May 16, 2024, 4:42 a.m. | Vladimir Jacimovic

cs.LG updates on arXiv.org arxiv.org

arXiv:2405.09453v1 Announce Type: new
Abstract: We propose the idea of using Kuramoto models (including their higher-dimensional generalizations) for machine learning over non-Euclidean data sets. These models are systems of matrix ODE's describing collective motions (swarming dynamics) of abstract particles (generalized oscillators) on spheres, homogeneous spaces and Lie groups. Such models have been extensively studied from the beginning of XXI century both in statistical physics and control theory. They provide a suitable framework for encoding maps between various manifolds and are …

abstract arxiv collective cs.lg data data sets dynamics generalized geometry machine machine learning math.mp math-ph matrix nlin.ao non-euclidean spaces swarming systems type

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