Nicolas Berkouk

Dan Meller, Nicolas Berkouk

We introduce the Singular Value Representation (SVR), a new method to represent the internal state of neural networks using SVD factorization of the weights. This construction yields a new weighted graph connecting what we call spectral neurons, that correspond to specific activation patterns of classical neurons. We derive a precise statistical framework to discriminate meaningful connections between spectral neurons for fully connected and convolutional layers. To demonstrate the usefulness of our approach for machine learning research, we highlight two discoveries we made using the SVR. First, we highlight the emergence of a dominant connection in VGG networks that spans multiple deep layers. Second, we witness, without relying on any input data, that batch normalization can induce significant connections between near-kernels of deep layers, leading to a remarkable spontaneous sparsification phenomenon.

Raphael Reinauer, Matteo Caorsi, Nicolas Berkouk

One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multi-)sets of points in $\mathbb{R}^2$ and cannot be seen in a straightforward manner as vectors. In this article, we introduce $\texttt{Persformer}$, the first Transformer neural network architecture that accepts persistence diagrams as input. The $\texttt{Persformer}$ architecture significantly outperforms previous topological neural network architectures on classical synthetic and graph benchmark datasets. Moreover, it satisfies a universal approximation theorem. This allows us to introduce the first interpretability method for topological machine learning, which we explore in two examples.