aiqbench analysis
This research demonstrates that simply varying temperature within a single model fails to capture the cross-question dependencies found in diverse ensembles, revealing a fundamental limit of self-consistency for estimating epistemic uncertainty. The study uses random-matrix theory to prove that only distinct models can surface structural gaps between questions, whereas repeated sampling from one instance remains largely noise-dominated across benchmarks like MMLU and GSM8K.
Stochastic Sampling is Epistemically Shallow: The Dimensionality Gap Between Temperature Variation and Model Diversity in LLMs
arXiv:2607.20464v1 Announce Type: new Abstract: When a language model gives different answers on repeated runs, does that variation reveal what it does not know? Self-consistency turns the variation into a per-question uncertainty estimate via majority voting. But does the same variation reveal cross-question structure -- related questions flipping together, the way a diverse ensemble does? We compare two regimes on the same questions: one model run $100$ times at $\tau=1$ versus an ensemble of $24$ LLMs run once each at $\tau=0$. A Marchenko--Pastur random-matrix test separates signal from sampling noise on both sides. Within any single model, at most one dimension rises above noise across five families and three benchmarks (MMLU, HellaSwag, GSM8K). Across the ensemble, four eigenvalues clear the noise edge, while a matched-difficulty Bernoulli null produces at most one in $500$ Monte Carlo draws. Self-consistency gives accurate per-question uncertainty but no detectable cross-question structure; only a diverse ensemble surfaces what a model does not know.
Abstract:When a language model gives different answers on repeated runs, does that variation reveal what it does not know? Self-consistency turns the variation into a per-question uncertainty estimate via majority voting. But does the same variation reveal cross-question structure -- related questions flipping together, the way a diverse ensemble does? We compare two regimes on the same questions: one model run $100$ times at $\tau=1$ versus an ensemble of $24$ LLMs run once each at $\tau=0$. A Marchenko--Pastur random-matrix test separates signal from sampling noise on both sides. Within any single model, at most one dimension rises above noise across five families and three benchmarks (MMLU, HellaSwag, GSM8K). Across the ensemble, four eigenvalues clear the noise edge, while a matched-difficulty Bernoulli null produces at most one in $500$ Monte Carlo draws. Self-consistency gives accurate per-question uncertainty but no detectable cross-question structure; only a diverse ensemble surfaces what a model does not know.
8 pages, 4 figures, 3 tables. Accepted at EIML@ICML 2026
Artificial Intelligence (cs.AI)
arXiv:2607.20464 [cs.AI]
(or arXiv:2607.20464v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.20464 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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