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We propose a new algorithm to learn a one-hidden-layer convolutional neuralnetwork where both the convolutional weights and the outputs weights areparameters to be learned. Our algorithm works for a general class of(potentially overlapping) patches, including commonly used structures forcomputer vision tasks. Our algorithm draws ideas from (1) isotonic regressionfor learning neural networks and (2) landscape analysis of non-convex matrixfactorization problems. We believe these findings may inspire furtherdevelopment in designing provable algorithms for learning neural networks andother complex models.

Improved Learning of One-hidden-layer Convolutional Neural Networks with Overlaps