Ranking Is Not Certification: Proxy Trust Signals in Symbolic Regression Separate Candidates Within a Problem but Collapse as Acceptance Gates
A symbolic-regression (SR) system that proposes a closed-form law usually also reports quantities that read as confidence: parsimony scores, ensemble stability, Bayesian predictive variance, conformal interval widths. We measure whether six such proxy trust signals — five computed without any target-region labels, plus one oracle-assisted extrapolation-excess gate — can separate a correct law from an engine-harvested stable-but-wrong one that fits the sampled region to R^2 >= 0.90. On a frozen 67-equation held-out test (60 scoreable clusters; hard negatives from PySR and gplearn), the answer splits cleanly across two estimands. Within a problem (ranking candidates for one dataset), five of the six signals stay clearly above chance, with concordance 0.63–1.00 across noise levels. Across problems (one acceptance threshold for all datasets — certification, in the limited sense of calibrated cross-problem acceptance), the same signals lose most of that advantage: at noise r=0.10 they degrade to chance-to-modest standardized partial AUC (0.49–0.71 in the low-false-positive regime) against the oracle target-region probe's 0.82; at r=0.30 both sides degrade, proxies to 0.48–0.58 and the oracle to 0.62. Ranking information does not transfer into calibrated acceptance, in part because the proxies' scales are not comparable across problems. The sharpest single finding: a SINDy-style inclusion-stability analogue is near-blind even for within-problem ranking (0.56–0.57 at all noise levels, against 1.00 for every other signal at zero noise), an effect that persists under both row and parametric bootstrap schemes. One signal (the excess gate) falls marginally below chance at the highest noise level; we treat this as a secondary observation. We provide no positive trust rule and make no claim that any interior-only signal can serve as a problem-transferable acceptance gate; all claims are scoped to this benchmark. Preprint. Not peer-reviewed. All claims are scoped to the benchmark described herein.
Authors
- Jun Liu (ORCID: https://orcid.org/0000-0001-7390-8958)
Institutions
- Chuzhou University (CN)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-06-12
- DOI
- https://doi.org/10.5281/zenodo.20664112
- Primary Topic
- Explainable Artificial Intelligence (XAI)
- Type
- preprint