Introducing Background Temperature to Characterise Hidden Randomness in Large Language Models

• URL: http://arxiv.org/abs/2604.22411v1
• Date: Fri, 24 Apr 2026 10:11:06 GMT
• Title: Introducing Background Temperature to Characterise Hidden Randomness in Large Language Models
• Abstract summary: We introduce the notion of emphbackground temperature $T_mathrmbg$, the effective temperature induced by an implementation-dependent perturbation process.<n>We propose an empirical protocol to estimate $T_bg$ via the equivalent temperature $T_n(I)$ of an ideal reference system.
• Score: 0.27299033472568546
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Even when decoding with temperature $T=0$, large language models (LLMs) can produce divergent outputs for identical inputs. Recent work by Thinking Machines Lab highlights implementation-level sources of nondeterminism, including batch-size variation, kernel non-invariance, and floating-point non-associativity. In this short note we formalize this behavior by introducing the notion of \emph{background temperature} $T_{\mathrm{bg}}$, the effective temperature induced by an implementation-dependent perturbation process observed even when nominal $T=0$. We provide clean definitions, show how $T_{\mathrm{bg}}$ relates to a stochastic perturbation governed by the inference environment $I$, and propose an empirical protocol to estimate $T_{bg}$ via the equivalent temperature $T_n(I)$ of an ideal reference system. We conclude with a set of pilot experiments run on a representative pool from the major LLM providers that demonstrate the idea and outline implications for reproducibility, evaluation, and deployment.

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