Study: Temperature Sampling Fails to Reveal Model Knowledge Structure

A new paper by Izhar Ali, accepted at EIML@ICML 2026, challenges the common practice of using stochastic sampling (temperature variation) in large language models to gauge uncertainty. The study compares running a single model 100 times at temperature τ=1 against an ensemble of 24 distinct LLMs run once each at τ=0. Using Marchenko–Pastur random-matrix tests on MMLU, HellaSwag, and GSM8K benchmarks, the author finds that temperature variation within one model yields at most one significant dimension of cross-question structure—barely distinguishable from noise. In contrast, the ensemble produces four eigenvalues that clearly exceed the noise threshold, while a matched-difficulty Bernoulli null model produces at most one such eigenvalue in 500 Monte Carlo draws.

The core insight is that self-consistency (majority voting across repeated runs) gives accurate per-question uncertainty estimates but reveals nothing about how related questions correlate—the kind of deep knowledge structure that a diverse ensemble exposes. This “epistemic shallowness” of temperature sampling means practitioners cannot rely on stochastic variation as a proxy for model diversity when probing what a model truly knows or does not know about a domain. The result has direct implications for uncertainty quantification in critical applications like medical diagnosis, legal analysis, and scientific reasoning, where understanding the boundaries of model knowledge is essential.