A three-layer network with layerwise gradient descent provably recovers the span of multiple quadratic features in O~(d^4) samples and then learns any polynomial link in the features.
What can resnet learn efficiently, going beyond kernels? Advances in Neural Information Processing Systems, 32, 2019
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Learning Hierarchical Polynomials of Multiple Nonlinear Features with Three-Layer Networks
A three-layer network with layerwise gradient descent provably recovers the span of multiple quadratic features in O~(d^4) samples and then learns any polynomial link in the features.