Piero Deidda

activity

20222025

collaborators

8 papers

cs.LG2025

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…

math.DS2025

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…

math.SP2025

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…

cs.LG2025

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…

math.SP2024

The graph $\infty$ -Laplacian eigenvalue problem

Piero Deidda, Martin Burger, Mario Putti +1

We analyze various formulations of the $\infty$ -Laplacian eigenvalue problem on graphs, comparing their properties and highlighting their respective advantages and limitations. Fir…

math.NA2024

Graph $p$ -Laplacian eigenpairs as saddle points of a family of spectral energy functions

Piero Deidda, Nicola Segala, Mario Putti

We address the problem of computing the graph $p$ -Laplacian eigenpairs for $p \in (2, \infty)$ . We propose a reformulation of the graph $p$ -Laplacian eigenvalue problem in terms of a…

cs.LG2024

Provable Emergence of Deep Neural Collapse and Low-Rank Bias in $L^{2}$ -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…

math.NA2022

Nodal domain count for the generalized graph $p$ -Laplacian

Piero Deidda, Mario Putti, Francesco Tudisco

Inspired by the linear Schrödinger operator, we consider a generalized $p$ -Laplacian operator on discrete graphs and present new results that characterize several spectral properti…

Stuart-Landau Oscillatory Graph Neural Network

Nonlinear Joint Spectral Radius

Nonlinear spectral graph theory

Are We Measuring Oversmoothing in Graph Neural Networks Correctly?

The graph ∞-Laplacian eigenvalue problem

Graph p-Laplacian eigenpairs as saddle points of a family of spectral energy functions

Provable Emergence of Deep Neural Collapse and Low-Rank Bias in L2-Regularized Nonlinear Networks

Nodal domain count for the generalized graph p-Laplacian

The graph $\infty$ -Laplacian eigenvalue problem

Graph $p$ -Laplacian eigenpairs as saddle points of a family of spectral energy functions

Provable Emergence of Deep Neural Collapse and Low-Rank Bias in $L^{2}$ -Regularized Nonlinear Networks

Nodal domain count for the generalized graph $p$ -Laplacian