Alternating projections on cleanly intersecting C^{2,1} submanifolds induce a retraction (second-order under C^{3,1}) on the intersection, with NewtonSLRA as an explicit second-order example.
Cambridge University Press, 2023
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Iso-Riemannian descent algorithm with convergence analysis under iso-convexity, iso-monotonicity and iso-Lipschitz conditions for optimization on learned Riemannian manifolds from data.
Heat kernel Sinkhorn algorithm on the 2-sphere converges to OT cost with O(n) memory and O(n^{3/2}) time per iteration, retaining geometric properties and applied to climate model evaluation.
DOODL learns a dictionary of spectral dynamics to approximate a manifold of related dynamical systems, enabling compact representations and improved operator estimation from short or partial trajectories.
NS-RGS uses Newton-Schulz iterations to avoid costly matrix decompositions in Riemannian optimization for orthogonal group synchronization, proving linear convergence with spectral initialization and showing 2x practical speedup.
citing papers explorer
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Retractions by Alternating Projections
Alternating projections on cleanly intersecting C^{2,1} submanifolds induce a retraction (second-order under C^{3,1}) on the intersection, with NewtonSLRA as an explicit second-order example.
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Iso-Riemannian Optimization on Learned Data Manifolds
Iso-Riemannian descent algorithm with convergence analysis under iso-convexity, iso-monotonicity and iso-Lipschitz conditions for optimization on learned Riemannian manifolds from data.
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Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons
Heat kernel Sinkhorn algorithm on the 2-sphere converges to OT cost with O(n) memory and O(n^{3/2}) time per iteration, retaining geometric properties and applied to climate model evaluation.
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Geometric Dictionary Learning of Dynamical Systems with Optimal Transport
DOODL learns a dictionary of spectral dynamics to approximate a manifold of related dynamical systems, enabling compact representations and improved operator estimation from short or partial trajectories.
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NS-RGS: Newton-Schulz based Riemannian gradient method for orthogonal group synchronization
NS-RGS uses Newton-Schulz iterations to avoid costly matrix decompositions in Riemannian optimization for orthogonal group synchronization, proving linear convergence with spectral initialization and showing 2x practical speedup.