  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.
