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A logifold structure on measure space (2405.05492v3)
Published 9 May 2024 in math.DG, cs.AI, cs.LG, and math.PR
Abstract: In this paper,we develop a local-to-global and measure-theoretical approach to understand datasets. The idea is to take network models with restricted domains as local charts of datasets. We develop the mathematical foundations for these structures, and show in experiments how it can be used to find fuzzy domains and to improve accuracy in data classification problems.
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