Timezone: »

An analytic theory of shallow networks dynamics for hinge loss classification
Franco Pellegrini · Giulio Biroli

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #1001

Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the training dynamics of a simple type of neural network: a single hidden layer trained to perform a classification task. We show that in a suitable mean-field limit this case maps to a single-node learning problem with a time-dependent dataset determined self-consistently from the average nodes population. We specialize our theory to the prototypical case of a linearly separable dataset and a linear hinge loss, for which the dynamics can be explicitly solved in the infinite dataset limit. This allow us to address in a simple setting several phenomena appearing in modern networks such as slowing down of training dynamics, crossover between feature and lazy learning, and overfitting. Finally, we asses the limitations of mean-field theory by studying the case of large but finite number of nodes and of training samples.

Author Information

Franco Pellegrini (École normale supérieure, Paris)
Giulio Biroli (ENS)

More from the Same Authors