7 papers
Are We Measuring Oversmoothing in Graph Neural Networks Correctly?
Kaicheng Zhang, Piero Deidda, Desmond Higham +1
Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drop…
Stuart-Landau Oscillatory Graph Neural Network
Kaicheng Zhang, David N. Reynolds, Piero Deidda +1
Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. I…
Provable Emergence of Deep Neural Collapse and Low-Rank Bias in -Regularized Nonlinear Networks
Emanuele Zangrando, Piero Deidda, Simone Brugiapaglia +2
We present a unified theoretical framework connecting the first property of Deep Neural Collapse (DNC1) to the emergence of implicit low-rank bias in nonlinear networks trained wit…
Nonlinear Joint Spectral Radius
Piero Deidda, Nicola Guglielmi, Francesco Tudisco
We introduce a nonlinear extension of the joint spectral radius (JSR) for switched discrete-time dynamical systems governed by sub-homogeneous and order-preserving maps acting on c…
The graph -Laplacian eigenvalue problem
Piero Deidda, Martin Burger, Mario Putti +1
We analyze various formulations of the -Laplacian eigenvalue problem on graphs, comparing their properties and highlighting their respective advantages and limitations. Fir…
Nonlinear spectral graph theory
Piero Deidda, Francesco Tudisco, Dong Zhang
Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defin…