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Beyond the Answer: Student-Conditioned Trace Construction for Reasoning Distillation

Shaoang Li, Yanhang Shi, Yufei Li, Mingfu Liang, Frank Shyu, Sandeep Pandey, Luke Simon, Xi Liu, Jian Li

arXiv:2610.23831v1cs.CLcs.LG

TL;DR

Reasoning traces can accompany correct answers without providing effective supervision for a particular student. ReDiST revises and repairs student-generated drafts, then selects and distills targets conditioned on the student. Experiments report gains across source-task and cross-benchmark settings, while noting that a reader's answer recovery does not establish stepwise correctness or learning benefit.

  • Problem

    A correct final answer does not ensure that a reasoning trace provides effective supervision, because its intermediate content may be difficult for the target student to learn.

    Source: §1 · p. 1

  • Method

    ReDiST revises answer-correct student drafts against evidence, repairs unsuccessful drafts with verified-answer guidance, and selects candidates using a frozen student-matched reader.

    Source: §1 · p. 2

  • Results

    ReDiST improves source-task and 2Wiki performance over answer-only and original-trace supervision across four students, with additional gains reported for 2Wiki supervision and transfer to MuSiQue.

    Source: §5 · p. 10

  • Takeaways & Limitations

    Trace teaching value should be assessed across source-task and cross-benchmark distributions, and trace targets should be designed alongside their supervision for the intended learner.

    Source: §5 · p. 10

    Successful answer recovery by the reader does not by itself establish stepwise correctness or learning benefit.

    Source: §3.2 · p. 5

Abstract

from arXiv · show

A reasoning trace can accompany a correct answer without providing effective supervision for a particular student. We study how to construct traces that improve learning beyond answer-only supervision by considering both their intermediate content and their accessibility to the target learner. We introduce ReDiST, a student-conditioned trace-construction and distillation framework for evidence-rich reasoning. Starting from the student's own attempts, ReDiST revises answer-correct drafts against the supplied evidence and repairs unsuccessful drafts with additional guidance from the verified answer. A frozen student-matched reader screens and ranks original and edited candidates using answer recovery and verified-answer probability, given the question, evidence, and candidate trace. We distill the selected targets while balancing trace and final-answer supervision with an auxiliary answer loss. Construction and selection occur offline, and inference uses only the distilled student. Experiments on question-answering benchmarks show that ReDiST can improve both source-task and cross-benchmark performance over answer-only, original-trace, and the evaluated trace-selection and rewriting baselines. Across supervision recipes, performance rankings can differ between source and transfer benchmarks, highlighting the importance of evaluating trace teaching utility across distributions.

1 Introduction

Reasoning traces can provide useful intermediate supervision, but a correct answer alone does not ensure a trace is learnable by a particular student. ReDiST constructs and selects student-conditioned traces, and its evaluations report gains across source-task and transfer settings.

1 Introduction

  • The paper frames the central challenge as constructing traces that improve learning beyond final-answer labels while remaining accessible to the target learner.A trace may be correct yet ineffective when it omits reasoning steps, elaborates unnecessarily, or uses unfamiliar expression.Source: §1 · pp. 1–2
  • Answer-only and original-trace supervision rank differently across source and transfer benchmarks, so higher source-task accuracy need not imply stronger transfer.With MuSiQue supervision, answer-only training raises Qwen3-8B MuSiQue EM from 34.2% to 56.2% but lowers 2Wiki EM from 51.6% to 47.9%; original traces yield 42.6% source EM and 52.1% transfer EM.Source: §1 · p. 1, Figure 1 · p. 2
  • ReDiST revises answer-correct student drafts against evidence, repairs unsuccessful drafts with verified-answer guidance, and selects candidates using a frozen student-matched reader.The reader screens and ranks original and edited candidates using answer recovery and verified-answer probability; training controls repair exposure and auxiliary answer loss.Source: §1 · p. 2, Figure 2 · p. 3
  • ReDiST improves source-task and 2Wiki performance over answer-only and original-trace supervision across four students from two model families.The primary Qwen3-8B comparison reports the highest point estimates across all four benchmarks, including 58.4% MuSiQue EM and 68.6% 2Wiki EM.Source: §1 · p. 2
  • The paper formulates incremental trace teaching utility relative to matched answer-only supervision for a specified student and evaluation distribution.Its contributions also include empirical comparisons across four target students and two model families.Source: §1 · p. 3

2 Problem Setting and Trace Teaching Utility

The setting constructs reasoning supervision from a student's attempts on question-and-evidence examples, without requiring gold reasoning traces. It separates the choice of traces from the training recipe and treats process content and student accessibility as distinct, interacting design considerations.

2.1 Evidence-Rich Reasoning Distillation

  • Training examples pair a question, supplied evidence, and verified answer; construction uses generated attempts and does not require gold reasoning traces.At inference, the trained student answers new questions from supplied evidence.Source: §2.1 · p. 3

2.2 Student-Relative Teaching Utility

  • Incremental trace teaching utility compares a constructed-trace student with a matched answer-only student under the same training protocol and evaluation distribution.The paired runs retain the same examples, labels, initialization, settings, update budget, and sampling schedule; complete-recipe comparisons may change these factors and are interpreted separately.Source: §2.1 · p. 3, §2.2 · p. 4

2.3 Design Considerations: Content and Accessibility

  • Trace construction must consider both supporting facts and intermediate relations and how readily the target student can use and learn from them.Content and accessibility are distinct, may interact, and neither alone determines downstream teaching utility.Source: §2.3 · p. 4

3 The ReDiST Framework

ReDiST constructs student-conditioned traces through evidence-guided revision or answer-assisted repair, frozen-reader selection, and distillation with separate controls for repair exposure and answer emphasis.

3 The ReDiST Framework

  • The three-stage pipeline edits student drafts, selects targets with a frozen student-matched reader, then distills them while controlling repair exposure and answer emphasis.Construction is offline; inference uses only the distilled student.Source: §3 · p. 4, §3.3 · p. 6

3.1 Student-Draft Revision and Repair

  • Answer-correct drafts receive evidence-guided revisions, while unsuccessful drafts receive the verified answer as additional guidance for repairing their supporting derivations.Revision aims to retain supported reasoning and clarify intermediate entities and relations; repair connects relevant evidence to the verified answer.Source: §3.1 · p. 5

3.2 Frozen-Student Target Selection

  • The frozen reader screens candidates by whether it recovers the verified answer and ranks those that pass by their verified-answer score.The reader receives the question, evidence, and candidate trace.Source: §3.2 · p. 5
  • If no candidate passes recovery, ReDiST retains an initially answer-correct draft or an empty trace; recovery alone does not establish stepwise correctness or learning benefit.Each retained example remains paired with the verified answer.Source: §3.2 · p. 5

3.3 Distillation and Supervision Allocation

  • Accepted repairs appear m times in the training mixture, while every other example appears once.Repair multiplicity controls accepted-repair exposure during training.Source: §3.3 · p. 5
  • The full-completion loss covers trace and answer tokens, while an auxiliary answer-token loss weighted by α adds emphasis to final-answer prediction.At α = 1, answer positions receive direct token supervision, but their predictions still condition on the preceding trace.Source: §3.3 · pp. 5–6

4 Experiments and Results

The experiments evaluate ReDiST against answer-only, original-trace, and trace-selection and rewriting baselines across source and transfer benchmarks, students, and supervision allocations. ReDiST leads the primary Qwen3-8B comparison across all eight metrics, while component results show that construction and answer-loss allocation affect source and transfer performance differently.

4.2 Source-task performance and transfer

  • ReDiST achieves the highest reported scores across all eight metrics, improving source-task performance and all three transfer benchmarks after MuSiQue supervision.The comparison uses Qwen3-8B; Table 1 evaluates MuSiQue, 2Wiki, HotpotQA, and QuALITY.Source: §4.2 · p. 7, Table 1 · p. 7
  • Answer-only training raises MuSiQue EM from 0.342 to 0.562 but lowers 2Wiki EM from 0.516 to 0.479; original traces yield 0.426 and 0.521, reversing their ranking.ReDiST improves both source and transfer performance over these references.Source: §4.2 · p. 7
  • ReDiST reaches 0.640 QuALITY accuracy and 0.573 hard-subset accuracy, above the raw model’s 0.623 and 0.561, while answer-only training lowers both.This long-document, multiple-choice transfer result contrasts with the weaker QuALITY performance of most trace-based recipes.Source: §4.2 · p. 7

4.3 Trace Construction and Supervision Allocation

  • Full ReDiST exceeds Selected student target by 3.2 points on MuSiQue EM, 10.9 on 2Wiki EM, and 8.3 on HotpotQA EM.Selecting among existing attempts already improves over Original target; full construction adds further gains, larger on the transfer benchmarks.Source: §4.3 · p. 8, Table 2 · p. 9
  • Removing student drafts from rewriting lowers EM by 0.030 on MuSiQue, 0.203 on 2Wiki, and 0.063 on HotpotQA; disabling repair also lowers transfer EM.With repair disabled, 2Wiki EM falls from 0.686 to 0.626 and HotpotQA EM from 0.633 to 0.576, while MuSiQue EM falls from 0.584 to 0.577.Source: §4.3 · pp. 8–9
  • With traces fixed, answer-loss allocation changes results: answer-only loss reaches 0.417 2Wiki EM and 0.480 HotpotQA EM, while trace-only reaches 0.404, 0.478, and 0.443 EM.The full α = 0.15 recipe reaches 0.686 2Wiki EM; the comparisons support retaining both trace and answer supervision.Source: §4.3 · p. 9

4.4 Generality across Student and Teacher Models

  • Across four students, ReDiST exceeds answer-only and original-trace supervision on both benchmarks, but leads 2Wiki EM in three comparisons, with Qwen3-4B the exception.For Gemma4-E4B, ReDiST reaches 0.723 2Wiki EM versus 0.682 for STaR and NLL; for Qwen3-4B, it reaches 0.630 versus NLL’s 0.635.Source: §4.4 · pp. 9–10, Table 3 · p. 10
  • Answer-only supervision beats original traces on MuSiQue but loses to them on 2Wiki for all four students; higher repair success also does not guarantee higher 2Wiki EM.For Gemma4-E4B, answer-only versus original traces yields 0.578 versus 0.456 MuSiQue EM and 0.449 versus 0.644 2Wiki EM; in the teacher sweep, 62.15% repair success accompanies 0.624 2Wiki EM, versus 61.78% and 0.686 for another teacher.Source: §4.4 · p. 10

5 Conclusion

ReDiST constructs reasoning supervision by revising student drafts against evidence, repairing unsuccessful drafts with answer guidance, and selecting targets with a frozen student-matched reader. Across the reported settings, it improves source and transfer performance, while component results support evaluating trace construction and answer supervision together.

5 Conclusion

  • ReDiST constructs targets through evidence-guided revision, answer-assisted repair, and frozen-student selection of student drafts.Construction and selection are assessed through source-task and cross-benchmark performance.Source: §5 · p. 10
  • Under MuSiQue supervision, ReDiST improves source-task and 2Wiki performance over answer-only and original-trace supervision across four students.A separate Qwen3-8B comparison extends the gains to 2Wiki supervision and MuSiQue transfer.Source: §5 · p. 10
  • Component comparisons show larger transfer gains from draft conditioning and repair, while loss ablations support joint supervision of reasoning traces and final answers.The conclusion recommends assessing teaching value on both source-task and cross-benchmark performance.Source: §5 · p. 10

A Related Work

Related work addresses trace construction, learner compatibility, distillation objectives, and evidence grounding. ReDiST combines editing student attempts with frozen student-matched candidate selection, then trains offline on a trace-and-answer completion.

Trace construction and self-training

  • Trace-construction work generates, corrects, or restructures reasoning targets; ReDiST edits the target student’s own attempts and gives verified-answer guidance only to repairs of unsuccessful drafts.The discussion identifies STaR, correction methods, and metacognitive rewriting as related approaches.Source: A Related Work · p. 14

Trajectory selection and learner compatibility

  • Learner-compatibility methods select or adapt trajectories for a particular student, whereas ReDiST creates edited candidates and selects among them with a frozen student-matched reader.The reader uses the student signal offline without training the rewrite model.Source: A Related Work · p. 14

Distillation objectives and training data

  • Prior distillation work varies objectives and data mixtures; ReDiST instead constructs targets offline and uses supervised finetuning on one completion containing the trace and verified answer.Source: A Related Work · p. 14

Evidence grounding and process measurement

  • Evidence-grounding and process-measurement work motivates examining supplied evidence and visible reasoning, which ReDiST treats as teaching targets rather than necessarily faithful accounts of computation.ReDiST revises and repairs student reasoning against the supplied evidence before distillation.Source: A Related Work · p. 14

B Experimental and Implementation Details

The appendix specifies construction, training, and evaluation details supporting the main comparisons.

B Experimental and Implementation Details

B.1 Tasks, students, and comparison endpoints

The experiments vary the target student, training source, and rewrite teacher to separate their effects. They evaluate source-task and transfer performance using task-specific metrics.

B.1 Tasks, students, and comparison endpoints

  • The primary comparison trains Qwen3-8B on MuSiQue and evaluates transfer to 2Wiki, HotpotQA, and QuALITY.The model sweep varies the target student, a second-source study trains on 2Wiki, and the rewrite-teacher sweep varies the teacher with Qwen3-8B initialization.Source: §B.1 · p. 15
  • QA uses answer EM and token F1, while QuALITY uses accuracy and hard-subset accuracy.Each metric is interpreted within its own task.Source: §B.1 · p. 15
  • The raw model anchors pre-training performance, and each student/task setting has its own answer-only reference for Equation (1).Source: §B.1 · p. 15

B.2 ReDiST implementation

ReDiST generates drafts from the target student, edits the selected draft according to answer correctness, and uses a frozen student-matched reader to choose teaching targets. The implementation then distills selected targets with configurable repair exposure and answer-loss weighting.

B.2 ReDiST implementation

  • ReDiST generates student drafts, selects an eligible draft, then revises it if answer-correct or repairs it with the verified answer if unsuccessful.The algorithm builds candidates from the original and edited traces before selecting a target for distillation.Source: §B.2 · pp. 15–16
  • The frozen reader ranks eligible drafts by verified-answer probability, preferring answer-correct drafts when available.It selects the candidate with the largest reader score; ties follow candidate order.Source: §B.2 · p. 15
  • Rewrite candidates are instructed to provide complete evidence-grounded explanations, preserve supported reasoning, remove unsupported content, and connect relevant entities and relations.Rewrites may reorder, replace, add, or remove steps rather than making only minimal edits.Source: §B.2 · p. 15
  • Deterministic validity checks remove malformed rewrite generations, while documented format-only cases are excluded before training.The algorithm also permits original-draft and answer-only fallbacks.Source: §B.2 · pp. 15–16
  • A candidate passes selection when the reader’s greedy answer matches the verified answer; if none passes, ReDiST retains an answer-correct original or uses answer-only supervision for an unsuccessful draft.The selected candidate is the passing candidate with the highest verified-answer score.Source: §B.2 · p. 15
  • The implementation distills selected targets with repair multiplicity m and answer-loss weight α, using 500 optimizer steps and a default 4 drafts and 4 rewrites.The default settings also use m = 4 and α = 0.15; the frozen reader is a copy of the target student unless specified otherwise.Source: §B.2 · p. 16

B.3 Baseline implementations

Baselines share the target student, sampled questions, training configuration, and evaluation setting, but differ in the source and filtering of their supervision targets. The section describes self-generated, teacher-selected, and teacher-rewritten alternatives alongside answer-only and raw-model references.

B.3 Baseline implementations

  • Baselines use the same target student, 4,000 training questions, LoRA and optimizer configuration, optimizer steps, and evaluation setting as ReDiST.They differ mainly in supervision target and which questions are retained.Source: §B.3 · p. 16
  • The baseline groups cover answer supervision, student-generated traces, teacher-candidate selection, and teacher rewriting.The taxonomy distinguishes methods by where their supervision targets come from.Source: §B.3 · p. 17, Table 4 · p. 17
  • The shared training source is 4,000 uniformly sampled questions, while evaluation uses 1,000 validation examples per benchmark and a fixed 300-question QuALITY set.Methods retain questions according to their acceptance rules; Answer-only uses all 4,000.Source: §B.3 · p. 17
  • STaR uses accepted gold-answer-hinted rationalizations for rejected questions, while keeping native traces for questions the student already solves.Questions failing both passes are discarded, and accepted rationalizations are otherwise used unchanged.Source: §B.3 · p. 17
  • NLL, RSR, and LARK select from a shared pool of teacher traces generated across six gold-blind reasoning-style prompts.Exact duplicate traces are collapsed within each question.Source: §B.3 · pp. 17–18
  • ReDiST repairs 1,004 of 1,625 unsuccessful MuSiQue drafts and 1,089 of 1,371 unsuccessful 2Wiki drafts.The remaining 621 unsuccessful MuSiQue drafts fall back to answer-only targets.Source: §B.3 · p. 18

B.4 Ablation details

The ablations change target construction, repair use, or loss allocation while controlling other training-mixture and optimization choices. This setup separates the effects of student drafts, rewriting, repair, and direct answer supervision.

B.4 Ablation details

  • Ablations compare full ReDiST with original targets, selected student drafts, fresh rewrites without student drafts, and repair-disabled targets.Fresh rewrite retains branch-specific answer access, while repair-disabled uses the unsuccessful original draft as its target.Source: §B.4 · pp. 18–19
  • Selected student target, Fresh rewrite, and Repair disabled retain full ReDiST’s repair exposure, even when their targets are not repairs.Questions with accepted ReDiST repairs appear m times in the training mixture.Source: §B.4 · p. 19
  • No Answer Auxiliary, Answer-Loss Only, and Trace-Only Control use full ReDiST’s same targets, repair exposure, prompt format, and optimizer settings.These controls differ only in which supervised positions receive loss.Source: §B.4 · p. 19
  • No Answer Auxiliary sets α = 0 for uniform token-averaged cross-entropy, while Answer-Loss Only sets α = 1 and supervises answer-content positions only.For Answer-Loss Only, the trace remains in the completion as conditioning context.Source: §B.4 · p. 19
  • Trace-Only Control computes loss over trace positions and gives answer tokens no direct supervision.Source: §B.4 · p. 19

C Additional Results

Additional results show that teacher choice, answer-loss allocation, and student model affect source and transfer outcomes differently. The appendix also specifies the prompts used to construct and select traces.

C Additional Results

  • Teacher rankings diverge by outcome: Gemma4-26B-A4B has the highest repair success (62.15%), Qwen3-8B the highest source-task EM (0.593), and Qwen3-14B the highest 2Wiki EM (0.686).Across teachers, MuSiQue EM ranges from 0.578 to 0.593 and 2Wiki EM from 0.620 to 0.686.Source: C Additional Results · p. 19, Table 6 · p. 19
  • Repair edits exceed revision edits for every teacher; for Qwen3-14B, Repair NED is 29.90% versus Revision NED of 1.15%, yet similar repair magnitudes need not yield similar transfer EM.Qwen3-14B and Gemma4-26B-A4B have Repair NED values of 29.90% and 30.04%, but different 2Wiki EM scores.Source: C Additional Results · p. 19
  • For MuSiQue-to-2Wiki transfer, ReDiST’s 5.3-point margin over MBT-R exceeds the bootstrap interval half-width, while source-task recipe ordering remains unresolved at this sample size.The fixed 1,000-question evaluation slice is resampled 10,000 times; intervals are roughly six points wide. In reverse transfer, ReDiST’s 2.4-point margin over MBT-R lies within the interval half-width.Source: C Additional Results · pp. 19–20, Table 8 · p. 20
  • At α = 0.15, both transfer benchmarks peak—2Wiki EM at 0.686 and HotpotQA EM at 0.633—while source-task EM is highest at α = 0 (0.592).Beyond α = 0.15, all three benchmarks decline; 2Wiki EM falls to 0.579 at α = 0.90.Source: C Additional Results · p. 20, Table 9 · p. 21
  • With 2Wiki supervision, ReDiST has the highest reported 2Wiki EM across four students and the highest MuSiQue transfer EM; under MuSiQue supervision, Qwen3-4B leads all but the two 2Wiki columns, where NLL is highest.For Gemma4-E2B, NLL matches transfer EM at 0.458.Source: C Additional Results · p. 20, Table 10 · p. 21, Table 11 · p. 21

D Prompts

  • The prompts vary by student-family template, while rewrite instructions require evidence-grounded reasoning and distinguish correcting unsuccessful drafts from improving correct drafts without changing their supported conclusion.The repair prompt treats the supplied answer as a checking hint, not evidence; student reasoning is typically requested in a concise 3–7-step chain.Source: D Prompts · pp. 22–23
  • The reader prompt evaluates candidate reasoning with the question and evidence, requiring multi-step answers in a fixed think/answer format and allowing UNANSWERABLE when evidence is insufficient.The reader prompt is wrapped according to the corresponding model family’s student prompt.Source: D Prompts · pp. 22–23

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