Mattia G. Bergomi (8/29/21): Comparing Neural Networks via Generalized Persistence

Artificial neural networks are often used as black boxes to solve supervised tasks. At each layer, the network updates its representation of the dataset to minimize a given error function, depending on the correct assignment of predetermined labels to each observed data point. On the other end of the spectrum, topological persistence is commonly used to compare hand-crafted low-dimensional data representations. Here, we provide an application of rank-based persistence, a generalized persistence framework that allows us to characterize the data representation generated at each layer of an artificial neural network and compare different neural architectures. Joint with Pietro Vertechi.