12 papers
Oscillatory Neural Dynamics over Sheaves
Jan-Willem Van Looy, Alessandro Trenta, Alessio Gravina +5
Effective long-range propagation remains a central challenge in graph neural networks, as increasing a model's propagation depth does not guarantee that distant nodes effectively i…
Finite semisimplicial sets, differential graded algebras, and cellular sheaves
Jan-Willem Van Looy, Ferdinando Zanchetta
We develop a differential graded model for finite non-singular semisimplicial sets and their cellular sheaves. To a finite non-singular semisimplicial set \(S\), we associate an ex…
Cartan flow matching
Francesco Ruscelli, Ferdinando Zanchetta, Rita Fioresi
We introduce Cartan flow matching, a general framework for training flow matching models on Riemannian symmetric spaces, i.e. Riemannian manifolds with the property that at any poi…
Sheaf Neural Networks and biomedical applications
Aneeqa Mehrab, Jan Willem Van Looy, Pietro Demurtas +5
The purpose of this paper is to elucidate the theory and mathematical modelling behind the sheaf neural network (SNN) algorithm and then show how SNN can effectively answer to biom…
A Multi-Label Temporal Convolutional Framework for Transcription Factor Binding Characterization
Pietro Demurtas, Ferdinando Zanchetta, Giovanni Perini +1
Transcription factors (TFs) regulate gene expression through complex and co-operative mechanisms. While many TFs act together, the logic underlying TFs binding and their interactio…
Bioinspired CNNs for border completion in occluded images
Catarina P. Coutinho, Aneeqa Merhab, Janko Petkovic +2
We exploit the mathematical modeling of the border completion problem in the visual cortex to design convolutional neural network (CNN) filters that enhance robustness to image occ…
On Gluing Data, Finite Ringed Spaces and schemes
Rita Fioresi, Angelica Simonetti, Ferdinando Zanchetta
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In thi…
Sheaves on Graphs and their Differential Calculi
Rita Fioresi, Angelica Simonetti, Ferdinando Zanchetta
In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized…
Enhancing CNNs robustness to occlusions with bioinspired filters for border completion
Catarina P. Coutinho, Aneeqa Merhab, Janko Petkovic +2
We exploit the mathematical modeling of the visual cortex mechanism for border completion to define custom filters for CNNs. We see a consistent improvement in performance, particu…
Graph Neural Networks and Time Series as Directed Graphs for Quality Recognition
Angelica Simonetti, Ferdinando Zanchetta
Graph Neural Networks (GNNs) are becoming central in the study of time series, coupled with existing algorithms as Temporal Convolutional Networks and Recurrent Neural Networks. In…
Geometric Deep Learning: a Temperature Based Analysis of Graph Neural Networks
M. Lapenna, F. Faglioni, F. Zanchetta +1
We examine a Geometric Deep Learning model as a thermodynamic system treating the weights as non-quantum and non-relativistic particles. We employ the notion of temperature previou…
Deep Learning and Geometric Deep Learning: an introduction for mathematicians and physicists
R. Fioresi, F. Zanchetta
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 successfull algorithms of Deep L…