Elenco seminari del ciclo di seminari
“GEOMETRIA E DEEP LEARNING”

In questo ciclo di seminari verranno esposte alcune tematiche correlate all'uso di metodi geometrici nel deep learning.

Francesco Vaccarino

On the geometry of learning

nel ciclo di seminari: GEOMETRIA E DEEP LEARNING

algebra e geometria

We will present and discuss the main geometric and topological approaches and results regarding Deep Neural Networks and Generative Adversarial Networks.

A Geometric Interpretation of Stochastic Gradient Descent

nel ciclo di seminari: GEOMETRIA E DEEP LEARNING

algebra e geometria

We start with a review of the main steps of the Deep Learning algorithm, together with some historical remarks. We then concentrate on the key ingredient, stochastic gradient descent (SGD), whose geometric significance appears elusive and was modelled using the SDE Fokker Planck by Chaudhari and Soatto. We then study a deterministic model in which the trajectories of our dynamical systems are described via geodesics of a family of metrics arising from the diffusion matrix (natural gradient method). These metrics encode information about the highly non-isotropic gradient noise in SGD. This is a joint work with S. Soatto (UCLA, Amazon) and P. Chaudhari (U. Penn.)