# Stochastic Sampling is Epistemically Shallow: The Dimensionality Gap Between Temperature Variation and Model Diversity in LLMs

arXiv: https://arxiv.org/abs/2607.20464 · HTML: https://mlsanity.com/paper/2607.20464/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 15 of 15)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Correlated Errors in Large Language Models](https://mlsanity.com/paper/2506.07962/) (2025)
- [metabench -- A Sparse Benchmark of Reasoning and Knowledge in Large Language Models](https://mlsanity.com/paper/2407.12844/) (2024)
- [General Scales Unlock AI Evaluation with Explanatory and Predictive Power](https://mlsanity.com/paper/2503.06378/) (2025)
- [Monte Carlo Temperature: a robust sampling strategy for LLM's uncertainty quantification methods](https://mlsanity.com/paper/2502.18389/) (2025)
- [Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantification](https://mlsanity.com/paper/2604.17112/) (2026)
- [JE-IRT: A Geometric Lens on LLM Abilities through Joint Embedding Item Response Theory](https://mlsanity.com/paper/2509.22888/) (2025)

## Built on by (most cited first, 1 of 1)

- [Decomposing Wrong-Consensus Agreement in LLM Self-Consistency](https://mlsanity.com/paper/2608.18795/) (2026)

## Abstract (arXiv)

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 τ=1 versus an ensemble of 24 LLMs run once each at τ=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.