Aug 2026· 2 citations· ⚡ 2 influential· 20 references
Computer Science
TL;DR
This version reports that the most natural repair also fails, and separates three signal failures that v1 treated as one, and reports that on hosted serverless inference at a small budget, three reasoning-native models could not be evaluated, for three separately measured reasons.
Abstract
Self-consistency via majority vote reduces per-problem accuracy on most GPQA Diamond problems for small instruction-tuned models: 56.6% of problems for Qwen2.5-7B and 65.7% for Llama-3-8B. The obvious remedy is a verifier-free confidence gate. This version reports that the most natural repair also fails, and separates three signal failures that v1 treated as one. A token-entropy gate fails for a measurement reason: averaged over a chain of some 602 tokens, the statistic is a measurement of the prose rather than of confidence in the answer. On Qwen2.5-7B-Instruct-Turbo, 198 problems at 64 samples each, a sample whose answer contradicts its own problem's plurality still emits that answer at a median margin of 20.52 nats, with 75.7% above 10 nats. Both quantities were pre-registered and tested once on 69 problems no exploratory analysis had read; both passed. The unit is the whole result: pooled across the benchmark the margin separates correct from incorrect samples by +0.0604 on the fraction above 10 nats [+0.0183, +0.1017], excluding zero; per-problem and paired it does not, at -0.0168 [-0.0527, +0.0182], crossing zero. The claim is not that token log-probabilities carry no information, but that a signal with real across-question discrimination is close to useless for the within-question decision a router faces. The plurality-agreement gate's failure remains without a mechanism, and we report it as an open problem. These new claims rest on one model: a registered second-model replication was sampled and could not be evaluated, and we report that rejection rather than the result. We separately report that on hosted serverless inference at a small budget, three reasoning-native models could not be evaluated, for three separately measured reasons; all three are downloadable, so this bounds what a metered per-token API buys rather than what is knowable.
Agreement among repeated samples of a language model is routinely read as evidence about answer reliability, yet wrong answers can agree just as strongly as right ones. This paper asks what information wrong-consensus agreement actually contains, and answers with a quantitative decomposition. A pluralistic agreement index Gamma, normalized by the reference scale d=(1-p)/(C-1), is split into a mechanical component (agreement delivered by a per-case answer preference alone) and a preference-unexplained residual. The mechanical reference is leak-free: each case's preference and accuracy are estimated from its other runs only. On public GPT-4.1 per-run data, coverage phi (the mechanical/empirical ratio) shows a benchmark-associated direction: 0.81-0.93 on multiple-choice GPQA-Diamond against 0.59-0.78 on open-domain AIME, where a residual of 1.54-2.80 Gamma units survives, more than absorbed by a calibrated run-level preference-heterogeneity reference. A controlled replication under one fixed protocol (four runs per question, K=32 votes) on five open-weights checkpoints (Qwen3.5-9B/122B, Qwen3.8-27B, Gemma4-26B/31B) finds near-complete mechanical coverage in all ten cells (phi approximately 1, with a small overshoot consistent with a quantified finite-donor plug-in bias), robust to a two-run design; the largest cell (qwen3.5-122b, p=0.222) sits inside the GPT-4.1 AIME accuracy range and still saturates (phi=1.041). A cross-system contrast at comparable aggregate accuracy contrasts near-complete mechanical agreement in the open-weights models against a larger preference-unexplained residual in the frontier family. This contrast is confounded with sampling protocol by design. Agreement is graded evidence, not certification. No new voting method is proposed; code and evidence are committed.
Li-Zhuo Zhang, Meng-Meng Tang, Chen-Feng Long et al.· 1 citation
Reinforcement learning with verifiable rewards (RLVR) and standard benchmark evaluation both rely on an automatic verifier that turns a free text answer into a binary reward. Prior work reports that one evaluation harness accepts only about 94% of its own ground truth answers, blaming LaTeX parsing. That is an aggregate: it does not say which answer forms consume the error budget. We supply the decomposition. We apply metamorphic testing to the verifier rather than the model, generating certified equivalent answer variants, that is, rewrites that preserve mathematical meaning by construction, so that any rejection is a provable false negative needing no human adjudication. We then measure rejection per answer category across four widely used verifiers over 307,420 verdicts. We find three things. (1) Self validation ranges from 53.8% to 95.2% on identical inputs, a spread of 41.3 points. The published figure describes one implementation, not the task; two configurations of the same library disagree on 49.9% of pairs. (2) The residual is not spread across parsing categories but concentrated in whitespace and punctuation, which account for 93.0% of in contract failures for the default LaTeX configuration. A trailing period or newline dominates the budget. (3) Separating rejection from execution failure shows that verifiers with similar aggregate error fail for opposite reasons, and that a reference numeric cascade accepts off by one wrong answers as a step function of magnitude, from 0% below 10^4 to 100% at or above, because its relative tolerance is scale invariant.
Paired equivalence testing at a declared margin is supply: paired equivalence testing at a declared margin, with certification tables giving the items an evaluation needs, computed from disagreement observed under compression, not from independent-binomial variance.
This work combines two diagnostics: a label-aware output-level audit score that ranks domains by confidence variation and overconfident mistakes under a forced-answer baseline, and an internal sensitivity probe that measures hidden-state movement.
Funnel of Thoughts (FoT) is introduced, an inference-time method that preserves the full 32-trajectory voted accuracy while halving its attention FLOPs, a 28.8% reduction in full-model inference cost.
Chanhee Park, Sun Han, Jeongho Yoon et al.· 0 citations
LLM judge panels are a standard evaluation tool, but prior work reports highly correlated panel errors: nine judges provide roughly the effective information of two independent ones, and aggregation closes only a small fraction of the gap. A natural remedy--a signal from a different evidence source, e.g., executing a test suite--produced no distinguishable change in the panel's effective-vote count at scale (-0.04, 95\% CI [-0.10, +0.02]). Aggregate dependence and conditional decision utility are different questions. Elementary majority arithmetic fixes the affected set for single-ballot substitution: only decisions with a one-vote margin can change. The empirical question is whether panel error rates rise and useful substitutions concentrate there. They do: the entire accuracy gain concentrates on these pivotal queries, where it is large (+10.4 to +23.3 percentage points across three headline configurations), and is exactly zero elsewhere. We confirm the pattern across three code benchmarks and four panel sizes (a 9-judge extension and 56 dependent subsampling checks, gain +6.5 to +16.1 percentage points). On HumanEval+/MBPP+, a majority-side replacement rule raises overall accuracy from 82.44\% to 85.62\% while invoking the signal on 16.2\% of queries; signal-only remains stronger at 87.60\%. Thus population-level dependence diagnostics and margin-stratified utility are complementary, and the affected-set characterization yields a call-reduction rule for any specified single-ballot substitution policy.
Shu Yang· 0 citations
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