most citedThe Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Above

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math.DG2026

Yang-Mills-Higgs: A Geometric Theory of Binary Labels on Non-Contractible Spaces

Catalin Vasii

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-…

math.DG2026

From Gradient Descent to Potential Theory: A Geometric Dictionary for Binary Classification

Catalin Vasii

We propose a dictionary between binary classification in machine learning and classical potential theory on vector bundles. Classifiers are parallel sections of vector bundles over…

math.DG2006★ 1 cited

The Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Above

Catalin C. Vasii

In this paper it is proven that the volume entropy of a riemannian metric evolving by the Ricci flow, if does not collapse, nondecreases. Therefore, it provides a sufficient condit…