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Neural Networks with Complex-Valued Weights Have No Spurious Local Minima (2103.07287v2)
Published 31 Jan 2021 in cs.LG and stat.ML
Abstract: We study the benefits of complex-valued weights for neural networks. We prove that shallow complex neural networks with quadratic activations have no spurious local minima. In contrast, shallow real neural networks with quadratic activations have infinitely many spurious local minima under the same conditions. In addition, we provide specific examples to demonstrate that complex-valued weights turn poor local minima into saddle points.
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