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Can a neural network minimizing cross-entropy learn linearly separable data?Despite progress in the theory of deep learning, this question remainsunsolved. Here we prove that SGD globally optimizes this learning problem for atwo-layer network with Leaky ReLU activations. The learned network can inprinciple be very complex. However, empirical evidence suggests that it oftenturns out to be approximately linear. We provide theoretical support for thisphenomenon by proving that if network weights converge to two weight clusters,this will imply an approximately linear decision boundary. Finally, we show acondition on the optimization that leads to weight clustering. We provideempirical results that validate our theoretical analysis.

Towards Understanding Learning in Neural Networks with Linear Teachers