Local Identifiability of Fully-Connected Feed-Forward Networks with Nonlinear Node Dynamics

TL;DR

This paper proves that fully-connected layered feed-forward networks with nonlinear node dynamics are generically locally identifiable through partial excitation and measurement, even when most nodes are unexcited and unmeasured, broadening understanding of network identifiability.

Contribution

It establishes the local identifiability of a broad class of nonlinear feed-forward networks with partial observations, extending previous results to more general functions and topologies.

Findings

Identifiability holds for fully-connected layered networks with nonlinear nodes.

Partial excitation and measurement suffice for local identifiability.

The results apply to neural networks with no offsets and analytic functions crossing the origin.

Abstract

We study the identifiability of nonlinear network systems with partial excitation and partial measurement when the network dynamics is linear on the edges and nonlinear on the nodes. We assume that the graph topology and the nonlinear functions at the node level are known, and we aim to identify the weight matrix of the graph. Our main result is to prove that fully-connected layered feed-forward networks are generically locally identifiable by exciting sources and measuring sinks in the class of analytic functions that cross the origin. This holds even when all other nodes remain unexcited and unmeasured and stands in sharp contrast to most findings on network identifiability requiring measurement and/or excitation of each node. The result applies in particular to feed-forward artificial neural networks with no offsets and generalizes previous literature by considering a broader class of functions and topologies.