26 citations · 37 across the 19 of their papers we have counts for
5 papers · 1 filter
Stable neural networks and connections to continuous dynamical systems
Matthias J. Ehrhardt, Davide Murari, Ferdia Sherry
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhanci…
Deep Network Trainability via Persistent Subspace Orthogonality
Alex Massucco, Davide Murari, Carola-Bibiane Schönlieb
Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing an…
Approximation theory for 1-Lipschitz ResNets
Davide Murari, Takashi Furuya, Carola-Bibiane Schönlieb
1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) b…
Enhancing Fourier Neural Operators with Local Spatial Features
Chaoyu Liu, Davide Murari, Lihao Liu +3
Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions…
Approximation properties of neural ODEs
Arturo De Marinis, Davide Murari, Elena Celledoni +3
We study the approximation properties of neural ordinary differential equations (neural ODEs) in the space of continuous functions. Since a neural ODE requires input and output dim…