Reviews: Tight Sample Complexity of Learning One-hidden-layer Convolutional Neural Networks

The authors consider the parameter recovery problem that the data are generated from a teacher network''. The goal is to learn the network from the generated data which are from Gaussian distribution and labeled by the teacher network'' with some white noises. A simple algorithm is proposed to learn the ground-truth parameters of a non-overlapping CNN, which is shown to converge efficiently with high probability with a small sample complexity bound. Due to the good properties of Gaussian inputs, the expectation of each update lies in the span of w t and w * (v t and v * as well). Also, with some properties of a specific good set'', as long as we haven't yet achieved optimality, the gradient in each step would be large enough and get closer to w *.