Regular Seminar Jim Halverson (Northeastern University in Boston)
We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of non-interacting field theories. Moving away from the asymptotic limit yields a non-Gaussian process and corresponds to turning on particle interactions, allowing for the computation of correlation functions of neural network outputs with Feynman diagrams. Minimal non-Gaussian process likelihoods are determined by the most relevant non-Gaussian terms, according to the flow in their coefficients induced by the Wilsonian renormalization group. This yields a direct connection between overparameterization and simplicity of neural network likelihoods. Whether the coefficients are constants or functions may be understood in terms of GP limit symmetries, as expected from 't Hooft's technical naturalness. General theoretical calculations are matched to neural network experiments in the simplest class of models allowing the correspondence. Our formalism is valid for any of the many architectures that becomes a GP in an asymptotic limit, a property preserved under certain types of training.
Journal Club Yifei He (IPhT Saclay)
room Zoom, instructions in abstract
An important example among the 2d geometrical critical phenomena is the critical Q-state Potts model, which describes the percolation in the limit Q-->1. In this talk I will consider the problem of determining the geometrical four-point functions (cluster connectivities) in this model. Connections with the minimal models are made which uncover remarkable properties of the Potts amplitudes. Such properties allow to deduce the existence of "interchiral conformal blocks" which can be constructed using the degeneracy in the Potts spectrum. Using these, I will then determine the four-point functions through numerical bootstrap. In addition, I will also discuss the logarithmic nature of the Potts CFT and hints of a full analytic solution of the model. ----- Part of London Integrability Journal Club. New participants please register using the form at integrability-london.weebly.com. The link will be emailed.