ReSolve: Reusing Candidate Reasoning through Selective Generative Moderation

1 Introduction

• Self-consistency votes by frequency over extracted final answers, leaving partial derivations that never reach an answer unused in its decision.The paper asks whether that reasoning already generated can be put to better use before spending computation on independent attempts.Source: §1 · p. 1
• ReSolve samples four solutions and invokes moderation when answer groups disagree or no answer is parseable, then updates the pool within a bounded loop.The controller selects instructions based on the answer distribution; the same model proposes and moderates, without reference answers at inference.Source: §1 · p. 2
• ReSolve returns 100 and 99 correct answers versus 91 and 92 for four-candidate voting across two pools, with no observed correct-to-incorrect changes.It uses 46–47% fewer total tokens than eight-sample self-consistency, without establishing an accuracy advantage over that baseline.Source: §1 · p. 2
• Removing visible derivations reduces accuracy from 100 to 93 correct answers despite more calls and tokens; always-on checking leaves accuracy at 97.Route-specific instructions do not establish an advantage over a generic Uniform moderator.Source: §1 · p. 2
• The paper frames candidate derivations as reusable inference computation and evaluates both recovery and preservation, including what moderation repairs and what it can lose.Its contributions include an explicit bounded procedure that reads candidate evidence when answers disagree or are unavailable, with token accounting for evidence access and generation.Source: §1 · p. 2
• The evaluation covers mathematical reasoning with a 4B backbone; fresh candidate pools do not establish generalization to new tasks or rule out benchmark familiarity.The pools test sensitivity to sampling, not broader task generalization.Source: §1 · p. 2

2.1 From candidate answers to candidate evidence

• Candidate answers are extracted and grouped; ReSolve packages representative arguments and answer-distribution information for moderation, which can generate beyond the fixed-pool selection oracle.The accounting separates recovery on oracle-unsolved problems from loss on oracle-solvable ones.Source: §2.1 · p. 3

2.2 Selective intervention and bounded feedback

• The controller bypasses agreement states and routes disagreement or no-answer states to checks, comparisons, reconciliation, or repair, then applies acceptance and stability rules within at most three calls.Generated responses update the answer histogram; acceptance conditions are not certificates of mathematical correctness.Source: §2.2 · pp. 3–4, Table 1 · p. 4

2.3 A fixed model and an explicit inference policy

• The proposer and moderator share Qwen3-4B-Thinking-2507 weights [2], with no parameter update, reference answers, or evaluator feedback during inference.The generated response enters the same answer-extraction and grouping pipeline as the original proposals.Source: §2.3 · p. 4

2.4 Accounting for inference computation

• Token accounting includes proposal and moderation input and output; moderation adds the cost of reading and extending evidence, while SC@8 generates four more independent solutions.Reported token counts characterize workload, not equivalent latency or FLOPs across arbitrary serving configurations.Source: §2.4 · p. 5

3.1 Evaluation design

• The evaluation repeats candidate sampling on the same 130 problems, using two pools and a prespecified Hybrid score that accepts either the rule grader or CV.The pools are not additional independent test problems.Source: §3.1 · p. 5, Table 2 · p. 6

3.2 Reusing four candidates versus sampling eight

• ReSolve improves same-pool voting from 91 to 100 correct in F2 and 92 to 99 in F3, with 16 fixes and no breaks across the two pools.These are repeated observations of the same 130 problems.Source: Table 2 · p. 6, §3.2 · p. 6
• ReSolve uses 12.46M versus 23.19M tokens in F2 and 12.35M versus 23.38M in F3, while its accuracy ordering over SC@8 does not establish superiority.The token totals include proposals and moderation input/output; ReSolve uses 46.3% and 47.2% fewer tokens, respectively.Source: §3.2 · p. 6, Figure 2 · p. 7

3.3 Does the visible candidate reasoning matter?

• Full solves 100 problems versus 93 for Answer-only after visible derivations are removed; Answer-only also uses more calls and moderator tokens.The intervention retains answer keys and counts and applies the same per-state output-cap rule.Source: §3.3 · pp. 7–8, Table 3 · p. 7

3.4 Does selective invocation save computation?

• Selective and always-on Uniform both solve 97 problems; selectivity cuts moderation tokens by approximately 54% and total pipeline tokens by approximately 6.2%.The control supports bypassing agreement states on this pool, not the claim that agreement guarantees correctness.Source: §3.4 · p. 8

3.5 Where gains and preservation failures occur

• F2 gains over SC@4 span four controller states, while fixed-pool oracle accounting shows recoveries and losses in both pools.ReSolve recovers three no-answer problems and loses two oracle-solvable problems in F2; F3 recovers two and loses three. Historical H1 and D1 controls are consistent with the interpretation, but differ in design or prompt wording.Source: Table 4 · p. 8, §3.5 · p. 9

3.6 A case of completing candidate evidence

• A historical-pool example completes a correct answer from a useful sum-of-squares identity despite no extractable answer among the four candidates.Uniform also succeeds, so the example illustrates evidence reuse rather than instruction superiority.Source: Table 5 · p. 9, §3.6 · p. 10

3.7 Token savings and sequential latency

• Triggered moderation has a median added time of 108 seconds, while logged end-to-end latency ratios do not establish a controlled production speedup.The audit reports 1.18 at the median and 1.41 at the 90th percentile on triggered problems; the serving configuration and timing controls limit interpretation.Source: §3.7 · p. 10

Sampling and adaptive computation

• Adaptive sampling and selective moderation allocate further computation from intermediate evidence, but differ in whether they generate independent attempts or inspect existing derivations.Prior work includes Adaptive-Consistency and test-time compute allocation [5] [6].Source: §4 · p. 10

Candidate selection and generative fusion

• Universal Self-Consistency selects a consistent candidate [7], while LLM-Blender combines pairwise ranking with generative fusion [8]; ReSolve tests visible derivations and selective invocation with shared candidates and fixed weights.It also measures recovery and preservation failures against a shared fixed-pool selection oracle.Source: §4 · p. 10

Verification and feedback

• Prior methods score intermediate steps [9], reconstruct masked values [10], revise outputs through feedback [11], or exchange arguments and condition generations on prior outputs [12] [14] [15].ReSolve’s controls separate derivation access, invocation, and instruction choice within a shared candidate pool.Source: §4 · pp. 10–11

Search over reasoning states

• Tree of Thoughts evaluates intermediate thoughts and backtracks [16], while Graph of Thoughts permits richer dependencies [17]; ReSolve instead uses answer histograms to control bounded interventions.It does not maintain an explicit proof-state search structure or assume a step-wise reward model, and no direct performance comparison is claimed.Source: §4 · p. 11

5 Discussion: practical interpretation

• When candidates disagree or lack a final answer, reading and extending existing derivations can recover useful work that voting discards.The answer-only control isolates the contribution of visible derivations under a shared output-cap rule; the always-on control finds extra verification unnecessary on the evaluated pool.Source: §5 · p. 11
• Further samples can supply a missing answer, whereas moderation can complete or correct reasoning already available.These are complementary failure modes in the comparison with SC@8.Source: §5 · p. 11
• Candidate generation and subsequent processing can be treated as separate inference decisions, with agreement checked before selected derivations are read and extended.ReSolve uses the same model as proposer and moderator, while the competitive Uniform control shows the design choices can be examined beyond one prompt family.Source: §5 · p. 11

6 Conclusion

• Across two candidate pools, ReSolve improves four-candidate voting with no observed regressions and uses 46–47% fewer tokens than eight-sample self-consistency, without establishing an accuracy advantage over it.Evidence removal and always-on checking support reuse and selectivity under the tested protocol.Source: §6 · p. 11
• ReSolve reuses reasoning from four generated solutions and continues only when candidates disagree or lack an answer.The conclusion treats already-incurred reasoning as evidence for further inference.Source: §6 · p. 11
• Evidence removal and always-on checking support both reuse and selectivity under the tested protocol.The conclusion does not claim specialized route instructions are necessary.Source: §6 · p. 11

A Implementation and inference protocols

• Answer grouping extracts the last boxed answer when available, otherwise uses short-answer patterns within the final 1,200 characters; normalization is not a symbolic-equivalence oracle.The same grouping rule is used for invocation and voting, independently of the evaluation grader.Source: A Implementation and inference protocols · p. 14
• The controller prioritizes zero parseable answers, then a single group, strict majority, two-group split, and fragmented disagreement; rendered evidence is capped by character limits.For answer groups, it exposes representative keys and counts; when no answer parses, it instead supplies up to six attempts for repair.Source: A Implementation and inference protocols · p. 14
• At the call limit, fallback selects the most frequent parseable key and its latest supporting response; without an extractable answer, it returns the first original response.A single answer group commits without a call, while other acceptance rules depend on the state and generated responses.Source: A Implementation and inference protocols · p. 14
• The principal protocol uses eight separately sampled proposals per problem, sharing the first four with moderation methods and reserving the rest for eight-sample controls.The proposer and moderator are the same model; F2 and F3 use the stated candidate-compaction and output-cap rules.Source: A Implementation and inference protocols · p. 14
• Historical H1/D1 studies share a 160-problem pool, and their overlapping results are not independent replications or pooled with fresh-protocol costs.F3’s batched implementation was checked for equivalent per-problem behavior, but its execution change is not a controlled latency comparison with F2.Source: A Implementation and inference protocols · pp. 14–15

• 100/99 ReSolve correct answers exceed SC@8's 94/96 and match or exceed Uniform's 97/99 under Hybrid in F2/F3.Hybrid and CV score the same outputs; the main text uses Hybrid.Source: Table 6 · p. 16, B Scores and paired comparisons · p. 16
• The within-pool Holm family covers SC@8 and Uniform; SC@4 is a secondary comparison, and tests use fixes and breaks.The combined problem-level tests are a separate analysis, not pooled-outcome McNemar tests.Source: Table 7 · p. 16, B Scores and paired comparisons · p. 16
• CV sensitivity scores the same outputs as Hybrid: F2/F3 totals are 100/97 for ReSolve, 93/94 for SC@8, and 97/97 for Uniform.Source: B Scores and paired comparisons · p. 16
• 16/260 is the combined Hybrid count difference versus SC@4 (6.15 percentage points, p = 0.0003); differences versus SC@8 and Uniform are 9/260 (3.46 points, p = 0.093) and 3/260 (1.15 points, p = 0.51).The sign-flip test groups repeated outcomes by problem across two candidate pools.Source: B Scores and paired comparisons · p. 16

B.1 Scorer disagreements and clipping

• 15 rule/CV disagreements occur among 1,258 unique scoring keys; provisional manual adjudications are not used as a third primary benchmark.The report avoids treating analyst judgment as a fully validated grading protocol.Source: Table 8 · p. 17, §B.1 · p. 17
• For CMIMC25 index 16, the rule accepts an equivalent-form answer that CV rejects; the recorded scoring policies are retained without counting this as a mathematical repair.Source: §B.1 · p. 17
• 291 scoring texts are clipped for verifier context, but replay checks find no removed existing final answers and no clipped ReSolve output in SC@8 or Uniform comparisons.The checks address answer loss, not the correctness of every retained derivation or verifier decision.Source: §B.1 · p. 17, Table 9 · p. 17

C Controlled evidence and invocation interventions

• Seven problems improve under Hybrid with Full derivations versus Answer-only, four with parseable candidate answers and three with none; Full has no Hybrid losses.The controlled intervention also keeps output caps matched to each state's Full rendering.Source: C Controlled evidence and invocation… · p. 18
• Both always-on Uniform variants show zero fixes and zero breaks across 86 agreement checks; their moderation-token totals are rounded.The variants reuse existing Uniform outputs elsewhere, so they are controls on the same underlying outputs, not independent replications.Source: C Controlled evidence and invocation… · p. 18

• For F2 Hybrid, SC@4 fixes 2, 1, 3, and 3 across dominant-answer, two-group, fragmented, and no-answer routes, respectively, with no breaks; SC@8 comparisons are 2/0, 0/0, 2/1, and 3/0 fixes/breaks.Both moderators solve three of six no-answer problems; these are descriptive strata, not independent significance tests.Source: D Route and recovery details · p. 19
• Only 54 of 86 skipped agreement problems have four parseable candidates, while 14 have just one; all 17 triggered SC@4-correct votes are preserved.The nine fixes occur among the other 27 triggered problems.Source: Table 11 · p. 19, D Route and recovery details · p. 19
• F2's three recoveries beyond Oracle@4 all arise in no-answer states, while both losses are fragmented; F3 instead has two recoveries and three losses.The aggregate oracle is only bounded for selection from its specified pool and evaluator, not a deployable baseline or upper bound for a generator with additional computation.Source: D Route and recovery details · p. 19

• H1 and D1 reuse a historical 160-problem pool, including 30 BRUMO25 questions; overlapping rows are reused observations, not independent samples.Source: Table 12 · p. 20, E Historical mechanism controls · p. 20
• 126 versus 119 Hybrid correct answers: one candidate-conditioned Uniform call outperforms a fresh solve on the same 58 triggered questions under a 16K output cap.The original answer is used on skipped questions; changing the prompt makes this less isolated than the final-protocol Answer-only intervention.Source: Table 13 · p. 20, E Historical mechanism controls · p. 20
• On ten no-answer problems, ReSolve solves four while SC@4 solves none; among 102 agreement states, nine errors remain unchanged by D1's always-on Uniform check.H1's Hybrid oracle decomposition is four recoveries and three losses.Source: E Historical mechanism controls · p. 20

F Case-study evidence

• The examples use zero-based historical-panel cache indices, and their mathematical descriptions are edited summaries rather than verbatim transcripts.Source: F Case-study evidence · p. 21
• Four unparseable initial answers make the quartic case a recovery example: a fourth unfinished attempt contains the identity yielding the correct sum, 322.The identity is independently checked; the example does not relabel the missing answers as observed length termination.Source: F Case-study evidence · p. 21
• In the AIME25 case, ReSolve corrects the 153 majority to 104 after two calls, while Uniform reaches 104 then returns to 153.The example illustrates discovering and retaining a correction, not that generic verification cannot find it.Source: F Case-study evidence · p. 21

G Evidence provenance and scope

• Evidence combines recomputed archived-record counts with completed reports; remote generation and grading artifacts were not replayed locally, and scope is specified-backbone mathematical inference with stated budgets.Source: G Evidence provenance and scope · p. 22