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Busemann functions

techniqueactiveprovisionalbusemann-functions-48644478·1 events·first seen 2d ago

Aliases: Busemann functions

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1-Lipschitz Neural Networks on Hadamard Manifolds

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4arXiv · cs.LG·2d ago·source ↗

1-Lipschitz neural networks on Hadamard manifolds via Busemann gradient flows

A new arXiv preprint constructs and analyzes 1-Lipschitz neural networks on Hadamard manifolds, including hyperbolic spaces and the manifold of symmetric positive definite (SPD) matrices. The architecture uses Busemann functions and gradient-descent-type layers that are geometry-preserving and quasi-α-firmly nonexpansive. Experiments demonstrate robust classification on the Poincaré disk and improved covariance reconstruction on the SPD manifold compared to Log-Euclidean and data-only baselines.

AI Safety Research 1-Lipschitz Neural Networks on Hadamard Manifolds Busemann functions