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Formal theory

Section status

Contributor: Unclaimed — this section has no named author yet. See Contribute.

Last reviewed: —

Status: Stub — a starting point only. The curated list is not yet written.

Overview

Formal theory uses machine learning differently from the rest of the field. It is not used to process data, but to search and characterize mathematical structures too large to enumerate. String compactifications, Calabi-Yau metrics, and the space of consistent effective field theories are all landscapes where a learned model can propose candidates or approximate objects with no closed form. The traffic also runs the other way, where field-theoretic methods are used to understand neural networks themselves, through correspondences between network ensembles and quantum field theories. That bidirectionality is unusual and makes this section a natural bridge to the wider physics-for-ML literature.

  • TASI Lectures on Physics for Machine Learning, Halverson (2024) (arXiv:2408.00082) — TASI lectures on physics for machine learning, covering both directions of the exchange
  • Machine Learning in Physics and Geometry, He et al. (2023) (arXiv:2303.12626) — machine learning in physics and geometry, a survey of the formal-theory applications

Curated paper list

This list is a seed, not a curated selection

A few landmark papers are listed to give the section a starting shape. A proper curated list — thematically grouped, with an annotation on every entry — is what this section still needs. See Contribute.

  • Machine Learned Calabi-Yau Metrics and Curvature, (2022) (arXiv:2211.09801) — machine-learned Calabi-Yau metrics and curvature, a representative instance of approximating objects with no closed form
  • Neural Network Field Theories: Non-Gaussianity, Actions, and Locality, Demirtas et al. (2023) (arXiv:2307.03223) — neural network field theories: non-Gaussianity, actions and locality — the ML-as-field-theory direction
  • Exploring the Truth and Beauty of Theory Landscapes with Machine Learning, Matchev et al. (2024) (arXiv:2401.11513) — exploring theory landscapes with machine learning, on the search-and-characterize use

Benchmarks, datasets & software

Not yet compiled for this section.

Open questions

What is settled here, what is contested, and what remains unsolved? This is the part a bibliography structurally cannot provide, and often the most useful paragraph on the page.

Further reading

Relevant work that is not an entry point — too specialized, too recent, or simply not where a newcomer should start. Suggestions that do not fit the curated list above belong here rather than being turned away.

Nothing listed yet.

Cross-references