High-Dimensional Structure Theory Team (Talk by Alvaro Fernandez)

The High-Dimensional Structure Theory Team hosts a one hour online talk by Alvaro Fernandez on spectral learning, an algorithm that combines the flexibility of neural networks with the structure of classical basis sets. Neural networks approximate high-dimensional functions well, but their unstructured and overparameterized form limits them for interpolation and for spaces that require boundary conditions or orthonormality. Classical approximation methods supply that structure but run into the curse of dimensionality. The talk covers how augmented basis sets are generated by pushing standard bases forward through normalizing flows, that is, invertible neural networks. The same transformation can be read the other way around: the target function is modified via the inverse mapping while the underlying basis stays intact, which keeps established analytical tools directly applicable. The working principle is demonstrated on the spaces of continuous and square-integrable functions, with the square-integrable case applied to solving the vibrational Schrodinger equation. The session runs 20:00 to 21:00 JST and is held online.