English

Geometry of Program Synthesis

Machine Learning 2021-03-31 v1 Artificial Intelligence Programming Languages

Abstract

We re-evaluate universal computation based on the synthesis of Turing machines. This leads to a view of programs as singularities of analytic varieties or, equivalently, as phases of the Bayesian posterior of a synthesis problem. This new point of view reveals unexplored directions of research in program synthesis, of which neural networks are a subset, for example in relation to phase transitions, complexity and generalisation. We also lay the empirical foundations for these new directions by reporting on our implementation in code of some simple experiments.

Keywords

Cite

@article{arxiv.2103.16080,
  title  = {Geometry of Program Synthesis},
  author = {James Clift and Daniel Murfet and James Wallbridge},
  journal= {arXiv preprint arXiv:2103.16080},
  year   = {2021}
}

Comments

16 pages, 7 figures

R2 v1 2026-06-24T00:40:40.040Z