A Gaussian-kernel diffusion operator on feature clouds yields closed-form class affinities and spectra in Gaussian models, with provably smooth observables under perturbations.
Ricci curvature of Markov chains on metric spaces.Journal of Functional Anal- ysis, 256(3):810–864
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AD-HMC achieves geometric convergence in Wasserstein distance for HMC with general asymmetrical auxiliary momentum distributions by restoring self-adjointness via direction alternation, with extensions to leapfrog integrators.
Ollivier-Ricci curvature is extended from manifolds and undirected graphs to directed graphs with applications to graph neural networks.
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Diffusion Operator Geometry of Feedforward Representations
A Gaussian-kernel diffusion operator on feature clouds yields closed-form class affinities and spectra in Gaussian models, with provably smooth observables under perturbations.
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Hamiltonian Monte Carlo with Asymmetrical Momentum Distributions
AD-HMC achieves geometric convergence in Wasserstein distance for HMC with general asymmetrical auxiliary momentum distributions by restoring self-adjointness via direction alternation, with extensions to leapfrog integrators.
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Ollivier-Ricci Curvature of Riemannian Manifolds and Directed Graphs with Applications to Graph Neural Networks
Ollivier-Ricci curvature is extended from manifolds and undirected graphs to directed graphs with applications to graph neural networks.