Cellular sheaves equip graphs with a``geometrical''structure by assigning vector spaces and
linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph …

Higher-order relations are widespread in nature, with numerous phenomena involving
complex interactions that extend beyond simple pairwise connections. As a result …

Abstract A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that
operates on a sheaf, an object that equips a graph with vector spaces over its nodes and …

In this paper, we unite concepts from Husserlian phenomenology, the active inference
framework in theoretical biology, and category theory in mathematics to develop a …

Attention has become a central inductive bias for deep learning models irrespective of
domain. However, increasing theoretical and empirical evidence suggests that Graph …

Abstract Systems neuroscience is facing an ever-growing mountain of data. Recent
advances in protein engineering and microscopy have together led to a paradigm shift in …

We consider a nonlinear flow on simplicial complexes related to the simplicial Laplacian and
show that it is a generalization of various consensus and synchronization models commonly …

Cyber-physical systems require the construction and management of various models to
assure their correct, safe, and secure operation. These various models are necessary …

The types of spaces where data resides-graphs, meshes, grids, manifolds-are becoming
increasingly varied and heterogeneous. Therefore, translating ideas, models, and …

Higher-order networks encode the many-body interactions existing in complex systems,
such as the brain, protein complexes, and social interactions. Simplicial complexes are …