Characterizing and Measuring the Similarity of Neural Networks with Persistent Homology Download PDF

Published: 28 Jan 2022, Last Modified: 13 Feb 2023ICLR 2022 SubmittedReaders: Everyone
Keywords: Neural Networks, Topological Data Analysis, similarity, Persistent Homology
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 a useful similarity measure.
One-sentence Summary: We provide a method to compare and characterize Neural Networks.
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