Characterizing and Measuring the Similarity of Neural Networks with Persistent Homology
This provides a novel similarity measure for neural networks, addressing a poorly understood structural analysis problem in machine learning, though it appears incremental as it applies an existing topological method to a new domain.
The paper tackled the problem of characterizing and measuring similarity between neural networks by representing them as abstract simplicial complexes and using Persistent Homology to analyze topological fingerprints, showing effectiveness as a descriptor across various architectures and datasets.
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.