Characterizing and Measuring the Similarity of Neural Networks with Persistent Homology

TL;DR

This paper introduces a novel topological data analysis method using persistent homology to characterize and measure the similarity of neural networks based on their structural properties.

Contribution

It proposes a persistent homology-based representation for neural networks, providing a new way to compare and analyze their structural similarities.

Findings

Effective in distinguishing different neural network architectures

Applicable across multiple datasets

Provides a topological 'fingerprint' for neural networks

Abstract

Characterizing the structural properties of neural networks is crucial yet poorly understood, and there are no well-established similarity measures between networks. In this work, we observe that neural networks can be represented as abstract simplicial complex and analyzed using their topological 'fingerprints' via Persistent Homology (PH). We then describe a PH-based representation proposed for characterizing and measuring similarity of neural networks. We empirically show the effectiveness of this representation as a descriptor of different architectures in several datasets. This approach based on Topological Data Analysis is a step towards better understanding neural networks and serves as a useful similarity measure.