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This paper investigates how prompt engineering and query protocols influence the beliefs and uncertainties of LLM surrogates used in low-data optimization. They introduce an uncertainty-alignment criterion to assess how well model uncertainty reflects ambiguity among sample-consistent functions. The key finding is that prompt structure, pointwise vs. joint querying, and the order of sequential evidence significantly impact the elicited surrogate belief, affecting downstream acquisition decisions and regret in Bayesian optimization.
LLM surrogates in low-data optimization are far more sensitive to prompt engineering and query protocols than previously appreciated, fundamentally altering their beliefs and downstream performance.
Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse observations, showing that it depends strongly on prompt text and query protocol. We introduce an uncertainty-alignment criterion that measures whether model uncertainty tracks residual ambiguity among sample-consistent functions. Across controlled inference tasks and Bayesian optimization studies, we find that structural prompts act as effective priors, POINTWISE and JOINT querying induce different beliefs, and sequential evidence leads to non-monotonic, order-sensitive confidence updates. These effects change downstream acquisition decisions and regret, showing that elicitation protocol is part of the LLM surrogate specification, not a formatting detail.
