论文标题
任何目标功能都存在于任何足够宽的随机网络的社区中：几何透视图
Any Target Function Exists in a Neighborhood of Any Sufficiently Wide Random Network: A Geometrical Perspective
论文作者
论文摘要
众所周知，任何目标函数都可以在任何随机连接的深网的足够小社区中实现，前提是宽度（层中的神经元数）足够大。关于这个惊人的事实有复杂的理论和讨论，但是严格的理论非常复杂。我们通过使用简单的模型来阐明其结构来提供基本的几何证明。我们表明，高维几何形状起着神奇的作用：当我们将半径1的高维球投射到低维子空间时，球体上的均匀分布将减少到可忽略的小协方差的高斯分布。
It is known that any target function is realized in a sufficiently small neighborhood of any randomly connected deep network, provided the width (the number of neurons in a layer) is sufficiently large. There are sophisticated theories and discussions concerning this striking fact, but rigorous theories are very complicated. We give an elementary geometrical proof by using a simple model for the purpose of elucidating its structure. We show that high-dimensional geometry plays a magical role: When we project a high-dimensional sphere of radius 1 to a low-dimensional subspace, the uniform distribution over the sphere reduces to a Gaussian distribution of negligibly small covariances.
