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

cs.CLOct 16, 2026

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

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

Organizations: Stony Brook University · Meta AI

Abstract

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.

Figures & tables

Figure 1: Source-task accuracy and cross-benchmark transfer respond differently to supervision. Qwen3-8B before task-specific training (Raw) and after training on MuSiQue with answer-only supervision, original student traces, or ReDiST . MuSiQue measures source-task performance, while 2Wiki and HotpotQA measure cross-benchmark performance. Dashed lines mark each benchmark’s raw-model EM. Values are EM point estimates from Table 1 . Comparisons between trained variants reflect complete training recipes.

Figure 2: ReDiST : student-conditioned trace construction and distillation. (a) Process content and student accessibility guide the design. (b) A rewrite model revises answer-correct student 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. (c) Repair exposure

m

and auxiliary answer-loss weight

\alpha

control how selected targets enter training. Teaching utility is evaluated through the trained student’s source-task and cross-benchmark performance.

	MuSiQue (Source)		2Wiki (Transfer)		HotpotQA (Transfer)		QuALITY (Transfer)
Method	EM $\uparrow$	F1 $\uparrow$	EM $\uparrow$	F1 $\uparrow$	EM $\uparrow$	F1 $\uparrow$	Acc. $\uparrow$	H.Acc. $\uparrow$
Raw Model	0.342	0.450	0.516	0.605	0.503	0.677	0.623	0.561
Answer-only	0.562	0.662	0.479	0.560	0.497	0.659	0.523	0.427
Original Trace	0.426	0.518	0.521	0.608	0.512	0.667	0.627	0.535
STaR	0.510	0.613	0.613	0.689	0.583	0.745	0.587	0.541
NLL	0.546	0.642	0.600	0.693	0.597	0.767	0.617	0.554

Table 1: Source-task and cross-benchmark performance after MuSiQue supervision. All systems use Qwen3-8B. Trained variants use only MuSiQue examples for gradient updates.

Figure 3: Evidence use in a selected 2Wiki example. Test-time reasoning excerpts from raw Qwen3-8B and Qwen3-8B students trained with MBT-R or ReDiST . MBT-R identifies the relevant directors but introduces an unsupported co-director. In contrast, the ReDiST output uses the relevant film–director–nationality links and answers correctly. Quoted model text is reproduced verbatim, with ellipses marking omissions, while highlights, correctness markers, and notes are author annotations.

		Source	Transfer
Variant	Controlled change	MuSiQue	2Wiki	HotpotQA
Full ReDiST	Reference recipe	0.584	0.686	0.633
Original target	No revision or repair	0.426	0.521	0.512
Selected student target	No revision or repair	0.552	0.577	0.550
Fresh rewrite	Rewrite without the original draft	0.554	0.483	0.570
Repair disabled	Original targets for repair cases	0.577	0.626	0.576

Table 2: ReDiST component and supervision-allocation ablations. Variants modify trace construction or answer-loss allocation relative to the full recipe. All entries are EM.

	Qwen3-4B		Qwen3-8B		Gemma4-E2B		Gemma4-E4B
Supervision	S	T	S	T	S	T	S	T
Raw model	0.293	0.225	0.342	0.516	0.225	0.518	0.425	0.643
Answer-only	0.558	0.440	0.562	0.479	0.514	0.368	0.578	0.449
Original trace	0.405	0.445	0.426	0.521	0.311	0.546	0.456	0.644
STaR	0.519	0.480	0.510	0.613	0.444	0.588	0.553	0.682
NLL	0.519	0.635	0.546	0.600	0.545	0.610	0.571	0.682

Table 3: Source-task and transfer performance across target students. All trained variants receive MuSiQue supervision. Columns report MuSiQue source-task (S) and 2Wiki transfer (T) EM for each student.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Category	Baseline	Trace source	Acceptance / selection
Reference	Raw Model	— (no training)	—
Answer supervision	Answer-only	— (gold answer only)	aligned question set
Self-generated	Original Trace	student, greedy	EM match, non-empty trace
	STaR	student, greedy (+ hint)	EM match, non-empty trace, closed tag (hint removed for training)
Trace selection	NLL	teacher, multi-prompt pool	$\arg\min$ mean student NLL
	RSR	teacher, multi-prompt pool	$\arg\min$ rank–surprisal ratio

Appendix

Table 4: Baseline taxonomy. “Student” denotes the untrained target student. The teacher is Qwen3-14B for Qwen students and Gemma4-26B-A4B for Gemma students.

Method	Kept	Dropped	Training mixture
MuSiQue supervision (4,000 training questions)
Answer-only	4,000	0	4,000 gold answers, no trace
Original trace	1,466	2,534	1,466 answer-correct greedy traces
STaR	3,671	329	1,466 native traces $+$ 2,205 accepted rationalizations (of 2,529 attempted)
NLL / RSR / LARK	2,477	1,523	2,477 selected teacher traces, one per question
MBT-R	3,995	5	3,995 rewrites of the student draft

Appendix

Table 5: Training data retained by each supervision method (Qwen3-8B student). Kept counts distinct training questions.

Rewrite teacher	Repair success	Token NED (%)		MuSiQue (Source)		2Wiki (Transfer)
	(%)	Revise	Repair	EM	F1	EM	F1
Qwen3-4B	57.97	0.98	18.31	0.581	0.691	0.648	0.733
Qwen3-8B	61.60	2.78	26.24	0.593	0.693	0.670	0.757
Qwen3-14B	61.78	1.15	29.90	0.584	0.681	0.686	0.780
Qwen3-30B-A3B	53.29	5.92	28.22	0.587	0.695	0.646	0.729
Gemma4-E4B	56.43	13.10	44.86	0.581	0.686	0.670	0.763

Appendix

Table 6: Rewrite-teacher comparison with a fixed student initialization. Each student is initialized from Qwen3-8B and distilled using MuSiQue supervision. We report repair success, token-level normalized edit distance (NED), and downstream EM/F1.

	2Wiki (Source)		MuSiQue (Transfer)		HotpotQA (Transfer)		QuALITY (Transfer)
Method	EM $\uparrow$	F1 $\uparrow$	EM $\uparrow$	F1 $\uparrow$	EM $\uparrow$	F1 $\uparrow$	Acc. $\uparrow$	H.Acc. $\uparrow$
Raw Model	0.516	0.605	0.342	0.450	0.503	0.677	0.623	0.561
Answer-only	0.698	0.775	0.482	0.579	0.630	0.763	0.537	0.465
Original Trace	0.599	0.676	0.387	0.486	0.589	0.736	0.620	0.567
STaR	0.675	0.731	0.448	0.548	0.597	0.740	0.623	0.535
NLL	0.677	0.763	0.463	0.561	0.616	0.762	0.607	0.522

Appendix

Table 7: Source-task and cross-benchmark performance after 2Wiki supervision. All systems use Qwen3-8B. Trained variants use only 2Wiki examples for gradient updates.

	MuSiQue-trained		2Wiki-trained
Supervision	MuSiQue (Source)	2Wiki (Transfer)	2Wiki (Source)	MuSiQue (Transfer)
Raw model	0.342 [0.313, 0.370]	0.516 [0.485, 0.547]	0.516 [0.485, 0.547]	0.342 [0.313, 0.370]
Answer-only	0.562 [0.531, 0.592]	0.479 [0.448, 0.510]	0.698 [0.669, 0.726]	0.482 [0.451, 0.513]
Original trace	0.426 [0.396, 0.457]	0.521 [0.490, 0.551]	0.599 [0.568, 0.629]	0.387 [0.357, 0.417]
STaR	0.510 [0.479, 0.542]	0.613 [0.583, 0.643]	0.675 [0.646, 0.704]	0.448 [0.417, 0.478]
NLL	0.546 [0.515, 0.577]	0.600 [0.570, 0.630]	0.677 [0.648, 0.705]	0.463 [0.433, 0.493]

Appendix

Table 8: Qwen3-8B source-task and transfer EM under MuSiQue and 2Wiki supervision. Each entry reports EM on a fixed 1,000-question validation slice with its 95% bootstrap interval.

$\alpha$	MuSiQue EM $\uparrow$	2Wiki EM $\uparrow$	HotpotQA EM $\uparrow$
0.00	0.592	0.652	0.630
0.15	0.584	0.686	0.633
0.30	0.572	0.653	0.602
0.60	0.575	0.616	0.587
0.75	0.558	0.610	0.590
0.90	0.535	0.579	0.567

Appendix

Table 9: Answer-loss weight sweep.

	Qwen3-4B		Qwen3-8B		Gemma4-E2B		Gemma4-E4B
Supervision	S	T	S	T	S	T	S	T
Raw model	0.225	0.293	0.516	0.342	0.518	0.225	0.643	0.425
Answer-only	0.678	0.425	0.698	0.482	0.628	0.401	0.687	0.458
Original trace	0.576	0.400	0.599	0.387	0.554	0.264	0.661	0.468
STaR	0.644	0.446	0.675	0.448	0.644	0.430	0.759	0.546
NLL	0.659	0.423	0.677	0.463	0.669	0.458	0.692	0.557

Appendix

Table 10: Source-task and transfer performance across target students. All trained variants receive 2Wiki supervision. Columns report 2Wiki source-task (S) and MuSiQue transfer (T) EM for each student.

	MuSiQue (Source)		2Wiki (Transfer)		HotpotQA (Transfer)		QuALITY (Transfer)
Method	EM $\uparrow$	F1 $\uparrow$	EM $\uparrow$	F1 $\uparrow$	EM $\uparrow$	F1 $\uparrow$	Acc. $\uparrow$	H.Acc. $\uparrow$
Raw Model	0.293	0.421	0.225	0.413	0.407	0.600	0.560	0.510
Answer-only	0.558	0.676	0.440	0.521	0.547	0.692	0.470	0.395
Original Trace	0.405	0.500	0.445	0.534	0.586	0.730	0.587	0.535
STaR	0.519	0.618	0.480	0.558	0.606	0.746	0.527	0.497
NLL	0.519	0.621	0.635	0.723	0.606	0.755	0.597	0.522

Appendix

Table 11: Source-task and cross-benchmark performance after MuSiQue supervision. All systems use Qwen3-4B. Trained variants use only MuSiQue examples for gradient updates. Bold: best value in each column.

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On-policy distillation transfers reasoning ability through dense token-level supervision, yet the nature of the transferable signal remains unclear. We discover that reasoning chains contain two types of knowledge that require different discovery mechanisms: decisions (where to branch), which surface through student uncertainty, and evidence (intermediate steps that justify decisions), which hides in positions where the student is confident yet wrong. Current methods capture only decisions; the substantive knowledge in evidence tokens remains untransferred. We propose DEAR(Decision-Evidence Aware Reasoning Distillation), which first identifies decisions via student entropy, then discovers their supporting evidence through hidden-state cosine similarity to decision anchors, boosted by teacher-student divergence to prioritize the largest knowledge gaps. Across three student-teacher configurations on math and code benchmarks, DEAR consistently outperforms standard OPD, with up to +2.5pp on competition math and +5.7pp on code generation.

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