RCCM: Diagnosing Gains and Harms in Reasoning-Prompt Transfer

Yuqi Zhang; Di Zhang

cs.CLOct 14, 2026

RCCM: Diagnosing Gains and Harms in Reasoning-Prompt Transfer

Authors: Yuqi Zhang, Di Zhang

Abstract

A reasoning prompt can improve one deployment and degrade another. RCCM (Reasoning-Control Capability Mismatch) examines these reversals by pairing answers to the same questions with records of how generation ends. Across five open-weight deployments and nine strategies, aggregate accuracy hides substantial question-level gains and harms; a common-budget MATH500 evaluation examines transfer on a separate sample. On 60 additional questions, concise reasoning improves Phi's automatic answer matching at a 2,048-token cap across three collections, but sharply reduces Qwen's. Author-reviewed final-answer commitments give a smaller, statistically unresolved Phi gain. Reserving an answer stage also improves matching, with additional input and call costs. These results show why a prompt benefit must be interpreted alongside its execution and evaluation: matching a reference answer need not mean delivering it, and an apparent compression benefit may admit another explanation. RCCM records this evidence for reproducible transfer comparisons.

Figures & tables

Block	Interface	Items	Models	Outcomes
Development	Historical	120	5	5,400
MATH500	Historical	500	3	9,000
Additional study	Chat	60	2	960 assigned
Repeated collections	Chat	Same 60	2	960 served
Answer-phase controls	Native raw	Same 60	2	960 logical / 1,049 calls

Table 1: Main evidence blocks. The last three share one 60-question set, not 180 independent questions. The original additional study has 957 served outputs and three terminal interface errors. Raw controls are analyzed separately from chat collections. Historical configurations are not replaced by current model identities.

Figure 1: Paired gains and harms relative to CoT on 120 development questions per deployment. CC denotes Concise CoT. Blue circles show baseline errors rescued by the target; orange squares show correct baseline answers harmed. Their directed difference is the net accuracy change, not a confidence interval. Deployment-specific caps are given in Section 4 .

Strategy	Qwen	Gemma	Llama	Mistral	Phi
CoT	73.3	70.0	57.5	10.0	69.2
Concise	72.5	65.8	57.5	5.0	77.5
CoD	46.7	50.8	50.0	9.2	81.7
KSD	73.3	72.5	70.0	5.8	68.3
Full-Retry	60.0	66.7	55.0	19.2	60.0
KSPAC-Repair	60.0	66.7	50.8	16.7	64.2

Table 2: Development answer accuracy (%),

n=120

per cell. Bold marks a point maximum. MCR-Route uses development information; its score is not unseen-data routing performance.

Strategy	Qwen	Gemma	Llama
CoT	72.6	70.8	42.0
Concise CoT	69.8	68.6	34.6
CoD	39.4	50.6	24.6
KSD	67.8	68.0	37.8
KSPAC-Check	71.4	74.8	41.4
MCR-Instruction	69.4	69.4	40.2

Table 3: MATH500 accuracy (%),

n=500

per cell, common 2,048-token cap. Check and Instruction are single-generation variants, distinct from the development pipelines.

Full $\to$ concise	$n$	$R$	$H$	Both	Neither
Length $\to$ normal	13	12	0	0	1
Length $\to$ length	21	2	2	1	16
Normal $\to$ normal	26	0	0	25	1
Normal $\to$ length	0	0	0	0	0
Total	60	14	2	26	18

Table 4: Phi development probes: stop-state and answer transitions. Both/Neither refer to correctness in both/neither condition. Row categories are exhaustive; stopping and correctness are different measurements.

Endpoint	Full	Concise	R/H	Change (pp)	Inference
Frozen matching	37	45	8/0	+13.3	8-way Holm $p=.03125$
Structural answer scope	32	44	12/0	+20.0	Sensitivity Holm $p=.00293$
Confirmed equivalent commitment	44	48	6/2	+6.7	Exploratory $p=.2891$

Table 5: Three endpoints on the original Phi/2,048 full-to-concise pair,

n=60

. Scope uses thought boundaries; commitment uses author-verified AI-assisted labels, with four uncertainties retained. Each endpoint has its own inference; none replaces the registered test.

Deployment / cap	Run-average (pp)	Question-cluster interval	Question + collection interval
Phi / 2048	$+18.3$	$[11.1,26.1]$	$[8.9,28.9]$
Phi / 4096	$+6.7$	$[0.0,13.3]$	$[-2.2,16.7]$
Qwen / 2048	$-50.6$	$[-63.3,-37.8]$	$[-63.3,-37.2]$
Qwen / 4096	$-56.7$	$[-68.3,-44.4]$	$[-68.9,-43.9]$

Table 6: Retrospective summaries of three chat collections on the same 60 questions. Pointwise 95% stratified bootstrap intervals keep paired observations together. The first conditions on the observed collections; the second also resamples their indices, a sensitivity based on only three collections. Raw controls are excluded; registered tests remain unchanged.

Arm	Matches	R/H vs F	Holm $p$	Calls	Output tok.	Input tok.
F: full	38	–	–	60	88991	6393
C: concise	41	6/3	$1$	60	70200	6513
A: full then answer	50	13/1	$0.031128$	86	88588	59556
W: warned then answer	51	13/0	$0.0043945$	89	86728	67369

Table 7: Phi/2,048 answer-phase comparison,

n=60

per arm. The native raw interface and generated-token cap are shared, not total compute. A/W reserve 128 tokens and continue only after a length stop. R/H and Holm

p

compare each arm with F in the full 24-test family. Commitment review does not cover these outputs.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Block	Design	Role
Development	120 questions, five deployments, nine strategies	Paired gains/harms and rankings
MATH500	500 questions, three deployments, six candidates; 2,048-token cap	Fixed-candidate evaluation on another set
Nine-condition profile	60 questions, four deployments, nine conditions	Marginal behavior under requests
Targeted probes	60 selected development questions per tested deployment	Joint stop/answer transitions
Additional study	60 questions, two deployments, four prompts, two budgets	Fixed registered contrasts; 960 assigned outcomes
Retrospective fitting	7,140 records; 80/20 response-level split	Association with observed features

Appendix

Table 8: Distinct units and purposes. Repeated strategies and resampling do not add independent questions or deployments.

Deployment	Cap / pair	Base	Target	$R/H$	$\Delta$ (pp)	Holm $p$	95% paired interval
Qwen	2048 / CoT–CoD	48	33	3/18	$-25.0$	.00894	$[-38.3,-11.7]$
Qwen	2048 / full–concise	42	12	1/31	$-50.0$	$1.08\!\times\!10^{-7}$	$[-63.3,-36.7]$
Qwen	4096 / CoT–CoD	46	31	5/20	$-25.0$	.02039	$[-40.0,-10.0]$
Qwen	4096 / full–concise	46	10	0/36	$-60.0$	$2.33\!\times\!10^{-10}$	$[-71.7,-48.3]$
Phi	2048 / CoT–CoD	37	43	8/2	$+10.0$	.32813	$[0.0,20.0]$
Phi	2048 / full–concise	37	45	8/0	$+13.3$	.03125	$[5.0,21.7]$

Appendix

Table 9: All eight registered contrasts on 60 additional questions per cell. Counts use the frozen answer-matching endpoint; intervals are pointwise. Phi CoD has one terminal interface failure at 2,048 tokens and two at 4,096; these yield no successful match, with unknown mathematical correctness. Full/concise are probe templates, not the main CoT/CoD templates.

Request	Level	Q	G	L	P
Length	Answer-only	47.8	31.1	36.1	55.0
	Concise	54.4	55.0	43.3	56.7
	Full	58.3	51.1	43.9	46.1
Structure	Free	39.4	39.4	31.1	53.3
	Simple	56.7	53.9	41.1	52.2
	Multi-stage	64.4	43.9	51.1	52.2

Appendix

Table 10: Marginal accuracy (%) in the nine-condition design. Q/G/L/P denote Qwen/Gemma/Llama/Phi. Each level pools three conditions on the same 60 questions: 180 responses, not 180 independent questions. These are conditional summaries, not isolated factorial effects.

Deployment	Baseline $\to$ target	Correct counts	$\Delta$ (pp)	95% interval	Holm $p$
Qwen	Free $\to$ multi-stage	37 $\to$ 42	$+8.3$	$[-1.7,18.3]$	.6797
Qwen	Simple $\to$ multi-stage	36 $\to$ 42	$+10.0$	$[-1.7,21.7]$	.5923
Gemma	No-check $\to$ self-check	34 $\to$ 38	$+6.7$	$[-8.3,21.7]$	.6797
Gemma	Self-check $\to$ repair	38 $\to$ 31	$-11.7$	$[-23.3,0.0]$	.5923
Phi	Full $\to$ concise	28 $\to$ 40	$+20.0$	$[8.3,31.7]$	.0293
Phi	Full $\to$ answer-only	28 $\to$ 33	$+8.3$	$[-1.7,20.0]$	.6797

Appendix

Table 11: All seven targeted development comparisons,

n=60

paired questions each. Pointwise intervals and one common Holm family are retained. Qwen/Gemma caps are 1,024 tokens, Phi’s is 2,048. Edits can change wording and organization together.

Archived pass rule	Qwen	Gemma	Llama	Phi
Output NO	28/32	33/36	50/50	1/37
Localization text	32/32	36/36	50/50	32/37
Re-answer match	4/32	2/36	10/50	4/37

Appendix

Table 12: Reference-assisted repair probes. Phi receives truncated visible traces; other inputs are complete. Localization requires at least 20 characters and specified error/step keywords. Requests are evaluated independently.

Deployment	Cap / pair	Base	Target	$R/H$	$\Delta$ (pp)	Holm $p$
Qwen	2048 / CoT–CoD	48	33	3/18	$-25.0$	.00745
Qwen	2048 / full–concise	42	12	1/31	$-50.0$	$1.08\!\times\!10^{-7}$
Qwen	4096 / CoT–CoD	46	31	5/20	$-25.0$	.01631
Qwen	4096 / full–concise	46	10	0/36	$-60.0$	$2.33\!\times\!10^{-10}$
Phi	2048 / CoT–CoD	33	41	12/4	$+13.3$	.23044
Phi	2048 / full–concise	32	44	12/0	$+20.0$	.00293

Appendix

Table 13: Retrospective scope sensitivity, all

n=60

assignments per cell. Holm is recalculated across these eight sensitivity tests and does not replace Table 9 . Missing scope is no observed delivered match.

Candidate	Supported condition
CoT	$u_{\mathrm{CoT}}<0.40$ and the best of the three compression candidates does not exceed CoT by at least 10 points
Concise/CoD/KSD	$a_{m}\geq a_{\max}-1$
KSPAC-Check	$a_{m}\geq\max(a_{\mathrm{CoT}},a_{\mathrm{KSD}})+1$
MCR-Instruction	The preceding count condition and $u_{m}-u_{\mathrm{CoT}}\leq 0.10$

Appendix

Table 14: Development-derived probe rules, replayed with integer counts and denominators. Their provenance does not establish pre-registration before all development observations.

Rule	Size	Near-best	Highest point
Direct top-1	1.00	67.0	34.7
Direct top-2	2.00	86.0	54.7
Direct top-3	3.00	96.0	76.0
Probe top-band	5.55	100.0	100.0
Guard	2.18	81.0	72.3
Direct, matched size	2.18	86.0	66.3

Appendix

Table 15: Candidate size and hit rates (%) across cached splits. Direct top-2 plus the same hard interface filter is unchanged at 86.0/54.7.

Deployment	Target	$n$	Base	Target	$R/H$	$\Delta$ (pp)	95% interval
Gemma	CoD	120	84	61	4/27	$-19.2$	$[-27.5,-10.8]$
Gemma	KSD	120	84	87	11/8	$+2.5$	$[-4.2,10.0]$
Gemma	Concise	120	84	79	7/12	$-4.2$	$[-11.7,2.5]$
Llama	CoD	120	69	60	15/24	$-7.5$	$[-17.5,2.5]$
Llama	KSD	120	69	84	25/10	$+12.5$	$[3.3,21.7]$
Llama	Concise	120	69	69	16/16	$+0.0$	$[-9.2,9.2]$

Appendix

Table 16: Development paired effects relative to CoT. Intervals are pointwise; full comparison families determine statistical top bands.

Deployment	Target	$n$	Base	Target	$R/H$	$\Delta$ (pp)	95% interval
Gemma	CoD	500	354	253	20/121	$-20.2$	$[-24.6,-16.0]$
Gemma	KSD	500	354	340	27/41	$-2.8$	$[-6.0,0.4]$
Gemma	Concise	500	354	343	30/41	$-2.2$	$[-5.6,1.0]$
Gemma	Check	500	354	374	41/21	$+4.0$	$[1.0,7.0]$
Gemma	Instruction	500	354	347	33/40	$-1.4$	$[-4.6,2.0]$
Llama	CoD	500	210	123	33/120	$-17.4$	$[-22.0,-12.8]$

Appendix

Table 17: MATH500 paired effects relative to CoT. Intervals are pointwise; full comparison families determine statistical top bands.

Features	Correctness	Interface event
Length	0.7029	0.8336
Deploy. + length	0.7940	0.9131
Method + deploy. + len.	0.8173	0.9433
Deploy. + control	0.7040	0.8920
Enriched	0.8021	0.9432

Appendix

Table 18: Added same-split AUC controls. Enriched is the original descriptor set in Figure H.1 . Output length is observed after generation, not a pre-inference measurement.

Deployment / cap	Request	Matches	Scope matches	Median tokens	Length stops	Unresolved scope
Qwen / 2048	full	42	42	426.5	0	0
Qwen / 2048	concise	12	12	4.5	0	0
Qwen / 4096	full	46	46	422.0	0	0
Qwen / 4096	concise	10	10	4.0	0	0
Phi / 2048	full	37	32	1864.0	26	24
Phi / 2048	concise	45	44	936.0	16	16

Appendix

Table 19: Observed execution on the 60 additional questions in each cell. All 480 full/concise responses were served; the three interface failures occur in a different arm.

Deployment / cap	Stop pair	$n$	Rescue	Harm	Both	Neither
Qwen / 2048	normal $\to$ normal	60	1	31	11	17
Qwen / 4096	normal $\to$ normal	60	0	36	10	14
Phi / 2048	length $\to$ length	15	0	0	0	15
Phi / 2048	length $\to$ normal	11	7	0	4	0
Phi / 2048	normal $\to$ length	1	1	0	0	0
Phi / 2048	normal $\to$ normal	33	0	0	33	0

Appendix

Table 20: Complete observed stop-pair categories for full-to-concise. Missing categories have zero observations. Row cells partition each 60-question comparison.

Deployment	Cap	Collection	Base	Target	Rescue/Harm	Change (pp)	Holm $p$
Phi	2048	1	35	46	14/3	$+18.3$	$0.0381775$
Phi	2048	2	34	48	14/0	$+23.3$	$0.000488281$
Phi	4096	1	41	48	10/3	$+11.7$	$0.18457$
Phi	4096	2	46	51	6/1	$+8.3$	$0.18457$
Qwen	2048	1	42	12	2/32	$-50.0$	$3.469\!\times\!10^{-7}$
Qwen	2048	2	43	12	1/32	$-51.7$	$4.750\!\times\!10^{-8}$

Appendix

Table 21: All eight new repeated-collection contrasts; each uses the same 60 paired questions and original answer-matching endpoint. No new independent sample is claimed.

Deploy. / cap	Run	Label eq.	Stop eq.	Text eq.	Output tok.	Input tok.	Time (s)
Phi / 2048	1	103/120	107/120	0/120	163027	12906	2671.0
Phi / 2048	2	110/120	112/120	0/120	157502	12906	2556.5
Phi / 4096	1	109/120	110/120	0/120	236087	12906	4396.3
Phi / 4096	2	105/120	107/120	0/120	221535	12906	3589.0
Qwen / 2048	1	114/120	120/120	55/120	36508	13000	816.7
Qwen / 2048	2	115/120	120/120	60/120	36371	13000	795.3

Appendix

Table 22: Agreement with the original collection and observed cost, pooling the 60 full and 60 concise responses only for descriptive agreement counts. Input-token counts need not equal uncached computation.

Request	Equiv.	Not equiv.	No final	Uncertain
Full	44	1	13	2
Concise	48	0	10	2

Appendix

Table 23: All 60 responses per request under the additional commitment rubric. Uncertain outcomes remain unresolved rather than being labeled mathematical errors.

Cell	Arm	Calls	$n$	$R$	$H$	$B$	$N$
Phi / 2048	A	1	34	2	0	32	0
Phi / 2048	A	2	26	11	1	5	9
Phi / 2048	W	1	31	2	0	29	0
Phi / 2048	W	2	29	11	0	9	9
Phi / 4096	A	1	46	0	0	45	1
Phi / 4096	A	2	14	9	0	1	4

Appendix

Table 24: Full-to-A/W outcomes by realized target call path. R/H: rescue/harm; B/N: both/neither correct. Each two-row partition sums to its 60 pairs and registered R/H. Triggering is an observed event, not an assigned causal treatment.

Deployment / cap	Arm	Calls	Two-phase	Output tok.	Input tok.	Time (s)	Median tok.
Phi / 2048	F	60	0	88991	6393	1908.4	1498.0
Phi / 2048	C	60	0	70200	6513	1487.6	967.0
Phi / 2048	A	86	26	88588	59556	1910.8	1575.5
Phi / 2048	W	89	29	86728	67369	1876.2	1783.5
Phi / 4096	F	60	0	127810	6393	2757.9	1549.5
Phi / 4096	C	60	0	101592	6513	2199.5	1073.5

Appendix

Table 26: Complete answer-phase cost ledger, 60 items per row. Each item remains within its generated-token cap across both stages. Injected prefixes consume input, not output, and extra calls/prefill mean this is not an equal-total-compute comparison. Input counts do not estimate uncached FLOPs.

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Large reasoning models (LRMs) often generate extensive chain-of-thought (CoT) traces before producing a final answer. As explicit textual artifacts, these traces can be passed to other models to solve the same task, enabling cross-model reasoning transfer. Yet successful transfer alone does not reveal how the provided CoT contributes to another model's answer. We study this question with a controlled provider--receiver framework, where a provider generates a reasoning trace and a receiver solves the same problem from increasingly longer trace prefixes. We compare force-answer, where the receiver answers directly from the prefix, with free-generation, where it may continue reasoning before answering. Across models and benchmarks, full traces often transfer successfully, but prefix trajectories reveal distinct mechanisms. In force-answer mode, AIME transfer is largely driven by explicit answer availability. MMLU-Pro instead reflects a larger role for receiver competence, while ZebraLogic depends on partial structured-answer information rather than complete-answer leakage alone. In free-generation mode, partial CoTs improve performance across benchmarks, indicating that prefixes can guide continued reasoning. Finally, answer agreement among receivers provides a gold-free signal for stopping provider reasoning early. Overall, cross-model CoT transfer is not a single phenomenon: it can reflect answer extraction, reasoning scaffolding, or receiver-dependent competence.

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