# Selection dynamics for deep neural networks

@article{Liu2019SelectionDF,
title={Selection dynamics for deep neural networks},
author={Hailiang Liu and Peter A. Markowich},
journal={arXiv: Analysis of PDEs},
year={2019}
}
• Published 22 May 2019
• Mathematics
• arXiv: Analysis of PDEs
This paper presents a partial differential equation framework for deep residual neural networks and for the associated learning problem. This is done by carrying out the continuum limits of neural networks with respect to width and depth. We study the wellposedness, the large time solution behavior, and the characterization of the steady states of the forward problem. Several useful time-uniform estimates and stability/instability conditions are presented. We state and prove optimality… Expand
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