深度 ReLU 网络鲁棒性理论下界研究

1. 12:00
   arXiv · Neural and Evolutionary Computing

   深度 ReLU 网络鲁棒性的理论下界

   论文给出参数化神经网络对随机输入扰动鲁棒性的理论下界，针对深度 ReLU 网络结合高维几何的测度集中与输入-输出函数几何结构新刻画，证明输入空间划分中每个凸多面体区域的面数至多等于网络单元数。研究还刻画局部鲁棒性随输入维度的标度，指出含脆弱点的决策边界邻域宽度随维度增加迅速收缩、随网络单元数仅对数增长。

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