论文标题
了解一个隐藏层的Relu网络的全球损失格局，第1部分：理论
Understanding Global Loss Landscape of One-hidden-layer ReLU Networks, Part 1: Theory
论文作者
论文摘要
对于一个隐藏的层次网络，我们证明所有可区分的局部最小值都是可微分区域内的全球。我们给出了可区分局部最小值的位置和损失，并表明这些局部最小值可以是隔离点或连续的超平面，具体取决于数据之间的相互作用，隐藏神经元的激活模式和网络大小。此外，我们为存在鞍点以及非差异的局部最小值及其位置（如果存在）提供了必要和足够的条件。
For one-hidden-layer ReLU networks, we prove that all differentiable local minima are global inside differentiable regions. We give the locations and losses of differentiable local minima, and show that these local minima can be isolated points or continuous hyperplanes, depending on an interplay between data, activation pattern of hidden neurons and network size. Furthermore, we give necessary and sufficient conditions for the existence of saddle points as well as non-differentiable local minima, and their locations if they exist.
