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An analytic theory of shallow networks dynamics for hinge loss classification*This article is an updated version of: Pellegrini F and Biroli G 2020 An analytic theory of shallow networks dynamics for hinge loss classification Advances in Neural Information Processing Systems vol 33 ed H Larochelle, M Ranzato, R Hadsell, M F Balcan and H Lin (New York: Curran Associates) pp 5356–67. (29th December 2021)
Record Type:
Journal Article
Title:
An analytic theory of shallow networks dynamics for hinge loss classification*This article is an updated version of: Pellegrini F and Biroli G 2020 An analytic theory of shallow networks dynamics for hinge loss classification Advances in Neural Information Processing Systems vol 33 ed H Larochelle, M Ranzato, R Hadsell, M F Balcan and H Lin (New York: Curran Associates) pp 5356–67. (29th December 2021)
Main Title:
An analytic theory of shallow networks dynamics for hinge loss classification*This article is an updated version of: Pellegrini F and Biroli G 2020 An analytic theory of shallow networks dynamics for hinge loss classification Advances in Neural Information Processing Systems vol 33 ed H Larochelle, M Ranzato, R Hadsell, M F Balcan and H Lin (New York: Curran Associates) pp 5356–67.
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 data and a linear hinge loss, for which the dynamics can be explicitly solved in the infinite dataset limit. This allows 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 assess the limitations of mean-field theory by studying the case of large but finite number of nodes and of training samples.