An analytic theory of shallow networks dynamics for hinge loss classification

• URL: http://arxiv.org/abs/2006.11209v1
• Date: Fri, 19 Jun 2020 16:25:29 GMT
• Title: An analytic theory of shallow networks dynamics for hinge loss classification
• Authors: Franco Pellegrini and Giulio Biroli
• Abstract summary: We study the training dynamics of a simple type of neural network: a single hidden layer trained to perform a classification task. We specialize our theory to the prototypical case of a linearly separable dataset and a linear hinge loss. This allow us to address in a simple setting several phenomena appearing in modern networks such as slowing down of training dynamics, crossover between rich and lazy learning, and overfitting.
• Score: 14.323962459195771
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. This allow us to address in a simple setting several phenomena appearing in modern networks such as slowing down of training dynamics, crossover between rich 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.

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