Back to Search
Start Over
Limiting free energy of multi-layer generalized linear models
- Publication Year :
- 2021
-
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.<br />43 pages
- Subjects :
- FOS: Computer and information sciences
82B44, 82D30
Information Theory (cs.IT)
Computer Science - Information Theory
Probability (math.PR)
FOS: Mathematics
FOS: Physical sciences
Disordered Systems and Neural Networks (cond-mat.dis-nn)
Condensed Matter - Disordered Systems and Neural Networks
Mathematics - Probability
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....e51827f438267ada4299243ba6c2c79b