Algebraic Geometry: A Window to Machine Learning

This IPAM workshop brings together researchers in algebraic geometry and machine learning to build mathematical frameworks for understanding learning systems. Recent work has revealed rich algebraic and geometric structure in neural networks, including algebraic invariants of model classes, symmetries and fibre structures in parameter spaces, and geometric subdivisions of data space such as Voronoi regions of estimators, offering ways to analyse networks beyond linearised regimes and to understand optimisation dynamics, implicit bias, generalisation and robustness. The workshop focuses on phenomena in modern deep learning that still lack adequate theory: feature learning, grokking, neural collapse, low-rank adaptation, network verification and compression, mild overparameterisation, and length generalisation in sequence-to-sequence models. Advances in computational algebra, polynomial invariants, tensor geometry and semi-algebraic methods will be connected with problems in learning theory and with applications such as certification, trustworthy AI, compression and privacy. The programme includes a poster session; registration includes a remote-participation option.