Geometry of Energy Landscapes and the Optimizability of Deep Neural Networks.
Phys Rev Lett
; 124(10): 108301, 2020 Mar 13.
Article
em En
| MEDLINE
| ID: mdl-32216422
ABSTRACT
Deep neural networks are workhorse models in machine learning with multiple layers of nonlinear functions composed in series. Their loss function is highly nonconvex, yet empirically even gradient descent minimization is sufficient to arrive at accurate and predictive models. It is hitherto unknown why deep neural networks are easily optimizable. We analyze the energy landscape of a spin glass model of deep neural networks using random matrix theory and algebraic geometry. We analytically show that the multilayered structure holds the key to optimizability Fixing the number of parameters and increasing network depth, the number of stationary points in the loss function decreases, minima become more clustered in parameter space, and the trade-off between the depth and width of minima becomes less severe. Our analytical results are numerically verified through comparison with neural networks trained on a set of classical benchmark datasets. Our model uncovers generic design principles of machine learning models.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Redes Neurais de Computação
/
Aprendizado de Máquina
Tipo de estudo:
Prognostic_studies
Idioma:
En
Ano de publicação:
2020
Tipo de documento:
Article