On the rates of convergence for learning with convolutional neural networks

arXiv:2403.16459v1 Announce Type: new
Abstract: We study the approximation and learning capacities of convolutional neural networks (CNNs). Our first result proves a new approximation bound for CNNs with certain constraint on the weights. Our second result gives a new analysis on the covering number of feed-forward neural networks, which include CNNs as special cases. The analysis carefully takes into account the size of the weights and hence gives better bounds than existing literature in some situations. Using these two results, …

abstract analysis approximation arxiv cnns convergence convolutional neural networks cs.lg math.st networks neural networks stat.ml stat.th study type