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On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy
Aratrika Mustafi, Soumya Mukherjee
Gradient-flow sampling interprets a Gibbs distribution as the minimizer of an energy functional over probability measures and generates dynamics converging to this target. Under sp…
Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer
Aratrika Mustafi, Soumya Mukherjee, Bharath K. Sriperumbudur
We develop a gradient flow on the space of probability measures defined on matrix-valued parameters induced by regularized Muon, an analytically smoothed version of the idealized M…
Sinkhorn Based Associative Memory Retrieval Using Spherical Hellinger Kantorovich Dynamics
Aratrika Mustafi, Soumya Mukherjee
We propose a dense associative memory for empirical measures (weighted point clouds). Stored patterns and queries are finitely supported probability measures, and retrieval is defi…