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

Characterizing and Measuring the Similarity of Neural Networks with Persistent Homology