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.

翻译：我们研究了神经网络采用复值权重的优势。我们证明了具有二次激活函数的浅层复神经网络不存在伪局部极小值。相比之下，在相同条件下，具有二次激活函数的浅层实神经网络则存在无穷多个伪局部极小值。此外，我们提供了具体示例来证明复值权重能够将不良的局部极小值转变为鞍点。