A convergence result of a continuous model of deep learning via \L{}ojasiewicz--Simon inequality

arXiv:2311.15365v2 Announce Type: replace
Abstract: This study focuses on a Wasserstein-type gradient flow, which represents an optimization process of a continuous model of a Deep Neural Network (DNN). First, we establish the existence of a minimizer for an average loss of the model under $L^2$-regularization. Subsequently, we show the existence of a curve of maximal slope of the loss. Our main result is the convergence of flow to a critical point of the loss as time goes to infinity. An …

abstract arxiv continuous convergence cs.lg deep learning deep neural network dnn flow gradient inequality loss math.ap math.fa math.pr network neural network optimization process regularization study type via