We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other complex models. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.
We propose an algorithm for provably recovering parameters (convolutional and output weights) of a convolutional network with overlapping patches. This paper studies the theoretical learning of one-hidden-layer convolutional neural nets, resulting in a learning algorithm and provable guarantees using the algorithm. This paper gives a new algorithm for learning a two layer neural network which involves a single convolutional filter and a weight vector for different locations.