A Shooting Formulation of Deep Learning
Abstract
Continuousdepth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the advantages of such continuous formulations, most current techniques are not truly continuousdepth as they assume \textit{identical} layers. Indeed, existing works throw into relief the myriad difficulties presented by an infinitedimensional parameter space in learning a continuousdepth neural ODE. To this end, we introduce a shooting formulation which shifts the perspective from parameterizing a network layerbylayer to parameterizing over optimal networks described only by a set of initial conditions. For scalability, we propose a novel particleensemble parametrization which fully specifies the optimal weight trajectory of the continuousdepth neural network. Our experiments show that our particleensemble shooting formulation can achieve competitive performance, especially on longrange forecasting tasks. Finally, though the current work is inspired by continuousdepth neural networks, the particleensemble shooting formulation also applies to discretetime networks and may lead to a new fertile area of research in deep learning parametrization.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.10330
 Bibcode:
 2020arXiv200610330V
 Keywords:

 Computer Science  Neural and Evolutionary Computing;
 Computer Science  Machine Learning;
 Mathematics  Optimization and Control