Abstract Graph Neural Networks (GNNs) are limited in their expressive power, struggle with
long-range interactions and lack a principled way to model higher-order structures. These …

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 …

The Language of Thought (LoT) hypothesis proposes that some collections of mental states
and processes are symbol systems to explain language-like systematic properties of …

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 …

Graph neural networks (GNNs) have demonstrated significant promise in modelling
relational data and have been widely applied in various fields of interest. The key …

Simplicial complexes can be viewed as high dimensional generalizations of graphs that
explicitly encode multi-way ordered relations between vertices at different resolutions, all at …

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a
given graph topology by dynamically learning it. However, most of LGI methods assume to …

In this expository paper, we want to give a brief introduction, with few key references for
further reading, to the inner functioning of the new and successful algorithms of Deep …

Persistent topological Laplacians constitute a new class of tools in topological data analysis
(TDA), motivated by the necessity to address challenges encountered in persistent …