ODSL Forum: A Study of Field Theories via Neural Network Architectures

by Dr Anindita Maiti (Harvard)

Friday 21 Jul 2023, 15:00 → 16:00 Europe/Berlin

Basement Seminar Room (Origins Cluster Building)

Title: A Study of Field Theories via Neural Network Architectures

Abstract: Neural Network (NN) output ensembles at initialization correspond to field theories. For certain constraints on NN architectures, such as infinite width, and independently, identically drawn parameters, such field theories are Gaussian; deviations from these architectural limits turn on field interactions. These architectural deviations, and corresponding field interaction strengths, can be controlled parametrically at initialization. At large deviations, such as those caused by small NN width, and dissimilar, non-identical NN parameters, these field theories are non-perturbative, with actions often difficult to deduce. Based on https://arxiv.org/abs/2307.03223, I will present a method, known as Edgeworth expansion, that can be used to construct the field theory actions in Neural Networks in terms of connected Feynman diagrams, where internal vertices of diagrams correspond to connected correlators of NN output ensembles. Further, specific interacting field theories can be obtained exactly through initializing Neural Networks with appropriate non-Gaussian parameter distributions. The non-Gaussianities of parameter distributions show up in the field theory action deformations. As an example, I will discuss the construction of ɸ4 scalar field theory in infinite width NN architectures.

Link to paper: https://arxiv.org/abs/2307.03223