Limiting free energy of multi-layer generalized linear models
Probability
2021-08-31 v1 Disordered Systems and Neural Networks
Information Theory
math.IT
Abstract
We compute the high-dimensional limit of the free energy associated with a multi-layer generalized linear model. Under certain technical assumptions, we identify the limit in terms of a variational formula. The approach is to first show that the limit is a solution to a Hamilton-Jacobi equation whose initial condition is related to the limiting free energy of a model with one fewer layer. Then, we conclude by an iteration.
Cite
@article{arxiv.2108.12615,
title = {Limiting free energy of multi-layer generalized linear models},
author = {Hong-Bin Chen and Jiaming Xia},
journal= {arXiv preprint arXiv:2108.12615},
year = {2021}
}
Comments
43 pages