Learning One Convolutional Layer with Overlapping Patches
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:17831791, 2018.
Abstract
We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches under mild conditions on the underlying distribution. We prove that our framework captures commonly used schemes from computer vision, including onedimensional and twodimensional “patch and stride” convolutions. Our algorithm– Convotron– is inspired by recent work applying isotonic regression to learning neural networks. Convotron uses a simple, iterative update rule that is stochastic in nature and tolerant to noise (requires only that the conditional mean function is a one layer convolutional network, as opposed to the realizable setting). In contrast to gradient descent, Convotron requires no special initialization or learningrate tuning to converge to the global optimum. We also point out that learning one hidden convolutional layer with respect to a Gaussian distribution and just one disjoint patch $P$ (the other patches may be arbitrary) is easy in the following sense: Convotron can efficiently recover the hidden weight vector by updating only in the direction of $P$.
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