# Deep Reinforcement Learning for Fano Hypersurfaces

arXiv: https://arxiv.org/abs/2603.15437 · HTML: https://mlsanity.com/paper/2603.15437/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 3 of 3)

- [Machine learning detects terminal singularities](https://mlsanity.com/paper/2310.20458/) (2023)
- [Machine learning the dimension of a Fano variety](https://mlsanity.com/paper/2309.05473/) (2023)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)

## Abstract (arXiv)

We design a deep reinforcement learning algorithm to explore a high-dimensional integer lattice with sparse rewards, training a feedforward neural network as a dynamic search heuristic to steer exploration toward reward dense regions. We apply this to the discovery of Fano 4-fold hypersurfaces with terminal singularities, objects of central importance in algebraic geometry. Fano varieties with terminal singularities are fundamental building blocks of algebraic varieties, and explicit examples serve as a vital testing ground for the development and generalisation of theory. Despite decades of effort, the combinatorial intractability of the underlying search space has left this classification severely incomplete. Our reinforcement learning approach yields thousands of previously unknown examples, hundreds of which we show are inaccessible to known search methods.