Stable Neural Flows

• URL: http://arxiv.org/abs/2003.08063v1
• Date: Wed, 18 Mar 2020 06:27:21 GMT
• Title: Stable Neural Flows
• Authors: Stefano Massaroli, Michael Poli, Michelangelo Bin, Jinkyoo Park, Atsushi Yamashita, Hajime Asama
• Abstract summary: We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. The learning procedure is cast as an optimal control problem, and an approximate solution is proposed based on adjoint sensivity analysis.
• Score: 15.318500611972441
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on asymptotic stability of the depth-flows, leading to robustness against input perturbations and low computational burden for the numerical solver. The learning procedure is cast as an optimal control problem, and an approximate solution is proposed based on adjoint sensivity analysis. We further introduce novel regularizers designed to ease the optimization process and speed up convergence. The proposed model class is evaluated on non-linear classification and function approximation tasks.

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