This paper addresses the following question of neural network identifiability: Does the input-output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and biases? Existing literature on the subject Sussman 1992, Albertini, Sontag et.al 1993, Fefferman 1994 suggests that the answer should be yes, up to certain symmetries induced by the nonlinearity, and provided the networks under consideration satisfy certain "genericity conditions". The results in Sussman 1992 and Albertini, Sontag et.al 1993 apply to networks with a single hidden layer and in Fefferman 1994 the networks need to be fully connected. In an effort to answer the identifiability question in greater generality, we derive necessary genericity conditions for the identifiability of neural networks of arbitrary depth and connectivity with an arbitrary nonlinearity. Moreover, we construct a family of nonlinearities for which these genericity conditions are minimal, i.e., both necessary and sufficient. This family is large enough to approximate many commonly encountered nonlinearities to arbitrary precision in the uniform norm.

本文研究神经网络的特定输入输出映射是否能唯一指定神经网络结构、权重和偏置，并探究其实现的通用性和稳健性，构建了一族非线性模型作为研究对象，并得出其必要通用性条件。

一类S型非线性函数的神经网络可辨识性