Cross-Model Disagreement as a Label-Free Correctness Signal

Matt Gorbett; Suman Jana

cs.AIMar 26, 2026

Cross-Model Disagreement as a Label-Free Correctness Signal

Authors: Matt Gorbett, Suman Jana

Organizations: Independent Researcher · Department of Computer Science, Columbia University, New York, NY 10027, USA

Abstract

Detecting when a language model is wrong without ground truth labels is a fundamental challenge for safe deployment. Existing approaches rely on a model's own uncertainty -- such as token entropy or confidence scores -- but these signals fail critically on the most dangerous failure mode: confident errors, where a model is wrong but certain. In this work we introduce cross-model disagreement as a correctness indicator -- a simple, training-free signal that can be dropped into existing production systems, routing pipelines, and deployment monitoring infrastructure without modification. Given a model's generated answer, cross-model disagreement computes how surprised or uncertain a second verifier model is when reading that answer via a single forward pass. No generation from the verifying model is required, and no correctness labels are needed. We instantiate this principle as Cross-Model Perplexity (CMP), which measures the verifying model's surprise at the generating model's answer tokens, and Cross-Model Entropy (CME), which measures the verifying model's uncertainty at those positions. Both CMP and CME outperform within-model uncertainty baselines across benchmarks spanning reasoning, retrieval, and mathematical problem solving (MMLU, TriviaQA, and GSM8K). On MMLU, CMP achieves a mean AUROC of 0.75 against a within-model entropy baseline of 0.59. These results establish cross-model disagreement as a practical, training-free approach to label-free correctness estimation, with direct applications in deployment monitoring, model routing, selective prediction, data filtering, and scalable oversight of production language model systems.

Figures & tables

Figure 1: Cross-model disagreement as a label-free correctness indicator. Given a prompt

x

, the generator (Llama-3-8B) produces an answer

\hat{y}

. The verifier (Qwen2.5-7B) performs a single forward pass over

(x,\hat{y})

with no generation required. The verifier assigns low probability to the token “1942”, the generator’s confident but incorrect answer. Cross-model perplexity ( CMP ) aggregates this surprise signal into a single correctness indicator, and high CMP flags a likely error.

Figure 2: CMP and CME performance across datasets compared to baselines. (A) Mean AUROC over all model pairs. G-Ent and G-PPL measure the generator’s own entropy and perplexity; CME and CMP measure the corresponding signals from a verifier model on the generator’s answer. APGR measures the fraction of the performance gap between weak and strong model that is recovered by routing, normalized so that random routing scores 0 and oracle routing scores 1; pairs with small gaps are excluded because the small denominator in the PGR formula produces unstable estimates. Error bars show standard error across pairs;

n

indicates the number of pairs per dataset.

					Acc.	AUROC $\uparrow$				APGR $\uparrow$
Dataset	Generator	Verifier	Acc g	Acc v	Gap	G-Ent	G-PPL	CMP	CME	G-Ent	G-PPL	CMP	CME
MMLU	Qwen-0.5B	Qwen-7B	0.42	0.72	0.30	0.588	0.556	0.841	0.583	0.521	0.501	0.793	0.497
	Llama-1B	Llama-3-8B	0.43	0.62	0.19	0.654	0.655	0.817	0.679	0.562	0.605	0.869	0.540
	Llama-1B	Qwen-7B	0.43	0.72	0.29	0.654	0.655	0.786	0.634	0.569	0.595	0.807	0.558
	OLMo-7B †	Qwen-7B	0.56	0.72	0.15	0.503	0.599	0.896	0.697	0.486	0.546	0.914	0.447
TriviaQA	Llama-3-8B	Mistral-7B	0.43	0.64	0.20	0.859	0.885	0.825	0.922	0.822	0.831	0.849	0.789

Table 1: Selected results across all four benchmarks. Bold = best per row separately for AUROC and APGR among G-Ent, G-PPL, CMP, CME. Same-size cross-family pairs marked

\dagger

. See Appendix for full results.

Figure 3: Top row: per-case signal means. Mean CMP (left axis, blue) and G-Ent (right axis, red) by outcome category. The shaded column highlights the “generator wrong only” case—confident errors the verifier does not share. On MMLU, CMP spikes

9\times

above the mean of the other three cases while G-Ent is flat (

1.0\times

); on TriviaQA the spike is

18\times

vs.

1.6\times

; on GSM8K both signals rise modestly (

3\times

and

1.4\times

), reflecting the difficulty of isolating chain-of-thought errors with token-level signals. Bottom row: accuracy by signal quintile. Samples sorted by signal strength (Q1 = lowest, Q5 = highest); bars show weak model accuracy within each bin. On MMLU, CMP produces a 74pp spread versus 23pp for G-Ent and 18pp for G-PPL. On TriviaQA (no context), all three signals are competitive (93pp, 80pp, 81pp). On GSM8K, CMP achieves a 50pp spread while G-PPL nearly collapses to 8pp, confirming that generator self-perplexity is uninformative on chain-of-thought tasks and that cross-model disagreement is doing genuine work.

	Mean AUROC $\uparrow$
Method	MMLU	TriviaQA	TriviaQA	GSM8K	Verifier work	Cost
		(ctx)	(no ctx)			vs. CMP
Single verifier prefill
P(True)	0.518	0.510	0.526	0.603	1 prefill	$\sim$ 1 $\times$
CME (ours)	0.628	0.759	0.737	0.621	1 prefill	1 $\times$
CMP (ours)	0.749	0.679	0.761	0.623	1 prefill	1 $\times$

Table 2: Mean AUROC across model pairs with capability gap

>

5pp, comparing CMP and CME against label-free baselines. Methods are grouped by computational cost tier; cost is per-sample overhead relative to a single verifier prefill, excluding shared generator inference.

T

= answer tokens;

k{=}10

for Semantic Entropy. Bold = best per column within tier; underline = best overall per column. Full per-pair results in Appendix 7 .

Figure 4: CMP AUROC versus capability gap across three benchmarks. On MMLU, AUROC is uncorrelated with gap (

\rho=+0.12

p=0.71

) and same-size cross-family pairs (blue) achieve the highest scores, suggesting model diversity drives the signal rather than capability asymmetry. On TriviaQA, gap correlates positively with AUROC (

\rho=+0.63

p=0.03

), indicating a stronger verifier helps when errors are knowledge-driven. GSM8K shows no significant trend (

\rho=-0.22

p=0.43

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

					AUROC $\uparrow$				APGR $\uparrow$
Generator	Verifier	Acc g	Acc v	Gap	G-Ent	G-PPL	CMP	CME	G-Ent	G-PPL	CMP	CME
Same-size cross-family
Mistral-7B	Qwen-7B	0.56	0.72	0.16	0.720	0.726	0.711	0.632	0.608	0.662	0.818	0.605
OLMo-7B	Qwen-7B	0.56	0.72	0.15	0.503	0.599	0.896	0.697	0.486	0.546	0.914	0.447
Llama-3-8B	Qwen-7B	0.62	0.72	0.10	0.652	0.684	0.694	0.635	0.617	0.652	0.910	0.603
Mistral-7B	Llama-3-8B	0.56	0.62	0.06	0.720	0.726	0.753	0.716	0.715	0.853	0.941	0.629

Appendix

Table 3: Full results on MMLU. Pairs grouped by type and sorted by capability gap (descending). † marks rows with

\text{gap}\leq 0.05

, which produce unstable APGR estimates due to the small PGR denominator and are excluded from the filtered mean. Bold = best per row among G-Ent, G-PPL, CMP, CME.

					AUROC $\uparrow$				APGR $\uparrow$
Generator	Verifier	Acc g	Acc v	Gap	G-Ent	G-PPL	CMP	CME	G-Ent	G-PPL	CMP	CME
Same-size cross-family
Llama-3-8B	Qwen-7B	0.43	0.65	0.21	0.859	0.885	0.772	0.875	0.796	0.808	0.807	0.757
Llama-3-8B	Mistral-7B	0.43	0.64	0.20	0.859	0.885	0.825	0.922	0.822	0.831	0.849	0.789
OLMo-7B	Qwen-7B	0.51	0.65	0.13	0.636	0.429	0.466	0.843	0.621	0.431	0.488	0.723
OLMo-7B	Mistral-7B	0.51	0.64	0.12	0.636	0.429	0.588	0.884	0.659	0.406	0.626	0.724

Appendix

Table 4: Full results on TriviaQA (with context). Pairs grouped by type and sorted by capability gap (descending). † marks rows with

\text{gap}\leq 0.05

. Bold = best per row among G-Ent, G-PPL, CMP, CME.

					AUROC $\uparrow$				APGR $\uparrow$
Generator	Verifier	Acc g	Acc v	Gap	G-Ent	G-PPL	CMP	CME	G-Ent	G-PPL	CMP	CME
Same-size cross-family
OLMo-7B	Llama-3-8B	0.39	0.67	0.29	0.774	0.504	0.706	0.807	0.664	0.484	0.628	0.601
OLMo-7B	Mistral-7B	0.39	0.66	0.28	0.774	0.504	0.812	0.883	0.659	0.491	0.729	0.634
OLMo-7B	Qwen-7B	0.39	0.59	0.21	0.774	0.504	0.673	0.849	0.635	0.480	0.616	0.596
Qwen-7B	Llama-3-8B	0.59	0.67	0.08	0.823	0.793	0.748	0.625	0.980	0.946	0.964	0.533

Appendix

Table 5: Full results on TriviaQA (no context). Pairs grouped by type and sorted by capability gap (descending). † marks rows with

\text{gap}\leq 0.05

. Bold = best per row among G-Ent, G-PPL, CMP, CME.

					AUROC $\uparrow$				APGR $\uparrow$
Generator	Verifier	Acc g	Acc v	Gap	G-Ent	G-PPL	CMP	CME	G-Ent	G-PPL	CMP	CME
Same-size cross-family
Mistral-7B	Qwen-7B	0.54	0.90	0.36	0.658	0.542	0.662	0.718	0.583	0.522	0.606	0.620
Mistral-7B	OLMo-7B	0.54	0.84	0.30	0.658	0.542	0.722	0.684	0.581	0.523	0.634	0.592
Llama-3-8B	Qwen-7B	0.61	0.90	0.29	0.593	0.577	0.609	0.508	0.549	0.534	0.594	0.492
Llama-3-8B	OLMo-7B	0.61	0.84	0.22	0.593	0.577	0.633	0.527	0.530	0.512	0.592	0.469

Appendix

Table 6: Full results on GSM8K. Pairs grouped by type and sorted by capability gap (descending). No row has

\text{gap}\leq 0.05

, so the filtered mean coincides with the full mean. Bold = best per row among G-Ent, G-PPL, CMP, CME.

Dataset	Generator	Verifier	Gap	CMP	CME	P(True)	V-Agree	Sem-Ent (k=10)
MMLU	Gemma-270M	Qwen-7B	+47.5	0.828	0.609	0.572	0.820	0.515
	Gemma-270M	Llama-3-8B	+37.4	0.710	0.597	0.503	0.739	0.515
	Qwen-0.5B	Qwen-7B	+29.9	0.841	0.583	0.551	0.843	0.633
	Llama-1B	Qwen-7B	+28.8	0.786	0.634	0.547	0.821	0.617
	Qwen-0.5B	Llama-3-8B	+19.9	0.749	0.639	0.498	0.784	0.633
	Llama-1B	Llama-3-8B	+18.8	0.817	0.679	0.475	0.748	0.617

Appendix

Table 7: AUROC by correctness signal across (generator, verifier, dataset) tuples with gap

>

5pp. CMP and CME are this paper’s cross-model perplexity / entropy signals (single prefill on the verifier). P(True), Verifier Agreement, and Semantic Entropy Kuhn et al. (2023) are external baselines. Bold = best AUROC per row.

Figure 5: Coverage–accuracy curves (single pair). At each coverage level we abstain on instances whose signal score exceeds a swept threshold and report generator accuracy on the retained subset. CMP (blue, solid) maintains higher accuracy than G-Ent (red, dashed) across nearly all operating points on both MMLU (Qwen-0.5B

\to

Qwen-7B) and GSM8K (Mistral-7B

\to

Llama-3-8B). The dotted line marks full-set accuracy.

Figure 6: Coverage–accuracy curves (averaged over all pairs). Curves are averaged across all 15 model pairs per benchmark; shaded bands show

\pm

1 SE. CMP consistently achieves higher accuracy than G-Ent at equal coverage on both MMLU and GSM8K.

Figure 7: CMP (filled circles) and within-model entropy (open squares) AUROC versus capability gap. The positive gap effect on TriviaQA is specific to CMP — entropy AUROC is uncorrelated with gap on all three datasets.

Figure 8: CMP advantage over within-model entropy (

\Delta

AUROC = CMP

-

G-Ent) versus capability gap. CMP ’s advantage grows significantly with gap on TriviaQA (

\rho=+0.81

p<0.01

), while on MMLU CMP leads regardless of gap size. GSM8K shows a positive but non-significant trend (

\rho=+0.39

p=0.16

				AUROC $\uparrow$			Baselines
Generator	Verifier	Acc g	Gap	CMP-Full	CMP-Final	P(True)	G-Ent	G-PPL
Qwen-0.5B	Qwen-7B	0.25	0.64	0.629	0.456	0.495	0.616	0.621
Llama-1B	Qwen-7B	0.38	0.51	0.668	0.755	0.463	0.543	0.523
Mistral-7B	Qwen-7B	0.51	0.39	0.668	0.574	0.487	0.655	0.539
Qwen-0.5B	Llama-3-8B	0.25	0.36	0.627	0.525	0.431	0.616	0.621
Llama-3-8B	Qwen-7B	0.61	0.28	0.590	0.584	0.476	0.596	0.577

Appendix

Table 8: GSM8K correctness prediction (AUROC): Full chain-of-thought CMP vs. final-answer-only CMP vs. P(True) verification prompting. CMP-Full and CMP-Final perform comparably, while P(True) is near random. Bold = best among CMP-Full, CMP-Final, P(True).

				APGR $\uparrow$			Baselines
Generator	Verifier	Acc g	Gap	CMP-Full	CMP-Final	P(True)	G-Ent	G-PPL
Qwen-0.5B	Qwen-7B	0.25	0.64	0.528	0.484	0.499	0.520	0.521
Llama-1B	Qwen-7B	0.38	0.51	0.574	0.621	0.481	0.511	0.503
Mistral-7B	Qwen-7B	0.51	0.39	0.590	0.524	0.506	0.575	0.513
Qwen-0.5B	Llama-3-8B	0.25	0.36	0.530	0.509	0.492	0.544	0.545
Llama-3-8B	Qwen-7B	0.61	0.28	0.614	0.579	0.488	0.551	0.538

Appendix

Table 9: GSM8K routing performance (APGR): Full chain-of-thought CMP vs. final-answer-only CMP vs. P(True). Pairs with gap

<

5pp excluded. Bold = best among CMP-Full, CMP-Final, P(True).

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