1-Lipschitz Neural Networks on Hadamard Manifolds
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 spaces. In this work, we construct and analyze a class of 1-Lipschitz neural networks on Hadamard manifolds. Our layers are of gradient-descent type, $1$-Lipschitz, and quasi-$α$-firmly nonexpansive. The core building blocks of the proposed architecture are Busemann functions, and we exploit the properties of Busemann gradient flows to design $1$-Lipschitz geometry-preserving layers. We provide explicit constructions and
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- PossiblePossibly related (embedding) · 50%Hamiltonian Neural Networks from a Differential Geometry Perspective [D] →
- PossiblePossibly related (embedding) · 47%Context and average best linear mappings [D] →
- LinkedLinked via arxiv author · 85%Davide Murari →
“1-Lipschitz Neural Networks on Hadamard Manifolds”
- LinkedLinked via arxiv author · 85%Marta Ghirardelli →
“1-Lipschitz Neural Networks on Hadamard Manifolds”
- LinkedLinked via arxiv author · 85%Ben Adcock →
“1-Lipschitz Neural Networks on Hadamard Manifolds”
- LinkedLinked via arxiv author · 85%Elena Celledoni →
“1-Lipschitz Neural Networks on Hadamard Manifolds”
- LinkedLinked via arxiv author · 85%Brynjulf Owren →
“1-Lipschitz Neural Networks on Hadamard Manifolds”
- LinkedLinked via arxiv author · 85%Carola-Bibiane Schönlieb →
“1-Lipschitz Neural Networks on Hadamard Manifolds”