[Dottorcomp] Seminari di Matematica Applicata, 01/04/2025

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 1 Aprile 2025, alle ore 15 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Stefano Coniglio (Università di Bergamo)

terrà un seminario dal titolo:

Advances in Spectral Graph and Hypergraph Learning: Towards More Expressive
Laplacian Matrices.

Abstract: Graphs and hypergraphs have gained increasing attention in deep
learning due to their effectiveness in modeling complex relationships
across various domains, including chemistry, biology, and social network
analysis. Hypergraphs, in particular, are crucial to capture real-world
phenomena that involve polyadic (many-to-many) relationships, extending
beyond the diadic (pairwise) connections typically represented by
(standard) graphs.
In this presentation, we will provide an overview of the Graph Neural
Network (GNN) and Graph Convolutional (Neural) Network (GCN) literature,
with a focus on the construction of spectral graph-convolutional operators
that are grounded in graph signal theory. Next, we will introduce some
recent advancements we made in this area, achieved through a series of
novel graph Laplacian matrices of increasing generality. Specifically, we
will present:
– The Sign-Magnetic Laplacian and SigMaNet, a generalized GCN capable of
processing both directed and undirected graphs with unrestricted edge
weights.
– A quaternion-valued extension of the Sign-Magnetic Laplacian, designed
for graphs with digons (antiparallel edges) and asymmetric weights, along
with its corresponding GCN, QuaterGCN.
– The Generalized Directed Laplacian and GeDi-HNN, a Hypergraph Neural
Network (HNN) tailored for learning tasks where hyperedge directionality is
essential.
– The Directed Line Graph Laplacian and DLGNet, an HNN designed for
chemical-reaction classification, where input directed hypergraphs are
transformed into directed line graphs with complex-valued edge weights.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/