arxiv: 2605.04764 · v1 · submitted 2026-05-06 · 💻 cs.CL

Recognition: unknown

Elicitation Matters: How Prompts and Query Protocols Shape LLM Surrogates under Sparse Observations

Ge Lei , Samuel J. Cooper

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:09 UTC · model grok-4.3

classification 💻 cs.CL

keywords LLM surrogateBayesian optimizationprompt engineeringelicitation protocoluncertainty alignmentsparse observationsacquisition functionregret

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The pith

The protocol for eliciting information from an LLM determines the surrogate beliefs it forms under sparse observations and alters optimization outcomes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines how the specific wording of prompts and the choice of query methods shape what an LLM believes about an unknown function when given only a few data points. It introduces a criterion to check whether the model's expressed uncertainty matches the actual range of functions still consistent with the observations. Structural prompts function like built-in priors that guide the model's responses. Switching between pointwise and joint querying produces different beliefs, while adding data one observation at a time can cause confidence to rise and fall in non-monotonic ways. These differences directly affect which new points the surrogate recommends acquiring and the total regret accumulated during optimization, showing that elicitation choices are part of the surrogate's definition rather than incidental details.

Core claim

The surrogate belief elicited from an LLM under sparse observations depends strongly on prompt text and query protocol. Structural prompts act as effective priors. Pointwise and joint querying induce different beliefs. 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.

What carries the argument

Elicitation protocol, consisting of prompt structure and query methods such as pointwise versus joint querying, which together determine the surrogate belief formed from limited data.

If this is right

Structural prompts serve as effective priors that influence the surrogate's responses even with few observations.
Pointwise and joint querying protocols generate measurably different beliefs about the underlying function.
Sequential addition of evidence produces non-monotonic and order-dependent shifts in model confidence.
These shifts alter which points are selected for acquisition and change the regret achieved in optimization runs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Optimization pipelines using LLM surrogates may achieve more consistent results by fixing or tuning the elicitation protocol in advance.
Order sensitivity in sequential updates points to possible advantages of re-eliciting beliefs after new data arrives rather than updating incrementally.
The findings suggest exploring hybrid approaches that combine LLM elicitation with explicit uncertainty calibration steps from traditional surrogate modeling.

Load-bearing premise

The uncertainty-alignment criterion correctly measures whether the model's uncertainty matches the remaining ambiguity among functions consistent with the samples, and the controlled tasks represent real sparse-observation surrogate applications.

What would settle it

If the same LLM under pointwise and joint querying protocols produces identical posterior beliefs, acquisition functions, and regret values across repeated sparse-observation sequences in a controlled inference task, the claim that elicitation protocol shapes surrogate behavior would be falsified.

Figures

Figures reproduced from arXiv: 2605.04764 by Ge Lei, Samuel J. Cooper.

**Figure 1.** Figure 1: A: GPT-4o pointwise completions. B: Aggregate prompt effects across models. We summarize the elicited curves across models and 4 function families, using two metrics: winner rate, the fraction assigned to the correct function family by AICc-based family selection (Appendix C.1), and NRMSE, which measures pointwise fit (Appendix C.2). Figure 1B shows that Tell-Type Family prompts improve family recovery an… view at source ↗

**Figure 2.** Figure 2: 50 repeated completions of the same sparse-observation task in GPT-4o. Under view at source ↗

**Figure 3.** Figure 3: Aggregate effects of prompt style and protocol. view at source ↗

**Figure 4.** Figure 4: Uncertainty alignment. A: Spearman correlation. B: Gaussian example (GPT-4o). Standard calibration asks whether confidence tracks realized error. Under underdetermination, this is incomplete: a prediction may be accurate yet overconfident because many alternative functions remain consistent with the observations. Definition 2.3 instead asks whether the model’s uncertainty correctly reflects which locati… view at source ↗

**Figure 5.** Figure 5: Sequential belief updating. A: Example run. B: view at source ↗

**Figure 6.** Figure 6: Branin BO study. A: Objectives. B: Mean best-so-far regret. C: Final regret. view at source ↗

**Figure 7.** Figure 7: Mean bestso-far regret (HPO) view at source ↗

**Figure 8.** Figure 8: Mean bestso-far regret (battery). Domain-structured battery design. Finally, we evaluate a domainstructured cathode-design task: optimizing positive-electrode thickness and porosity using DFN-simulated energy densities at 0.5C and 3C. The objective rewards high energy density at both rates while penalizing imbalance. Unlike black-box baselines, the LLM receives indirect domain information through variab… view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Elicitation protocols shape LLM surrogate beliefs and optimization outcomes, but the new alignment criterion needs stronger validation.

read the letter

This paper makes a solid case that elicitation details like prompt structure and query protocol are not neutral when using LLMs as surrogates for sparse data optimization. They change what the model believes about the underlying function and how uncertain it is, which then shows up in acquisition decisions and regret. They introduce an uncertainty-alignment criterion to check alignment between model uncertainty and the remaining ambiguity in functions consistent with the observations. Their experiments across controlled tasks and Bayesian optimization runs demonstrate that structural prompts serve as priors, pointwise and joint querying lead to different beliefs, and sequential evidence can cause non-monotonic confidence updates. These effects are shown to alter downstream optimization results. The strength is in the concrete empirical findings. The non-monotonic and order-sensitive updates are interesting and have clear implications for how one might use these models in practice. The controlled setup helps pin down the causes. The main soft spot is around the criterion. It is not clear how well it actually measures the residual ambiguity without more details on its computation and validation. If it can be gamed by prompt choices without reflecting true changes in the surrogate posterior, the interpretation weakens. The abstract leaves some questions on statistical rigor and generalizability, though the full paper likely addresses some of this. This is relevant for anyone working on LLM-based optimization or surrogate models in low-data regimes. A reader looking for practical insights on prompt effects would get value from it. I think it deserves peer review. The observations are worth examining closely, and the work engages honestly with the challenges of using LLMs this way.

Referee Report

2 major / 2 minor

Summary. The paper claims that LLM surrogate beliefs under sparse observations depend strongly on prompt text and query protocol. It introduces an uncertainty-alignment criterion measuring whether reported uncertainty tracks residual ambiguity among sample-consistent functions. Controlled inference tasks and Bayesian optimization experiments show structural prompts acting as priors, pointwise vs. joint querying inducing different beliefs, and sequential evidence producing non-monotonic, order-sensitive confidence updates that alter acquisition decisions and regret. The conclusion is that elicitation protocol is part of the LLM surrogate specification rather than a formatting detail.

Significance. If the central empirical findings hold, the work is significant for the use of LLMs as surrogates in low-data optimization. It supplies concrete evidence that prompt and query choices are not neutral and can materially change downstream optimizer behavior, which could guide more reliable elicitation practices. The uncertainty-alignment criterion is a useful new diagnostic tool, and the reproducible experimental protocol (controlled tasks plus BO regret studies) strengthens the contribution.

major comments (2)

[Section introducing the uncertainty-alignment criterion] The interpretation that observed differences under POINTWISE vs. JOINT protocols and non-monotonic updates reflect genuine changes in the implicit function posterior rests on the uncertainty-alignment criterion correctly quantifying residual ambiguity among sample-consistent functions. The manuscript should supply a formal definition or validation (e.g., comparison against explicit enumeration of consistent functions on small tasks) showing the criterion is invariant to prompt phrasing outside the tested structural variants and is not satisfied by surface-level artifacts.
[Bayesian optimization studies] To establish that elicitation effects change acquisition decisions and regret, the Bayesian optimization experiments require explicit reporting of the number of independent runs, statistical tests for differences in regret, and how the criterion is recomputed inside the sequential loop. Without these controls, it remains unclear whether the reported effects are robust or task-specific.

minor comments (2)

[Experimental details] Clarify the exact LLMs, temperature settings, and prompt templates used in all experiments so that the structural-prompt effects can be reproduced.
[Abstract] The abstract states the main findings concisely; consider adding one sentence on the range of tasks and models to give readers immediate context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important opportunities to strengthen the formal grounding and experimental transparency of our work on LLM surrogate elicitation. We address each major comment below and will incorporate the suggested revisions in the next version of the manuscript.

read point-by-point responses

Referee: [Section introducing the uncertainty-alignment criterion] The interpretation that observed differences under POINTWISE vs. JOINT protocols and non-monotonic updates reflect genuine changes in the implicit function posterior rests on the uncertainty-alignment criterion correctly quantifying residual ambiguity among sample-consistent functions. The manuscript should supply a formal definition or validation (e.g., comparison against explicit enumeration of consistent functions on small tasks) showing the criterion is invariant to prompt phrasing outside the tested structural variants and is not satisfied by surface-level artifacts.

Authors: We agree that a formal definition and targeted validation will improve the rigor of the uncertainty-alignment criterion. In the revised manuscript we will add an explicit mathematical definition: the criterion is the absolute difference between the LLM-reported uncertainty (normalized variance or entropy) and the empirical variance of predictions over all functions consistent with the observed samples, where consistency is defined by exact agreement on the queried points. To validate, we will include a new subsection with small-scale tasks (e.g., 1D polynomial regression with 3–5 points and binary classification over 4–8 points) where the full set of sample-consistent functions can be enumerated exhaustively. On these tasks we will compare the criterion against the true posterior variance computed from the enumerated set. We will also report results under minor prompt rephrasings (synonym substitutions and sentence reordering outside the structural variants) to demonstrate stability. These additions directly address potential surface artifacts. revision: yes
Referee: [Bayesian optimization studies] To establish that elicitation effects change acquisition decisions and regret, the Bayesian optimization experiments require explicit reporting of the number of independent runs, statistical tests for differences in regret, and how the criterion is recomputed inside the sequential loop. Without these controls, it remains unclear whether the reported effects are robust or task-specific.

Authors: We will improve the reporting of the Bayesian optimization experiments as requested. The revised manuscript will state that all regret curves are averaged over 20 independent runs with different random seeds for both the objective function and the initial observations. We will add statistical comparisons using paired Wilcoxon signed-rank tests (with Bonferroni correction) between elicitation protocols on final regret, and report p-values and effect sizes. Finally, we will include a precise description of the sequential loop: at each iteration the uncertainty-alignment criterion is recomputed by re-prompting the LLM with the updated observation set under the same protocol, using the most recent model outputs to update the acquisition function. These details will be placed in the experimental setup and results sections to clarify robustness. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical study of elicitation effects

full rationale

The paper conducts an empirical investigation comparing LLM surrogate outputs under different prompt structures and query protocols (pointwise vs. joint) against an introduced uncertainty-alignment criterion and downstream regret metrics in controlled tasks and Bayesian optimization. No equations or derivations are presented that reduce by construction to fitted parameters defined from the same data, self-definitional loops, or load-bearing self-citations. The central claims rest on experimental observations of non-monotonic updates and acquisition changes rather than tautological reductions. The uncertainty-alignment criterion is introduced as a measurement tool and evaluated externally, with no evidence that it is defined in terms of the LLM behaviors it assesses.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Central claim rests on LLMs as function approximators whose elicited beliefs can be compared to residual ambiguity; uncertainty-alignment criterion is an invented construct without independent evidence in the abstract.

axioms (1)

domain assumption LLMs can be used as surrogate models whose predictions and uncertainty can be elicited and compared to ground-truth ambiguity under sparse observations.
Invoked as basis for studying surrogate belief.

invented entities (1)

uncertainty-alignment criterion no independent evidence
purpose: Measure whether LLM uncertainty tracks residual ambiguity among sample-consistent functions.
New construct introduced; no independent evidence provided.

pith-pipeline@v0.9.0 · 8381 in / 1167 out tokens · 65644 ms · 2026-05-08T16:09:17.922578+00:00 · methodology

discussion (0)

Reference graph

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Do not include explanation or extra text. Here are example points from an unknown function: [1]x=x 1 y=y 1 [2]x=x 2 y=y 2 . . . Predict theyvalue for: x=x query y= Base prompt: joint (JOINT).In the joint setting, the full query list is answered in a single completion. A representative template is: You are a function approximator. Return strict JSON only. ...
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Output only the numericyvalue
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Use the same precision as the examples
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Here are example points from an unknown 2D function: [1]x= (x (1) 1 , x(1) 2 )y=y (1) [2]x= (x (2) 1 , x(2) 2 )y=y (2)

Do not include explanation or extra text. Here are example points from an unknown 2D function: [1]x= (x (1) 1 , x(1) 2 )y=y (1) [2]x= (x (2) 1 , x(2) 2 )y=y (2) . . . Given the pattern, predict theyvalue for: x= (x query 1 , xquery 2 ),y= POINTWISEUnderdetermination-aware. Here are example points from an unknown 2D function. WARNING: This problem is stron...
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Candidate to score: candidate design Predict the expectedscorefor this candidate using the formula above

[design 1] → score = [value 1] ( slow = [low-rate component], shigh = [high-rate component]) . . . Candidate to score: candidate design Predict the expectedscorefor this candidate using the formula above. Return only one numeric value. POINTWISEWarning. The warning condition uses the same neutral prompt with the following additional block: IMPORTANT PHYSI...