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math.NA2026
1-Lipschitz Neural Networks on Hadamard Manifolds
Davide Murari, Marta Ghirardelli, Ben Adcock +3
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…
math.NA2025
Conditional Stability of the Euler Method on Riemannian Manifolds
Marta Ghirardelli, Brynjulf Owren, Elena Celledoni
We derive nonlinear stability results for numerical integrators on Riemannian manifolds, by imposing conditions on the ODE vector field and the step size that makes the numerical s…
math.NA2023
Optimization via conformal Hamiltonian systems on manifolds
Marta Ghirardelli
In this work we propose a method to perform optimization on manifolds. We assume to have an objective function defined on a manifold and think of it as the potential energy of…