# Geometry of Program Synthesis

arXiv: https://arxiv.org/abs/2103.16080 · HTML: https://mlsanity.com/paper/2103.16080/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 8 of 8)

- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Neural GPUs Learn Algorithms](https://mlsanity.com/paper/1511.08228/) (2015)
- [Deep Learning is Singular, and That's Good](https://mlsanity.com/paper/2010.11560/) (2020)
- [Neural Programmer: Inducing Latent Programs with Gradient Descent](https://mlsanity.com/paper/1511.04834/) (2015)
- [TerpreT: A Probabilistic Programming Language for Program Induction](https://mlsanity.com/paper/1608.04428/) (2016)
- [Adaptive Neural Compilation](https://mlsanity.com/paper/1605.07969/) (2016)

## Built on by (most cited first, 1 of 1)

- [Interpretability for Turing Machines](https://mlsanity.com/paper/2609.04661/) (2026)

## Abstract (arXiv)

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.