Parameter identifiability of a deep feedforward ReLU neural network

TL;DR

This paper investigates conditions under which the parameters of a deep ReLU neural network can be uniquely identified from its function on a subset of inputs, impacting interpretability and security.

Contribution

It provides a set of conditions for parameter identifiability in deep ReLU networks, establishing when parameters can be uniquely recovered from the network's function.

Findings

Parameters are identifiable up to permutation and positive rescaling.

Identifiability depends on network architecture and input subset.

Results enable understanding of interpretability and privacy implications.

Abstract

The possibility for one to recover the parameters-weights and biases-of a neural network thanks to the knowledge of its function on a subset of the input space can be, depending on the situation, a curse or a blessing. On one hand, recovering the parameters allows for better adversarial attacks and could also disclose sensitive information from the dataset used to construct the network. On the other hand, if the parameters of a network can be recovered, it guarantees the user that the features in the latent spaces can be interpreted. It also provides foundations to obtain formal guarantees on the performances of the network. It is therefore important to characterize the networks whose parameters can be identified and those whose parameters cannot. In this article, we provide a set of conditions on a deep fully-connected feedforward ReLU neural network under which the parameters of the network are uniquely identified-modulo permutation and positive rescaling-from the function it implements on a subset of the input space.