# Nonlinear network identifiability: The static case

arXiv: https://arxiv.org/abs/2309.06854 · HTML: https://mlsanity.com/paper/2309.06854/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [Learning Genetic Circuit Modules with Neural Networks: Full Version](https://mlsanity.com/paper/2509.19601/) (2025)

## Abstract (arXiv)

We analyze the problem of network identifiability with nonlinear functions associated with the edges. We consider a static model for the output of each node and by assuming a perfect identification of the function associated with the measurement of a node, we provide conditions for the identifiability of the edges in a specific class of functions. First, we analyze the identifiability conditions in the class of all nonlinear functions and show that even for a path graph, it is necessary to measure all the nodes except by the source. Then, we consider analytic functions satisfying f(0)=0 and we provide conditions for the identifiability of paths and trees. Finally, by restricting the problem to a smaller class of functions where none of the functions is linear, we derive conditions for the identifiability of directed acyclic graphs. Some examples are presented to illustrate the results.