8 papers
1-Lipschitz Neural Networks on Hadamard Manifolds
Davide Murari, Marta Ghirardelli, Ben Adcock +4
Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability. Most existing constraining strategies are designed for Euclidean space…
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…
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…
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…
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…