Neuron birthdeath dynamics accelerates gradient descent and converges asymptotically
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:55085517, 2019.
Abstract
Neural networks with a large number of parameters admit a meanfield description, which has recently served as a theoretical explanation for the favorable training properties of models with a large number of parameters. In this regime, gradient descent obeys a deterministic partial differential equation (PDE) that converges to a globally optimal solution for networks with a single hidden layer under appropriate assumptions. In this work, we propose a nonlocal mass transport dynamics that leads to a modified PDE with the same minimizer. We implement this nonlocal dynamics as a stochastic neuronal birth/death process and we prove that it accelerates the rate of convergence in the meanfield limit. We subsequently realize this PDE with two classes of numerical schemes that converge to the meanfield equation, each of which can easily be implemented for neural networks with finite numbers of parameters. We illustrate our algorithms with two models to provide intuition for the mechanism through which convergence is accelerated.
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