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The Dynamics of Learning: A Random Matrix Approach
Zhenyu Liao · Romain Couillet

Wed Jul 11 07:20 AM -- 07:40 AM (PDT) @ K1 + K2

Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we introduce a random matrix-based framework to analyze the learning dynamics of a single-layer linear network on a binary classification problem, for data of simultaneously large dimension and size, trained by gradient descent. Our results provide rich insights into common questions in neural nets, such as overfitting, early stopping and the initialization of training, thereby opening the door for future studies of more elaborate structures and models appearing in today's neural networks.

Author Information

Zhenyu Liao (L2S, CentraleSupelec)

Zhenyu Liao is a second year Ph.D. student, under the supervision of Prof. [Romain Couillet](http://romaincouillet.hebfree.org/) and Prof. [Yacine Chitour](http://www.l2s.centralesupelec.fr/en/perso/yacine.chitour), with the [Signals and Statistics group](http://www.l2s.centralesupelec.fr/en/signals/presentation-signal-statistics-group) of [Laboratoire des signaux et systèmes](https://www.l2s.centralesupelec.fr/en), [CentraleSupélec](http://www.centralesupelec.fr/en), [University Paris-Saclay](https://www.universite-paris-saclay.fr/en). He received his B.Sc degree in [Optical & Electronic Information](http://english.oei.hust.edu.cn/) from [Huazhong University of Science & Technology](http://english.hust.edu.cn/), China and his M.Sc. degree in Signal and Image Processing from [CentraleSupélec](http://www.centralesupelec.fr/en)/[Paris-Sud University](http://www.u-psud.fr/en/index.html), France in 2016.

Romain Couillet (CentralSupélec)

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