(untitled) (Journal of Computational Mathematics, 2021)
We study a class of deep neural networks with architectures that form a directed acyclic graph (DAG). For backpropagation defined by gradient descent with adaptive momentum, we show weights converge for a large class of nonlinear activation functions. The proof generalizes the results of Wu et al. (2008) who showed convergence for a feed-forward network with one hidden layer. For an example of the effectiveness of DAG architectures, we describe an example of compression through an AutoEncoder, and compare against sequential feed-forward networks under several metrics.