Organizations: Faculty of Arts and Science, Beijing Normal University, Zhuhai 519087, China · Institute of Artificial Intelligence and Future Networks, Beijing Normal University, Zhuhai 519087, Guangdong, China · School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China · Guangdong Key Lab of AI and Multi-Modal Data Processing, Beijing Normal-Hong Kong Baptist University, Zhuhai 519087, China
Small language models deployed under cost, latency, or privacy constraints cannot simply switch to larger models when reasoning fails. Multi-candidate generate-then-rerank offers a natural test-time scaling route. However, more candidates do not always yield higher accuracy. We identify a previously overlooked bottleneck between generation and selection: a correct answer may appear in the candidate pool yet fail to be selected because it is incomplete, unparseable, or misaligned with the answer mode the fixed selector expects. We term this loss the hidden interface tax and formalize a coverage-conversion decomposition that distinguishes raw oracle coverage from selectable coverage, the subset of problems where a correct candidate can actually be consumed by the selector. We propose Compatibility-Aware Candidate Construction (CACC), an interface layer between the candidate source and the fixed selector that repairs fragments, aligns answer modes, and removes selector-confusing noise without retraining either component. On numeric reasoning (GSM8K, competition_math), CACC raises both oracle coverage and final accuracy. On GPQA Diamond, CACC alone improves final accuracy from 5.6% to 19.2% (+13.6 pp); combined with proposer-side strengthening it reaches 25.8% (+20.2 pp). On MMLU-Pro, CACC exposes a coverage-conversion gap: answer-mode-compatible construction raises oracle coverage, but final accuracy decreases by 0.85 pp under the original selector; adding proposer-side strengthening improves final accuracy.
Figures & tables
Figure 1: The missing candidate-interface layer in small-model multi-candidate reasoning. Existing methods optimize the candidate source or the selector, while whether the pool contains parseable, answer-mode-compatible, and selector-consumable candidates remains an independent bottleneck.
Figure 2: The offline–online flow of CACC . Lower half: offline calibration produces a frozen rulebook and routing policy. Upper half: online inference applies gold-free diagnostics and construction to the raw candidate pool before the fixed selector.
Figure 3: Main results across reasoning regimes. Panel A: Base/CACC oracle, V|O, and final. Panel B: latent coverage upper bound and selected final accuracy with CACC -vs-Base delta. Panel C: Δ oracle, Δ V|O, and Δ final separating coverage, conversion, and final. Panel D: four-step MMLU-Pro mechanism chain. Exact numbers are in Table 1 and Appendix Tables 2 , 3 .
Regime
Dataset
Method
Oracle
V|O
Final
Δ Final
Ratio
Numeric
GSM8K
Base
0.4882
0.5885
0.2873
ref.
1.00 ×
Numeric
GSM8K
SP †
0.6471
0.5714
0.3698
+8.25pp
1.29 ×
Numeric
GSM8K
CACC
0.6391
0.5682
0.3632
+7.59pp
1.26 ×
Numeric
GSM8K
CACC + SP †
0.6962
0.6017
0.4189
+13.16pp
1.46 ×
Numeric
CompMath
Base
0.3210
0.4732
0.1519
ref.
1.00 ×
Numeric
CompMath
SP †
0.4616
0.6014
0.2776
+12.57pp
1.83 ×
Table 1: Candidate-interface results. Δ Final and Ratio are computed against the Base row within the same dataset. † uses a Qwen3-8B proposer (different compute regime from the Qwen3-1.7B generator). Paired tests for CACC vs Base are in Appendix Table 10 .
Unit
Comparison
Ob
Oa
Vb
Va
Fb
Fa
ΔO
ΔV
ΔF
MMLU-Pro
no- AMC numeric → CACC
0.0369
0.4767
0.2590
0.4777
0.0096
0.2277
+43.98
+21.87
+21.81
MMLU-Pro
CCR+ AMC → CACC
0.4775
0.4767
0.4754
0.4777
0.2270
0.2277
-0.08
+0.23
+0.07
MMLU-512
diverse → CACC
0.4609
0.5547
0.4492
0.3592
0.2070
0.1992
+9.38
-9.00
-0.78
MMLU-512
CACC → +hygiene
0.5547
0.5547
0.3592
0.4049
0.1992
0.2246
+0.00
+4.58
+2.54
GSM8K full
SP → PS x CACC
0.6111
0.7195
0.5943
0.4700
0.3632
0.3381
+10.84
-12.43
-2.50
Table 2: Coverage–selection decomposition on audit rows (outside Table 1 ). O,V,F denote oracle, V|O, and final; b/a denote before/after; Δ in percentage points.
Type
Dataset
Method / transition
Oracle
V|O
Final
ΔF
Readout
MMLU-Pro
numeric scoring → MCQ reparse
0.0369 → 0.4072
0.2590 → 0.5800
0.0096 → 0.2362
+22.66pp
AMC
MMLU-Pro
MCQ reparse → CACC
0.4072 → 0.4767
0.5800 → 0.4777
0.2362 → 0.2277
-0.85pp
SP
MMLU-Pro
CACC → CACC + SP
0.4767 → 0.5527
0.4777 → 0.5312
0.2277 → 0.2936
+6.59pp
SP
GPQA
CACC → CACC + SP
0.4545 → 0.4899
0.4222 → 0.5258
0.1919 → 0.2576
+6.57pp
Recovery
MMLU-Pro
CACC → +hygiene
0.5547 → 0.5547
0.3592 → 0.4049
0.1992 → 0.2246
+2.54pp
Recovery
GPQA
CACC → +hygiene
0.5127 → 0.4931
0.3961 → 0.5386
0.2031 → 0.2656
+6.25pp
Table 3: Ablation, recovery, and interaction evidence. Reports oracle, V|O, and final before → after with the final delta; sample sizes, wins/losses, p -values, scope, and artifact statuses are in Appendix Tables 10 , 11 , and 12 .
Control
Evaluation
N
Base
CACC
ΔF
Target verifier, canonical
GPQA
198
16.16
24.92
+8.75
Target verifier, canonical
MMLU held-out
11,520
26.40
27.84
+1.44
32B candidate judge
GPQA
198
6.57
23.23
+16.67
Mistral generator
MMLU confirm
512
14.22
15.94
+1.72
Prospective ARC reuse
ARC-Challenge
256
69.92
70.70
+0.78
Fresh generation
Evaluation
N
CACC
CD
CD+ CACC
Table 4: Additional controls. Final accuracies are percentages; gains are percentage points. Frozen-pool rows reuse the original candidates. Target-verifier rows are three-seed means; Mistral is a five-seed mean. CD uses fresh paired generation and a common canonical selector, with its own baseline.
Appendix figures & tables21 assets
Supplementary material from the paper’s appendix.
Appendix
Evidence unit
N
Mode
Oracle
Final
V|O
Use in paper
GSM8K Base
1319
numeric
644/1319
379/1319
0.5885
Numeric baseline
GSM8K CACC
1319
numeric
843/1319
479/1319
0.5682
Numeric main result
CompMath Base
3199
numeric
1027/3199
486/3199
0.4732
Numeric baseline
CompMath CACC
3199
numeric
1419/3199
825/3199
0.5814
Numeric main result
MMLU no- AMC numeric
12032
numeric
444/12032
115/12032
0.2590
Archived collapse provenance
MMLU MCQ reparse
12032
choice_letter
4900/12032
2842/12032
0.5800
Readout recovery
Appendix
Table 5: Evidence units, sizes, and core metrics. The table lists sample size, answer mode, oracle, final, and V|O for the main evidence units in the main text.
Component
Work and accounting boundary
Upstream generation
Audited contract: 16 sequences, at most 128 new tokens each; pool construction precedes retention.
Completion construction
One additional batch of 4 sequences, at most 160 new tokens each, per example.
Routing / normalization
Deterministic diagnostics, parsing, sanitization, and deduplication.
Fixed selector
Two yes/no continuation scores per retained candidate; batching determines forward-pass count.
Stronger proposer
Qwen3-8B replaces or augments the 1.7B source in the composition setting; accounted separately.
Appendix
Table 6: Inference operations in the audited configuration.
Diagnostic
Setting
Oracle
V|O
Final
ΔF
Note
Sample sweep
cap 8, samples 4
0.6422
0.5844
0.3753
ref.
Fewer samples but high conversion
Sample sweep
cap 8, samples 32
0.6429
0.4517
0.2904
-8.49pp
Similar oracle, lower conversion
Retained-cap sweep
cap 8
0.6391
0.5682
0.3632
ref.
CACC canonical retained cap
Retained-cap sweep
cap 16
0.8249
0.3998
0.3298
-3.34pp
Larger retained pool raises oracle but hurts conversion
Appendix
Table 7: GSM8K candidate-budget diagnostics: oracle, V|O, and final do not move synchronously when sample count or retained cap changes.
Table 9: MMLU-Pro parser and scoring provenance: this comparison is a scoring/readout-path ablation, not an ablation between two independent candidate pools.
Figure 4: Mechanistic analysis of the coverage–conversion gap, compatibility, policy tradeoffs, and recovery closure. Panel A: oracle, V|O, and final decomposition. Panel B: unconverted gap between oracle and final. Panel C: interaction delta matrices for Δ oracle, Δ V|O, and Δ final. Panel D: before → after slopes. Paired statistics are in Tables 3 and 10 .
Figure 5: Bootstrap confidence intervals for second-family paired recovery. Both closure intervals lie above zero, supporting recoverable compatibility.
Evidence unit
Split / scope
Before
After
ΔF
w/l
Statistical detail
Artifact
Second-family recovery
MMLU confirm-512
102/512 (0.1992)
115/512 (0.2246)
+2.54pp
17/4
McNemar p=0.007197 ; CI [0.0078, 0.0430]
Paired JSONL
Second-family recovery
GPQA-128
26/128 (0.2031)
34/128 (0.2656)
+6.25pp
9/1
McNemar p=0.02148 ; CI [0.0156, 0.1172]
Paired JSONL
Selection rescue
MMLU-Pro
0.2936
0.3320
+3.84pp
613/150
McNemar p=3.43×10−67
Paired pred.
Selection rescue
GPQA
0.2576
0.2929
+3.53pp
10/3
McNemar p=0.0923
Paired pred.
Coverage pressure
GSM8K full
0.3632
0.3381
-2.50pp
summary
Oracle +10.84pp; V|O -12.43pp
Summary only
Second-family smoke
GSM8K-128
27/128 (0.2109)
29/128 (0.2266)
+1.56pp
7/1
Smoke row
Paired rows available
Appendix
Table 10: Paired statistics and diagnostic details for the mechanism rows in Table 3 .
Evidence unit
Candidate pool
Prediction records
Paired statistics
Manuscript use
Main Base / CACC rows
available
available
row-level deltas
Frozen result rows
MMLU no- AMC numeric view
archived
available
provenance audit
Scoring/readout-path provenance
MMLU MCQ reparse
archived scoreboard
available
provenance audit
MCQ Readout recovery
Second-family closure
available
available
McNemar + bootstrap
Frozen paired recovery
Conversion-aware rescue
available
available
McNemar where available
Gap narrowing evidence
Power Sampling x CACC
summary + pool
summary metrics
aggregate diagnostic
Diagnostic summary-only
Appendix
Table 11: Artifact availability matrix: artifact completeness and paper use of each evidence unit.
Method
Task
Correct / N
Final
Extra cost
Artifact status
Self-Refine
GSM8K full
643/1319
0.4875
5.0 calls/example
Full row available
Self-Refine
CompMath numeric
789/3199
0.2466
17.0 calls/example
Full row available
Self-Refine
MMLU-Pro
2838/12032
0.2359
17.0 calls/example
Full row available
Self-Refine
GPQA Diamond
24/198
0.1212
17.0 calls/example
Full row available
Self-Refine
GSM8K-128
51/128
0.3984
eval-128
Small reference row
ToT-lite
GSM8K-128
37/128
0.2891
eval-128
Small search baseline row
Appendix
Table 12: External baseline provenance and artifact status.
Component
Diagnostic trigger
Online action
Frozen output
CCR
partial derivation, missing final answer, fragmented numeric form
repair final-answer span and recover parseable candidate text
frozen rulebook ( \textscCCR/\textscAMC/\textscSCH ) and routing policy π(ϕ,K)↦a
Appendix
Table 18: Notation summary. Symbols are introduced in Sections 3 and 4 and used throughout the paper.
Benchmark
Split / N
Mode
Retained cap
Parser / scoring endpoint
GSM8K
clean test, N=1319
numeric
8
numeric exact match on final boxed span
competition_math:numeric
numeric subset, N=3199
numeric
8
numeric exact match on normalized final span
MMLU-Pro
test, N=12032
MCQ
8
benchmark-locked choice-letter reparse
GPQA Diamond
full, N=198
MCQ
8
benchmark-locked choice-letter reparse
MMLU-Pro confirm-512
confirm split, N=512
MCQ
8
second-family paired closure run
GPQA-128
subset, N=128
MCQ
8
second-family paired closure run
Appendix
Table 19: Per-benchmark setup details. The retained cap is shared across compared methods on each benchmark.
Evaluation
N
Seed
Base
CACC
ΔF
95% CI
p
GPQA
198
14251
15.66
24.24
+8.59
[2.53,15.15]
.0137
GPQA
198
20260724
16.67
26.26
+9.60
[3.54,15.66]
.00432
GPQA
198
314159
16.16
24.24
+8.08
[1.52,14.65]
.0259
MMLU held-out
11,520
14251
26.35
28.07
+1.73
[1.04,2.43]
6.48×10−7
MMLU held-out
11,520
20260724
26.52
28.15
+1.63
[0.94,2.34]
4.23×10−6
MMLU held-out
11,520
314159
26.35
27.31
+0.96
[0.26,1.68]
.00799
Appendix
Table 20: Target-verifier canonical results on original pools. CIs are paired per-seed 95% bootstrap intervals for ΔF (pp); p is the per-contrast exact McNemar value, without a cross-row multiplicity adjustment.
Evaluation
Cell
O
V∣O
F
GPQA ( N=198 )
Base
20.71
82.93
17.17
CACC
51.01
45.54
23.23
CD
75.25
39.60
29.80
CD+ CACC
81.82
35.19
28.79
MMLU confirm ( N=512 )
Base
31.45
72.05
22.66
CACC
48.83
60.00
29.30
Appendix
Table 21: Fresh-generation four-cell outcomes. O , V∣O , and F are percentages.
Evaluation
N
Selector
Base
CACC
ΔF
p
GPQA
198
Majority
16.67
19.70
+3.03
.2101
GPQA
198
8B option-logprob
17.68
28.28
+10.61
.00460
GPQA
198
1.7B candidate judge
5.56
18.69
+13.13
4.23×10−5
GPQA
198
32B candidate judge
6.57
23.23
+16.67
1.07×10−6
MMLU full
12,032
Majority
21.17
18.48
-2.69
3.43×10−18
MMLU confirm
512
8B option-logprob
32.62
32.62
0.00
1.000
Appendix
Table 22: Selector-family results on original pools. Accuracies are percentages; p is the exact paired McNemar value for each row, without a table-wide adjustment.
Condition
O
V
F
Base
85.16
82.11
69.92
CACC
91.02
77.68
70.70
Appendix
Table 23: Prospective ARC-Challenge results ( N=256 ). Oracle ( O ), conditional conversion ( V ), and final accuracy ( F ) are percentages.
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.
Bangji Yang, Jiajun Fan, Hongbo Ma +6
University of Illinois at Urbana-Champaign · Rutgers University · University of Illinois Chicago +2
Language-model benchmarks collapse two distinct measurement questions into a single accuracy score: whether a response reached an evaluable state, and whether its answer was judged correct. We introduce a two-layer evaluation framework that separates scorer-independent execution evidence, including termination, answer exposure, parseability, and completion length, from scorer-dependent correctness. Across 2,550 outputs from five fixed Qwen and DeepSeek configurations on MATH and ARC-Challenge, matched 2,048-token limits produce sharply different execution mixtures: 49 of 450 Qwen MATH outputs terminate without a final answer, compared with 5 of 300 DeepSeek MATH outputs and none of the 750 ARC outputs. Among the same 300 DeepSeek MATH question-model pairs, no missing-final length termination is observed at 8,192 tokens. A coverage-audited targeted verification study further shows that candidate-selection and aggregation policies can substantially alter comparative accuracy estimates. These results demonstrate that accuracy conflates execution case mix with verification policy. Evaluations of test-time methods should therefore report pre-intervention execution states, verification coverage, and scorer provenance alongside accuracy.
Zongyou Yang, Yinghan Hou
Dyson School of Design Engineering Imperial College London London, United Kingdom · Department of Electrical and Electronic Engineering Imperial College London London, United Kingdom
Multiple-choice and candidate-selection evaluations are widely used to assess LLM reasoning and decision-making, yet most benchmarks contain relatively small candidate sets. It remains unclear whether conclusions drawn from these settings remain valid as the candidate space scales. We systematically evaluate LLMs as the number of competing candidates increases and find substantial accuracy degradation across tasks, prompting strategies, and model scales. Controlled analyses show that standard long-context retrieval explanations cannot fully account for this degradation. Instead, we identify two systematic failure patterns. First, gold-margin collapse: the score gap between the correct answer and the strongest distractor progressively shrinks, driven primarily by weakening confidence in the correct answer. Second, earlier candidate preferences become increasingly difficult to overturn, with later candidates exerting progressively weaker influence on the final prediction. Motivated by these findings, we evaluate hierarchical partitioning and permutation-based inference, which improve accuracy by roughly 20 percentage points at N=160 on both HotpotQA and MIMIC. Overall, our results identify candidate-set scale as an important evaluation-protocol variable and show that strong small-option performance does not necessarily imply robust large-scale candidate comparison.
Yu-Chi Lin, Aryan Seth, Anshul Aravind +4
University of California, Los Angeles · University of Cincinnati