In many applications, we desire neural networks to exhibit invariance or equivariance to
certain groups due to symmetries inherent in the data. Recently, frame-averaging methods …

Simplicial complexes are generalizations of classical graphs. Their homology groups are
widely used to characterize the structure and the topology of data in eg chemistry …

Spectral clustering is a well-known technique which identifies k clusters in an undirected
graph, with n vertices and weight matrix W∈ R n× n, by exploiting its graph Laplacian L (W) …

Complex networks are used as a tool for data representation and model a wide range of
natural and artificial systems and networks with their many interdependent components. The …

Clustering is an unsupervised machine learning technique that serves to extract patterns in
unlabeled datasets by grou** their elements based on a similarity measure. A priori …

We show that, with very high probability, the random graph Laplacian has simple spectrum.
Our method provides a quantitatively effective estimate of the spectral gaps. Along the way …

With the advent of quantum and quantum-inspired machine learning, adapting the structure
of learning models to match the structure of target datasets has been shown to be crucial for …

The problem of multiway partitioning of an undirected graph is considered. A spectral
method is used, where the largest eigenvalues of the normalized adjacency matrix …

Identifying building conditions for user safety is an urgent matter, especially in earthquake-
prone areas. Clustering buildings according to their conditions in the categories of danger …

We study problems of robustness of linear stability under structured matrix perturbations.
Perturbations are restricted to lie in a prescribed structure space, which can be an arbitrary …