Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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Cambridge University Press, Cambridge, UK (2023)
26 Pith papers cite this work, alongside 421 external citations. Polarity classification is still indexing.
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representative citing papers
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
The Riemannian Multiobjective Proximal Gradient Method (RMPGM) directly optimizes vector-valued composite objectives on Riemannian manifolds and converges globally to Pareto stationary points with an O(1/k) rate.
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
Under fixed innovation coupling, finite-horizon optimizers admit minimal pathwise realizations and incidence-identifiable Möbius effects, with a five-term readout transfer from hidden relaxation and a closed reduced-value factorial experiment.
RDGC is the least affine-invariant length of an admissible metric path to a Hessian-relative condition target, with global Green and bordered Jacobi–KKT response laws on Hadamard path space.
LoRA-Muon applies Muon's spectral steepest descent to low-rank factors with split weight decay, acting as a transferable proxy for full-rank Muon and Shampoo optimizers.
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
Establishes Riemannian gradient flow equivalence for neural MMS steps, linear convergence under convexity conditions, and O(δ) tracking bounds for inexact iterates.
Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann manifolds.
A Riemannian L-BFGS method with adapted Cauchy-point bound handling outperforms classical interior-point and L-BFGS-B solvers on mixed manifold-plus-bounds problems by orders of magnitude.
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
Negative curvature makes barrier parameters for geodesic balls and triangles in hyperbolic space grow polynomially with diameter, blocking efficient interior-point methods for exponentially large domains in scaling problems.
A Grassmannian-metric-ball model of data uncertainty yields a closed-form robust least-squares solver that strengthens robustness and scaling in finite-horizon data-driven predictive control.
A Riemannian variable-projection method computes the nearest matrix with multiple eigenvalues (and structured variants) by minimizing a closed-form objective over the Stiefel manifold.
A new adaptive two-metric projection method for ℓ1 minimization with global convergence, finite-time manifold identification, and superlinear local rate under an error bound condition.
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
A nonmonotone subgradient algorithm is developed for upper-C^2 optimization on submanifolds with stationarity and KL-based convergence guarantees.
Riemannian conditional gradient methods are introduced for composite optimization on manifolds, achieving O(1/k) convergence for adaptive and diminishing steps and O(1/ε²) iteration complexity for Armijo steps.
On the random-field XY model, Riemannian Monotonic Basin Hopping finds lower-energy states than MultiStart at lower computational cost in the tested L=10–32 instances.
citing papers explorer
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Fast Computation of Free-Support Wasserstein Medians
Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
-
Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
-
A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds
The Riemannian Multiobjective Proximal Gradient Method (RMPGM) directly optimizes vector-valued composite objectives on Riemannian manifolds and converges globally to Pareto stationary points with an O(1/k) rate.
-
Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
-
A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
-
Profile Likelihood Inference for Anisotropic Hyperbolic Wrapped Normal Models on Hyperbolic Space
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
-
Diffusion Processes on Implicit Manifolds
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
-
Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions
Under fixed innovation coupling, finite-horizon optimizers admit minimal pathwise realizations and incidence-identifiable Möbius effects, with a five-term readout transfer from hidden relaxation and a closed reduced-value factorial experiment.
-
Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response
RDGC is the least affine-invariant length of an admissible metric path to a Hessian-relative condition target, with global Green and bordered Jacobi–KKT response laws on Hadamard path space.
-
LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold
LoRA-Muon applies Muon's spectral steepest descent to low-rank factors with split weight decay, acting as a transferable proxy for full-rank Muon and Shampoo optimizers.
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Operator-norm bounds and a quadratic lower-growth example for the special Euclidean algebra se(3)
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
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Wasserstein Least Squares: A Canonical Regression Method for Probability Distributions
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
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Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework
Establishes Riemannian gradient flow equivalence for neural MMS steps, linear convergence under convexity conditions, and O(δ) tracking bounds for inexact iterates.
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Nystr\"om Approximation on Manifolds
Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann manifolds.
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A Riemannian quasi-Newton algorithm for optimization with Euclidean bounds
A Riemannian L-BFGS method with adapted Cauchy-point bound handling outperforms classical interior-point and L-BFGS-B solvers on mixed manifold-plus-bounds problems by orders of magnitude.
-
Scale selection for geometric medians on product manifolds
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
-
Negative curvature obstructs the existence of good barriers for interior-point methods
Negative curvature makes barrier parameters for geodesic balls and triangles in hyperbolic space grow polynomially with diameter, blocking efficient interior-point methods for exponentially large domains in scaling problems.
-
Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach
A Grassmannian-metric-ball model of data uncertainty yields a closed-form robust least-squares solver that strengthens robustness and scaling in finite-horizon data-driven predictive control.
-
Nearest matrix with multiple eigenvalues by Riemannian optimization
A Riemannian variable-projection method computes the nearest matrix with multiple eigenvalues (and structured variants) by minimizing a closed-form objective over the Stiefel manifold.
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On the resolution of $\ell_1$-norm minimization via a two-metric adaptive projection method
A new adaptive two-metric projection method for ℓ1 minimization with global convergence, finite-time manifold identification, and superlinear local rate under an error bound condition.
-
Density Evolution: A Multiscale View of Density Estimation
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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A Nonmonotone Descent Method for Optimization Problems Defined by Upper-$\mathcal{C}^2 $ Functions over Submanifolds
A nonmonotone subgradient algorithm is developed for upper-C^2 optimization on submanifolds with stationarity and KL-based convergence guarantees.
-
Riemannian conditional gradient methods for composite optimization problems
Riemannian conditional gradient methods are introduced for composite optimization on manifolds, achieving O(1/k) convergence for adaptive and diminishing steps and O(1/ε²) iteration complexity for Armijo steps.
-
Nonconvex optimization methods for ground states in disordered continuous-spin models
On the random-field XY model, Riemannian Monotonic Basin Hopping finds lower-energy states than MultiStart at lower computational cost in the tested L=10–32 instances.
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Entanglement is Half the Story: Post-Selection vs. Partial Traces
A hybrid tensor network framework interpolates between classical and quantum models via controllable post-selection, with a trainable hyperparameter that complements bond dimension to enhance quantum machine learning.
- Generalization of Zeroth-Order Method for Quotients of Quadratic Functions