Riemannian metrics for neural networks I: Feedforward networks

Yann Ollivier (1, 2)

1 LRI - Laboratoire de Recherche en Informatique
2 TAO - Machine Learning and Optimisation

We describe four algorithms for neural network training, each adapted to different scalability constraints. These algorithms are mathematically principled and invariant under a number of transformations in data and network representation, from which performance is thus independent. These algorithms are obtained from the setting of differential geometry, and are based on either the natural gradient using the Fisher information matrix, or on Hessian methods, scaled down in a specific way to allow for scalability while keeping some of their key mathematical properties.

Domaines: Réseau de neurones [cs.NE]; Apprentissage [cs.LG]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Géométrie différentielle [math.DG]

Yann Ollivier. Riemannian metrics for neural networks I: Feedforward networks. Information and Inference, 2015, 4 (2), pp.108-153. ⟨10.1093/imaiai/iav006⟩. ⟨hal-00857982⟩