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Sponsored Artificial Intelligence: A Modern Approach, Global Edition Artificial Intelligence: A Modern Approach, Global Edition

Author

Nicholas Pischke

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Open access Aug 2026

Duality, Fréchet differentiability and Bregman distances in hyperbolic spaces

For general hyperbolic metric spaces, we introduce a new notion of a dual system (extending the influential notion from the context of normed linear spaces) that allows for a uniform study of different notions of duality for these nonlinear spaces. Using this abstract notion of duality, we lift various notions from c...

Nicholas Pischke · 4 citations
Preprint Sep 2026

Strong laws, random monotone vector fields and gradient flows on metric spaces of nonpositive curvature

Using a novel effective non-asymptotic concentration inequality, we establish a distribution-uniform generalization of Sturm's strong law of large numbers for inductive means of $L^1$-sequences of i.i.d. random variables on (separable) Hadamard spaces. Building on that, we establish a strong law of large numbers for in...

Nicholas Pischke · 0 citations
Preprint Jul 2026

A relaxed-inertial proximal point algorithm for strongly quasiconvex equilibrium problems on Hadamard manifolds

We study a proximal point type method for approximating solutions to equilibrium problems generated by pseudomonotone and strongly quasiconvex bifunctions over Hadamard manifolds, that is complete simply connected Riemannian manifolds of nonpositive sectional curvature. Next to the usual proximal step, the method we co...

Luisa Marie Després, Nicholas Pischke · 0 citations

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