Port-Hamiltonian Approach to Neural Network Training
This addresses the challenge of discrete optimization methods in neural networks, offering a continuous alternative that could improve training stability and convergence.
The paper tackles the problem of neural network training by proposing a framework where parameters evolve as solutions of ordinary differential equations, ensuring convergence to a minimum of the objective function through a port-Hamiltonian system approach.
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.