【Team】High-Dimensional Structure Theory Team
【Date】2026/July/29(Wednesday) 20:00-21:00(JST)
【Speaker】Talk by Alvaro Fernandez
Title: Spectral learning: Using normalizing flows to augment basis sets
Abstract:
Neural networks represented a major breakthrough for high-dimensional function approximation. However, their unstructured and overparameterized nature limits their effectiveness in interpolation and structured spaces (e.g., those requiring boundary conditions or orthonormality). Conversely, classical approximation methods provide the required functional structure but suffer from the curse of dimensionality. In this seminar I present spectral learning, an algorithm that combines neural network flexibility with basis set structure. In spectral learning, augmented basis sets are generated by pushing forward standard bases through normalizing flows, i.e., invertible neural networks. Alternatively, this transformation can be interpreted as modifying the target function via the inverse mapping while keeping the underlying basis intact, allowing established analytical tools to be directly applied. The working principle of spectral learning is demonstrated for the spaces of continuous and square-integrable functions, with the latter applied to solve the vibrational Schrödinger equation.
