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Yang-Mills-Higgs: A Geometric Theory of Binary Labels on Non-Contractible Spaces
We reformulate binary classification on a manifold M as a Yang-Mills-Higgs variational problem. Labelled data is encoded as a functor from the fundamental groupoid of M to the one-object groupoid B(Z_2), whose monodromy class in H^1(M, Z_2) is a topological obstruction to realising the classifier by
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