruct on MBPP+.The ratio compares observed repeats with the frequency expected from independent sampling.Source: Table 9 · p. 12, A Repeated wrong answers under… · p. 13

B.1 Memory context construction

  • On carry steps, the context combines the original problem, the previous response, and the verifier feedback with an improvement instruction.The previous response is the only earlier attempt retained within a restart segment; task-specific prompts define the blind correction instructions.Source: §B.1 · p. 13, §B.3 · p. 15

B.2 Restart with blind revision

  • At restart steps 1, 6, 11, 16, and 21, LEAF drafts from the plain prompt, then revises that draft using a blind instruction without verifier feedback.Only the revised response is verified and counted; its response and feedback become memory for the next carry step.Source: §B.2 · p. 14

B.4 Self-distillation implementation

LEAF’s policy update distills from contexts generated by successful, non-truncated rollouts. The implementation samples student responses from plain prompts and trains against the current policy conditioned on a selected teacher context.

B.4 Self-distillation implementation

  • For each problem with eligible data, LEAF draws a context from successful, non-truncated rollout responses, dropping exact repeats of earlier correct responses.The context is the full dialogue that produced the response, including earlier attempts and feedback at carry steps or the draft and blind instruction at restarts.Source: §B.4 · p. 16
  • Each update samples one student response from the plain prompt per problem and runs 20 update steps with batches of 128 problems.The student response is generated with vLLM; the implementation trains a LoRA adapter with a frozen backbone.Source: §B.4 · p. 16
  • The teacher is the current policy conditioned on the selected context followed by the same student response, with teacher logits computed without gradients.Student and teacher logits are compared at every response position over the full vocabulary.Source: §B.4 · p. 16

C Exploration setup details

  • The exploration setup gives each method up to 24 verifier calls per problem and a five-GPU-hour-per-benchmark limit on one H200 GPU.Both Qwen3-8B and Olmo-3-7B-Instruct are evaluated under this setup.Source: C Exploration setup details · p. 17

C.1 Datasets

The evaluation spans four datasets, with benchmark-specific verifiers and coding feedback based on public tests. The appendix details the test protocol, metrics, compute accounting, and baseline implementations behind the exploration results.

C.1 Datasets

  • The exploration pool contains 1,409 problems: 500 MATH-500, 131 LiveCodeBench, 378 MBPP+, and 400 SciKnowEval.Benchmarks are trained and evaluated separately; SciKnowEval includes selected open-ended question-answering and relation-extraction tasks across four domains.Source: §C.1 · p. 17

C.2 Public and private tests

  • For coding tasks, LEAF receives verifier feedback from public tests, but a response counts as correct for pass rate only if it passes both public and private tests.LCB uses a fixed split of test cases; MBPP+ uses its three prompted asserts as public tests and plus_input cases as private tests.Source: §C.2 · p. 17

C.3 Verifiers and feedback

  • MATH-500 and SciKnowEval provide verdict-only feedback; SciKnowEval uses the run’s base model as an LLM judge, with the same verifier used for every method.MATH-500 feedback does not reveal the reference answer or extracted final answer.Source: §C.3 · pp. 17–18

C.4 Metrics and compute measurement

  • The reported pass rate aligns methods by each problem’s graded-answer count, and runs stop at the earlier of 24 steps or the five-hour cutoff.GPU hours and FLOPs are tracked with method-specific token accounting; the FLOPs estimate uses model size and forward- and training-token counts.Source: §C.4 · p. 18

C.5 Implementation details

  • The baselines include plain-prompt random sampling, GRPO, SDPO, SCoRe, and SEED, with distinct sampling, distillation, correction, or skill-collection procedures.For example, SDPO distills from a successful same-group response plus feedback on a failed attempt, while SCoRe uses two-turn trajectories.Source: §C.5 · pp. 19–20

D Exploration results by benchmark and seed

  • The per-seed and per-benchmark measurements provide the underlying detail for the aggregate exploration results.The appendix identifies these measurements as the basis for the reported exploration results in Table 1 and Figure 3.Source: D Exploration results by benchmark and… · p. 21

D.1 Results by seed

LEAF leads the reported exploration comparisons across seeds and benchmarks, with lower compute than most RL baselines. The generalization evaluation trains on one set and tests on its matching held-out set using fixed dataset selections across seeds.

D.1 Results by seed

  • LEAF has the highest pass rate on both models at every run seed, with SCoRe second highest; LEAF’s pass rate varies by less than 0.5 pp across seeds on each model.Table 12 contains the per-seed macro-averaged pass rates.Source: §D.1 · p. 21
  • 4.07× is LEAF’s verifier-call speedup over Random Sampling under the same pass-rate-matching definition used for its SCoRe comparison.The speedup is computed on curves averaged over the two models; Table 14 reports speedup ratios.Source: §D.1 · p. 21

D.2 Results by benchmark

  • LEAF has the highest average accuracy on all four benchmarks for both models, while its pass-rate lead varies by benchmark and model.On Qwen3-8B, its pass rate is highest on LCB and SciKnowEval, ties for highest on MBPP+, and is below other methods on MATH-500.Source: §D.2 · p. 21

D.3 Cost by benchmark

  • LEAF uses fewer GPU hours than every RL baseline on all benchmarks except Olmo-3-7B-Instruct LCB, and its PFLOPs are below all four RL baselines on every benchmark.LEAF uses more GPU hours than Random Sampling on every benchmark; its total GPU hours on Olmo-3-7B-Instruct are about two thirds of the cheapest RL baseline’s.Source: §D.3 · p. 21

E Generalization setup details

  • Generalization runs train a separate adapter on each training set and test on its matching benchmark, with the same training and test problems across three seeds.Seeds vary problem order and sampling-related randomness; each run uses one H200 GPU.Source: E Generalization setup details · p. 21

E.1 Training sets

The appendix details the training and evaluation setup, then reports seed-level generalization and pass@4 results. LEAF has the highest Overall accuracy at every seed on both models, with benchmark-specific exceptions on LCB and Qwen3 pass@4.

E.1 Training sets

  • Training sets are disjoint from test sets; LCB retains 478 problems, MATH samples 500 Level 5 problems, and SciKnowEval uses 400 problems.The SciKnowEval training problems are not in its 400-problem test set.Source: §E.1 · pp. 21–22, Table 15 · p. 22

E.2 Test protocol

  • Evaluation samples four responses per test problem and reports avg@4 and pass@4, with Overall defined as the mean avg@4 across LCB, MATH-500, and SciKnowEval.LCB responses are graded on public and private tests, MATH-500 with math-verify, and SciKnowEval with the base-model judge.Source: §E.2 · p. 22

E.3 SFT baseline

  • The SFT baseline rewrites verified rollout answers into self-contained solutions, verifies the rewrites, then trains on accepted solutions.A pair is dropped if all five rewrite rounds fail verification; supervised training uses the same LoRA configuration, learning rate, batch size, and steps as LEAF’s policy update.Source: §E.3 · pp. 22–23

E.4 Training budgets

  • LEAF collects rollout data for K = 20 steps, then performs 20 policy-update steps with batches of 128 problems.The update samples a student response from the plain prompt and draws a successful context uniformly; GRPO, SDPO, and SCoRe receive 20 verifier calls per training problem, while SEED receives 15.Source: §E.4 · p. 23

E.5 Cost accounting

  • Cost accounting includes LEAF’s exploration rollout and policy update, while SFT also includes rewriting and verification.LEAF’s exploration rollout takes 1.58 GPU hours on Qwen3-8B and 9.93 on Olmo-3-7B-Instruct; its policy update takes 2.12 and 4.11 GPU hours, respectively.Source: §E.5 · p. 24

F Generalization results by benchmark and seed

F.1 Results by run seed

  • LEAF has the highest Overall accuracy at every run seed on both models, though it does not lead every benchmark or pass@4 comparison.On Qwen3-8B, it leads MATH-500 but not LCB; on Olmo-3-7B-Instruct, it leads MATH-500 and SciKnowEval, while SDPO exceeds it on LCB at seed 2.Source: §F.1 · p. 25

F.2 Pass@4

  • Olmo-3-7B-Instruct LEAF has the highest pass@4 on all three test sets; Qwen3-8B LEAF leads only on MATH-500.On Qwen3-8B, SEED and GRPO exceed LEAF on LCB, while SFT leads on SciKnowEval.Source: §F.2 · p. 25

F.3 Training cost by training set

The appendix breaks down training costs and examines response lengths during exploration and after policy updates. LEAF’s training FLOPs are substantially below those of the RL baselines, while its post-update test responses are longest across the evaluated cells.

F.3 Training cost by training set

  • LEAF’s training FLOPs are a quarter to a third of those of the four RL baselines on both models.Its exploration rollout accounts for less than half of total GPU hours on Qwen3-8B and about 70% on Olmo-3-7B-Instruct; Table 19 separates costs by training set and stage.Source: §F.3 · p. 25

G Additional ablation results

  • The additional ablation results use mostly single-run measurements, except response-length analysis, which uses all three run seeds.Exploration reports mean accuracy over 24 steps and cumulative pass rate at the last step.Source: G Additional ablation results · p. 26

G.1 Response length

  • After policy update, LEAF has the longest test responses in all six model–test-set cells; on Qwen3-8B MATH-500, mean length more than doubles and truncation reaches 6.33%.During exploration, LEAF’s response length varies by benchmark and model rather than consistently exceeding Random Sampling.Source: §G.1 · p. 26, Table 21 · p. 26

G.2 Restart, last response, feedback and history

The ablations examine restart schedules, memory components, interleaved updates, trace types, and divergence choices. They show trade-offs among accuracy, pass rate, and cost, with outcomes varying by model and benchmark.

G.2 Restart, last response, feedback and history

  • Removing the last response lowers mean accuracy on every benchmark for both models, with the largest drops on LCB: about 8 pp on Qwen3-8B and 10 pp on Olmo-3-7B-Instruct.Removing feedback lowers Qwen3-8B LCB pass rate by more than 8 pp and lowers MBPP+ pass rate on both models.Source: §G.2 · p. 27, Table 23 · p. 27
  • Restarting every 2 steps gives the highest averaged final pass rate (83.105%) and highest GPU hours (4.930), while no restart gives the highest mean accuracy (70.600%) and lowest GPU hours (3.165).No restart also has lower MBPP+ pass rates than LEAF on both models.Source: §G.2 · pp. 27–28, Table 26 · p. 28
  • History-compression outcomes vary: the tail and head-and-tail treatments are within 0.4 pp in Qwen3-8B Overall pass rate, while the tail exceeds head-and-tail on Olmo-3-7B-Instruct.On Olmo-3-7B-Instruct LCB, the tail has the highest pass rate of the tested treatments; the summary block has the lowest pass rate and mean accuracy.Source: Table 24 · p. 28, §G.2 · p. 29

G.3 Interleaved updates

  • Interleaved updates increase GPU hours on every benchmark for every tested interval, while accuracy and pass-rate effects differ by model and benchmark.On Olmo-3-7B-Instruct, updating every step gives the highest SciKnowEval pass rate and a higher Overall pass rate; on Qwen3-8B, all intervals lower LCB and MATH-500 pass rates versus no update.Source: Table 25 · p. 28, §G.3 · p. 29

G.4 Rollout traces in the policy update

  • On MATH and SciKnowEval, LEAF has lower repeat rates than the base model on both models.On Olmo-3-7B-Instruct SciKnowEval, LEAF raises wrong-to-right from about 29% for the base model to about 51%; on Qwen3-8B LCB, LEAF has lower wrong-to-right but higher restart-step accuracy.Source: §G.4 · pp. 30–31, Table 28 · p. 30

G.5 Divergence in the policy update

  • Divergence variants trade off benchmark performance: JSD is 13.1 pp below reverse KL on Qwen3-8B MATH-500, and forward KL is 6.6 pp below reverse KL on Olmo-3-7B-Instruct MATH-500.Both runs are also more than 5 pp below Base on MATH-500; forward KL leads on SciKnowEval avg@4 for Olmo-3 and pass@4 for Qwen3.Source: §G.5 · p. 31, Table 30 · p. 31
  • Policy-update accuracy exceeds base-model accuracy in all six cells, while exceeding with-context rollout accuracy in three cells.The three cells are Qwen3-8B MATH and SciKnowEval, and Olmo-3-7B-Instruct SciKnowEval; relative gain is about half on Qwen3-8B LCB and below a quarter on Olmo-3 LCB and MATH.Source: Table 32 · p. 31, §G.5 · p. 32

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