Port-Hamiltonian Approach to Neural Network Training
Abstract
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but are solutions of an ordinary differential equation (ODE); however, these networks are still optimized via discrete methods (e.g. gradient descent). In this paper, we explore a different direction: namely, we propose a novel framework for learning in which the parameters themselves are solutions of ODEs. By viewing the optimization process as the evolution of a port-Hamiltonian system, we can ensure convergence to a minimum of the objective function. Numerical experiments have been performed to show the validity and effectiveness of the proposed methods.
Cite
@article{arxiv.1909.02702,
title = {Port-Hamiltonian Approach to Neural Network Training},
author = {Stefano Massaroli and Michael Poli and Federico Califano and Angela Faragasso and Jinkyoo Park and Atsushi Yamashita and Hajime Asama},
journal= {arXiv preprint arXiv:1909.02702},
year = {2019}
}
Comments
To appear in the Proceedings of the 58th IEEE Conference on Decision and Control (CDC 2019). The first two authors contributed equally to the work