Bootcamp on geometry and graph learning
summary
Bootcamp surveys concrete math-for-ML results and working code: a Berkovich analytification / polydisc approach gives path-connected non‑Archimedean embeddings (code + global minima proofs, preprint forthcoming) for hierarchy data; ReLU MLPs admit tropical rational function representations (useful for exact linear‑region counts via OSCAR); standard discrete curvatures match the recent balanced‑Forman rewiring accuracy but compute orders of magnitude faster; persistent homology separates clean vs poisoned LLM activations across layers; MLPs predict Fano variety invariants (dimension, singularities) used for conjecture discovery.
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chapters (18)
- 0:00Geometry in graph ML
- 1:08Algebra and geometry for graphs
- 3:58Graph neural networks and their limitations
- 7:48Algebra with symmetries
- 13:51Topology and graph theory
- 19:18Geometry with metric spaces
- 24:10Non-Archimedean ML for hierarchies
- 32:35Curvature and graph rewiring
- 41:37Algebraic geometry for ML
- 44:34Tropical geometry and NNs
- 57:37Linear regions and tropical functions
- 1:01:09Tropical curves and metric graphs
- 1:04:45NNs for math discovery
- 1:08:59Topology with persistent homology
- 1:17:13Generalization and homology dimension
- 1:21:09LLM interpretability and attacks
- 1:24:06Enriching GNNs with math
- 1:27:18Q&A on topology
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