ReSolve: Reusing Candidate Reasoning through Selective Generative Moderation

Bangji Yang; Jiajun Fan; Hongba Ma; Xi Zhu; Weizhi Zhang; Minghao Guo; Ye Li; Hamid Palangi

cs.AIOct 1, 2026

ReSolve: Reusing Candidate Reasoning through Selective Generative Moderation

Authors: Bangji Yang, Jiajun Fan, Hongba Ma, Xi Zhu, Weizhi Zhang, Minghao Guo, Ye Li, Hamid Palangi, +1 more

Organizations: University of Illinois at Urbana-Champaign · Tsinghua University · Rutgers University · University of Illinois Chicago · Google

Abstract

Sampling multiple solutions spends computation on intermediate deductions and unfinished arguments as well as final answers. We introduce ReSolve, a training-free inference procedure that reuses this candidate reasoning through selective generative moderation. An answer-distribution controller invokes a model to examine existing derivations when candidates disagree or lack a parseable answer, then incorporates the generated solution into a bounded loop. Under Hybrid scoring on 130 competition-mathematics problems evaluated with two independently sampled candidate pools, ReSolve obtains 100 and 99 correct answers, compared with 91 and 92 for voting over the same four candidates, with no correct-to-incorrect changes relative to that vote in either pool. Eight-sample self-consistency obtains 94 and 96 correct answers while consuming substantially more tokens; ReSolve uses 46.3% and 47.2% fewer tokens in the two evaluations. A controlled ablation removes visible derivations while retaining answer keys, vote counts, and the per-state output-cap rule, reducing accuracy from 100 to 93 correct despite increasing computation. Selective and always-on Uniform moderation both solve 97 problems, while selectivity reduces moderation tokens by approximately 54% and total pipeline tokens by 6.2%. These results support candidate reasoning as reusable inference computation. They do not establish an accuracy advantage over additional sampling or a distinct benefit from specialized route instructions.

Figures & tables

Figure 1 : Selective reuse of candidate reasoning. Four sampled solutions provide both an answer distribution and visible derivations. Agreement permits a direct decision; otherwise, a generative moderator checks, repairs, or completes candidate reasoning. New solutions update the pool until acceptance or the call limit. Proposer and moderator share existing model weights, and reference answers are absent at inference.

State	Histogram condition	Intervention
No final answer	$n_{C}=0$	Complete or repair unfinished attempts
Agreement	One valid answer group	Commit without a new call
Dominant answer	Top share $>\tau$	Audit the majority and competing evidence
Two groups	Two groups, no dominant answer	Adjudicate the competing arguments
Fragmented	More than two, no dominant answer	Reconcile useful deductions

Table 1: Controller states, evaluated in the displayed order. Shares use the number of parseable answers. In particular, agreement can occur with fewer than

K

parseable candidates. We use

\tau=0.5

Method	F2 correct	F2 (%)	F3 correct	F3 (%)
SC@4	91	70.00	92	70.77
SC@8	94	72.31	96	73.85
Direct32	82	63.08	80	61.54
Uniform	97	74.62	99	76.15
ReSolve	100	76.92	99	76.15
Oracle@4	99	76.15	100	76.92

Table 2: Hybrid results on two independent candidate pools for the same 130 problems. ReSolve and Uniform access only the first four candidates. Oracle rows use evaluation reference answers. The evaluations are repeated observations of the same questions.

Figure 2 : Accuracy and token cost with Hybrid scoring. (a) F2 controls, including the answer-only intervention; the star marks ReSolve. (b) Whole-pipeline token cost for ReSolve and SC@8 on both independent candidate pools. Each method’s total includes the proposals it uses and all moderation input/output tokens.

F2 configuration	Correct / 130	Calls	Moderation (M)
ReSolve (Full)	100	51	0.753
Answer-only	93	65	1.276
Uniform loop, selective	97	50	0.706
Uniform loop, always-on	97	136	1.522
Uniform one-call, selective	97	44	0.619
Uniform one-call, always-on	97	130	1.435

Table 3: F2 controls under Hybrid. Moderation tokens include inputs and outputs; all rows share an additional 11.711M proposal tokens. Full versus Answer-only removes derivations under the same per-state output-cap rule. Selective versus always-on Uniform adds agreement checks, shared across the two Uniform variants.

F2 initial state	$N$	vs. SC@4	vs. SC@8	vs. Uniform
Agreement	86	0/0	0/0	0/0
Dominant answer	18	2/0	2/0	3/0
Two groups	8	1/0	0/0	0/0
Fragmented	12	3/0	2/1	1/1
No answer	6	3/0	3/0	0/0

Table 4: F2 fixes/breaks by initial state under Hybrid. Comparators isolate same-pool voting, additional proposals, and the moderation instruction. Small strata are descriptive.

Example: a quartic root (CMIMC25, cache index 7). Problem: Let $P(x)=x^{4}+20x^{3}+29x^{2}-666x+2025>0$ for real $x$ . A first-quadrant root has the form $r=(a+bi+\sqrt{c+di})/2$ , with integer $a,b,c,d$ . Find $a+b+c+d$ . Reference answer: 322.
Initial candidate pool / SC@4	ReSolve
All four attempts lack an extractable final answer, so answer voting has no valid answer to select. However, the fourth attempt already contains $\color[rgb]{0,0,0}P(x)=(x^{2}+10x-36)^{2}+(x+27)^{2}.$ This useful intermediate identity remains visible in the moderator’s actual input.	Checks the decomposition and completes the complex quadratic: $x^{2}+(10-i)x-(36+27i)=0.$ The discriminant is $243+88i$ , giving $r=\frac{-10+i+\sqrt{243+88i}}{2}.$ Thus $-10+1+243+88=322$ .
Extracted answers: $[\bot,\bot,\bot,\bot]$	One moderation call. Answer: $\boxed{322}$ ✓

Table 5 : Completing candidate reasoning on CMIMC 2025. The initial pool has no extractable final answer, but contains an identity that supports a correct completion. All descriptions are edited summaries, not verbatim model quotations.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Method	AIME24	AIME25	CMIMC25	HMMT25	Total
SC@4	26/26	24/24	25/24	16/16	91/90
Oracle@4	27/27	25/25	27/26	20/20	99/98
SC@8	27/27	25/25	26/25	16/16	94/93
Oracle@8	27/27	25/25	28/27	20/20	100/99
ReSolve	27/27	25/25	27/27	21/21	100/100
Uniform	27/27	26/26	25/25	19/19	97/97

Appendix

Table 6: F2 per-task correct counts as Hybrid/CV. Task sizes are 30, 30, 40, and 30. Hybrid and CV score the same outputs; the main text uses Hybrid.

Pool	Score	Comparator	Fix/break	Exact $p$	Holm $p$
F2	Hybrid	SC@8	7/1	0.07031	0.14062
F2	Hybrid	Uniform	4/1	0.37500	0.37500
F2	Hybrid	SC@4	9/0	0.00391	—
F3	Hybrid	SC@8	7/4	0.54883	1.00000
F3	Hybrid	Uniform	2/2	1.00000	1.00000
F3	Hybrid	SC@4	7/0	0.01562	—

Appendix

Table 7: Within-pool tests for ReSolve. Holm correction covers SC@8 and Uniform within each pool and score. SC@4 is a secondary comparison. Combined problem-level tests use a different analysis described in the text.

Method	F2 rule	F2 CV	F2 Hybrid	F3 CV	F3 Hybrid
ReSolve	100	100	100	97	99
Uniform	97	97	97	97	99
SC@8	94	93	94	94	96
SC@4	91	90	91	91	92
Direct32	81	81	82	79	80

Appendix

Table 8: Scoring sensitivity on shared outputs. F2 rule values are from the audit; F2 Hybrid/CV values are reconciled to archived outcomes. Provisional manual judgments do not replace recorded scores.

CV contrast	Discordant problems	Clipped inputs
ReSolve vs. SC@8	9	2
ReSolve vs. Uniform	5	0
ReSolve vs. Answer-only	8	2
ReSolve vs. Direct32	23	17
ReSolve vs. Oracle@4	6	17
ReSolve vs. Oracle@8	7	39

Appendix

Table 9: Reported replay of CV clipping on discordant F2 comparisons. Oracle comparisons inspect candidate scoring inputs as well as moderator outputs, so input counts can exceed problem counts. Rows overlap and must not be summed. No existing final answer is removed; clipped Answer-only outputs already lacked final answers before clipping.

Initial state	$N$	ReSolve	SC@4	SC@8	Uniform	Oracle@4
Agreement	86	74	74	74	74	74
Dominant answer	18	14	12	12	11	14
Two groups	8	5	4	5	5	5
Fragmented	12	4	1	3	4	6
No answer	6	3	0	0	3	0

Appendix

Table 10: F2 route-wise Hybrid correct counts, recomputed from archived per-question records. Agreement is defined by answer groups rather than correctness.

Parseable candidates	Agreement problems	Correct under Hybrid
1	14	6
2	7	5
3	11	10
4	54	53

Appendix

Table 11: F2 agreement states by the number of parseable initial candidates. SC@4 and ReSolve share the skipped outputs; all 86 added Uniform checks leave correctness unchanged. Counts are descriptive.

Method	AIME24	AIME25	BRUMO25	CMIMC25	HMMT25	Total
Oracle@4	27/26	25/25	24/24	30/30	20/20	126/125
SC@4	23/23	24/24	24/24	29/29	19/19	119/119
ReSolve	26/26	26/26	24/24	30/30	21/21	127/127
Matched operation	25/25	26/26	24/24	31/31	20/20	126/126
Uniform, closed loop	26/26	25/25	24/24	31/31	20/20	126/126
Operation permutation 1	24/24	26/26	24/24	32/32	20/20	126/126

Appendix

Table 12: H1 training-free results as Hybrid/CV counts (

N=160

). Task sizes are 30, 30, 30, 40, and 30. All rows share the same four-candidate pool.

Configuration	H/CV	Calls	Input/q (K)	Output/q (K)	Total/q (K)
SC@4	119/119	0	0.00	0.00	87.67
ReSolve	127/127	74	2.01	4.56	94.24
Uniform, closed loop	126/126	68	1.78	4.36	93.80
One specialized call, original gate	125/125	58	1.50	3.56	92.73
One Uniform call, original gate	126/126	58	1.50	3.74	92.90
One Uniform call, validity gate	126/126	86	1.71	5.82	95.20

Appendix

Table 13: D1 on the H1 pool (

N=160

). Input/output columns count moderation only; total includes proposals. Calls are panel totals and tokens are per-question means. The original gate triggers on 58 questions.

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