arXiv Machine Learning By Vladimir Ja\' cimovi\'c

Information-Geometric Optimization on Spheres

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arXiv:2606. 07588v1 Announce Type: cross Abstract: We consider the black-box optimization problem on a sphere.

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arXiv AI
Jun 24

The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space

arXiv:2606. 24157v1 Announce Type: new Abstract: The space $\mathcal{P}_2(\mathbb{R}^d$) of probability measures with finite second moment carries a natural geometry: the quadratic Wasserstein distance W_2 makes it a complete metric space and, following Otto, a (formal) Riemannian manifold whose geodesics are the optimal-transport interpolations.

By Yian Yao, Weiwei Zhang
arXiv AI
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Finding Kissing Numbers with Game-theoretic Reinforcement Learning

arXiv:2511. 13391v4 Announce Type: replace-cross Abstract: Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a defining challenge in discrete geometry.

By Chengdong Ma, Th\'eo Tao Zhaowei, Pengyu Li, Minghao Liu, Haojun Chen, Zihao Mao, Bo Li, Yuan Cheng, Yuan Qi, Yaodong Yang