LLM Auditing of Symbolic Regression Expressions Works Best as Comparative Ranking Under Clinician Oversight

The interpretability gap that symbolic regression keeps reopening

Grammar-guided genetic programming and its variants can evolve explicit equations that relate anthropometric inputs to body fat percentage, and earlier work showed these models can reach test R² near 0.85 while remaining more compact than black-box alternatives [3]. That earlier study compared Grammatical Evolution, Context-Free Grammar Genetic Programming, and Dynamic Structured Grammatical Evolution on NHANES 2017–18 data, concluding that DSGE was more robust in fitness variability while CFG could occasionally reach lower minimum fitness values [3]. The anchor paper builds directly on that pool of models, selecting two DSGE expressions and two CFG-GP expressions with test R² between 0.837 and 0.849 and complexity ranging from 14 to 68 operations [1].

The unresolved problem is that an equation can be readable as syntax yet implausible as physiology. The anchor paper's own examples show terms such as hip cubed times waist divided by leg length squared, or height divided by age squared, that the LLM itself flagged as non-standard or physiologically unclear [1]. This is the gap the new work targets: not whether symbolic regression can produce equations, but whether LLMs can help a clinician decide which equation deserves trust.

Why comparative ranking outperformed isolated term explanation

The anchor study's central empirical finding is that clinician assessments favored comparative model-ranking outputs over isolated term-level interpretations across the three LLMs tested [1]. In the DeepSeek-R1 outputs, for example, the model ranked DSGE-M21 first across interpretability, physiological plausibility, simplicity, and practical use, and placed the longer CFG-GP models at the bottom as likely overfitted [1]. Clinicians scored the DeepSeek-R1 interpretation of DSGE-M18 higher than the Gemma3 interpretation on every evaluated statement, with plausibility ratings of 3, 4, and 5 from the three physicians [1].

The interpretation is that ranking forces the LLM to commit to relative judgments, which gives clinicians something concrete to accept or reject. Isolated term explanations, by contrast, can sound plausible term by term while missing the global behavior of a nonlinear expression. The paper itself notes that the sign-based prompt heuristic, where negatives indicate decrease and positives indicate increase, should not be read as the global marginal effect of a variable when inputs appear in multiple nonlinear sub-expressions [1]. That caveat is a direct warning against treating term-level LLM narration as a substitute for model-level reasoning.

Instability and hallucination risk remain inside the audit loop

The same study that found comparative ranking useful also found that DeepSeek-R1 did not reproduce identical orderings across three runs, with middle positions fluctuating by one place even though the prompt explicitly instructed consistent answers [1]. Gemma3's ranking remained identical across runs, which suggests the variability is tied to reasoning-model behavior rather than to the ranking task itself [1]. This matters because a clinical audit tool that changes its ranking between identical queries is harder to defend in a regulated workflow.

Broader evidence on LLM reliability reinforces the concern. Semantic entropy work shows that hallucination is detectable as uncertainty over meaning, and that models can be confidently wrong on questions where knowledge is lacking [7]. A large-scale review of AI mobile app reviews found that user-reported hallucinations cluster around factual incorrectness and fabricated information, with strongly negative sentiment and lower star ratings [6]. In medical multiple-choice tasks, models can achieve moderate diagnostic accuracy while still relying on shallow patterns or hallucinated logic, with high grounding-deviation scores even for correct answers [4]. The anchor paper's own observation that LLMs produced physiologically and mathematically questionable explanations is therefore consistent with a wider pattern, not an isolated artifact [1].

Clinician-in-the-loop is the method, not a courtesy

The anchor study used three clinicians to score LLM outputs, which is a small panel but aligns with a reproducible evaluation tradition. A five-dimension clinician-in-the-loop framework for generative AI in healthcare used 41 board-certified physicians and pharmacists, with a modified Delphi protocol to resolve disagreements, and argued that multi-evaluator approaches reduce unwarranted misclassification compared with single-reviewer models [5]. That framework also separates helpfulness, comprehension, correctness, completeness, and clinical harmfulness, which is a more granular structure than the anchor study's statement-level Likert items [5].

The comparison is instructive rather than dismissive. The anchor study's contribution is not a new evaluation framework but a demonstration that LLM auditing of symbolic regression can be inserted into an existing clinician-evaluation workflow. The limitation is that three clinicians and four expressions cannot establish generalizable reliability. The paper itself frames LLMs as better suited to comparative auditing under expert oversight than to autonomous validation [1], and the broader clinical AI literature supports that framing: a systematic review of clinical language model adaptation found that 25 of 35 studies were at high risk of bias, largely because of limited external validation and incomplete methodological reporting [8].

What remains uncertain before this becomes a pipeline

The evidence boundary is narrow. Four expressions, three LLMs, three repeated runs, and three clinicians cannot support claims about other clinical variables, larger model pools, or different grammar-guided GP variants [1]. The anchor paper does not report inter-rater reliability statistics for the clinician panel, and the small number of raters limits any inference about scoring stability. The ranking variability observed in DeepSeek-R1 also means that repeated audits of the same expression set could produce different orderings, which would complicate any attempt to use LLM rankings as a screening gate [1].

A separate line of work suggests a complementary direction. In formation pressure prediction, a dimensionally consistent pressure-ratio symbolic regression framework produced an explicit auditable equation with MARE around 10% under depth-block validation, and the authors emphasized that the symbolic structure's value is auditability and local recalibration rather than universal accuracy [2]. That is a different domain, but the lesson transfers: symbolic regression models earn trust through transparent structure and recalibration against local reference data, not through LLM narration alone. The open question for the anchor paper's line of work is whether comparative LLM ranking can be validated against clinician consensus at scale, and whether it improves decision quality or merely adds a plausible-sounding layer over the same uncertainty.

About These Sources

This research page is built on 8 studies (6 peer-reviewed, 2 preprints) — published from 2023 to 2026, 7 from 2024 or later, 3 in Q1 journals, collectively cited 538 times — selected as the most relevant from 13 studies that passed quality screening, drawn from 138 papers retrieved from a database of over 500 million.

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