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Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation — arXiv:2610.42024

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.42024
License (as archived): CC0-1.0
Archived: 2026-11-03T07:53:19.094Z
SHA-256 of the archived text: aa54b3040644642f086dcb08bb01181a24d2262522142bd1d065f56d369315f5
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How to cite

Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation — arXiv:2610.42024 — arXiv (en), https://arxiv.org/abs/2610.42024 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fcbc7cbda94d (Metraipolis archive dc_fcbc7cbda94d, sha256 aa54b3040644642f086dcb08bb01181a24d2262522142bd1d065f56d369315f5)

BibTeX

@misc{dcfcbc7cbda94d,
  title = {Know When the Equation Is Wrong: Structural Uncertainty for LLM-Guided Symbolic Regression under Extrapolation — arXiv:2610.42024},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.42024},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fcbc7cbda94d; sha256 aa54b3040644642f086dcb08bb01181a24d2262522142bd1d065f56d369315f5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.42024. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Large language models (LLMs) can help discover mathematical equations from data, but most LLM-guided symbolic regression methods focus on a single best equation without quantifying uncertainty over alternative functional forms. This is challenging because distinct equations can fit the observed data similarly while producing substantially different extrapolations. Our experiments on the LLM-SRBench dataset show that standard conformal intervals achieve nominal in-distribution coverage but frequently fail under extrapolation. To tackle this challenge, we introduce LLM-SR-UQ, a framework that retains competing equation structures and uses their disagreement to characterize uncertainty about the underlying functional form. We extend the standard fixed-width conformal approach to quantify structural intervals, which measure disagreement among candidate equations and identify where prediction intervals should widen. Extensive experiments show our framework substantially improves coverage attainment by incorporating structural disagreement while preserving in-distribution coverage. Our approach also shows good generalizability when it is applied to other symbolic-regression methods.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2610.42024 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T07:49:31.183Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).