Paper
Deep Reinforcement Learning for Fano Hypersurfaces
Authors
Marc Truter
Abstract
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.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.15437v1</id>\n <title>Deep Reinforcement Learning for Fano Hypersurfaces</title>\n <updated>2026-03-16T15:42:12Z</updated>\n <link href='https://arxiv.org/abs/2603.15437v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.15437v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.AG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <published>2026-03-16T15:42:12Z</published>\n <arxiv:comment>10 pages, 10 figures, 1 table</arxiv:comment>\n <arxiv:primary_category term='math.AG'/>\n <author>\n <name>Marc Truter</name>\n </author>\n </entry>"
}