26 citations · 37 across the 19 of their papers we have counts for
9 papers · 1 filter
Approximation Theory for Lipschitz Continuous Transformers
Takashi Furuya, Davide Murari, Carola-Bibiane Schönlieb
Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz const…
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…
Symplectic Neural Flows for Modeling and Discovery
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulation…
Hamiltonian Matching for Symplectic Neural Integrators
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical…
Resilient Graph Neural Networks: A Coupled Dynamical Systems Approach
Moshe Eliasof, Davide Murari, Ferdia Sherry +1
Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to inp…
Designing Stable Neural Networks using Convex Analysis and ODEs
Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt +3
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lip…
Dynamical systems' based neural networks
Elena Celledoni, Davide Murari, Brynjulf Owren +2
Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is…