In linear detectable settings with nondegenerate noise, the MFEnKF contracts to the Gaussian subspace at explicit rates and its uniformly continuous moments coincide almost surely with the optimal filter in large time.
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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.
AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
A new type of PDE for selective density-constrained crowd motion is obtained as the stiff limit of conservation laws, with existence of solutions proven via uniform BV estimates and compactness.
VGF solves behavior-regularized RL by transporting particles from a reference distribution to the value-induced optimal policy via discrete value-guided gradient flow.
Newton's recursive mixture estimator is a discrete gradient flow on the Fisher-Rao manifold of probability measures.
Helmholtz Distillation plus Negative Caching amortizes Energy Matching to 3D CT volumes, producing a conservative prior that improves FID and sparse-view reconstruction over pure flow baselines.
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
A λ-convex variational surrogate for shallow NN training yields global well-posedness, almost C³ regularity, and an explicit linear-system solution with 1/α generalization and O(1/N) finite-width rates.
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
wAR-Tok adds a Wasserstein-gradient-flow prior-matching term to tokenizer training so that discrete tokens become easier for autoregressive priors to model, cutting AR loss and raising generation FID on CIFAR-10 and ImageNet while keeping reconstruction quality comparable.
Galaxy evolution is cast as a geometrically constrained reaction-transport process on probability measures, using Wasserstein distance and CD(K,∞) conditions to enforce energy dissipation and interaction closure.
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
A latent-cluster quasi-Bayesian method with restarted updates yields sublinear cumulative Wasserstein-1 regret for online distributional prediction under drift and adversarial corruption.
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 quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
Establishes stability bounds for SHK flows yielding dimension-free controls on log-likelihood ratios and divergences, then applies them to time-dependent Pure-DP and Approximate-DP certificates for exponential-mechanism samplers.
Numerical experiments on McKean-Vlasov equations with attractive kernels reveal alternating aggregation-diffusion regimes in transient clustering, with density peak height only partially coupled to energetic mechanisms.
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Large-time behavior and accuracy of the Mean-Field Ensemble Kalman Filter in the Linear Detectable Setting
In linear detectable settings with nondegenerate noise, the MFEnKF contracts to the Gaussian subspace at explicit rates and its uniformly continuous moments coincide almost surely with the optimal filter in large time.
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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.
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The physics of AI weather models
AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
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A stiff limit of non-homogeneous conservation laws for crowd motion modeling
A new type of PDE for selective density-constrained crowd motion is obtained as the stiff limit of conservation laws, with existence of solutions proven via uniform BV estimates and compactness.
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Reinforcement Learning via Value Gradient Flow
VGF solves behavior-regularized RL by transporting particles from a reference distribution to the value-induced optimal policy via discrete value-guided gradient flow.
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Newton's Algorithm as a Gradient Flow: A Geometric Framework for Recursive Mixture Estimation
Newton's recursive mixture estimator is a discrete gradient flow on the Fisher-Rao manifold of probability measures.
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Projected Energy Matching for Generative 3D Priors
Helmholtz Distillation plus Negative Caching amortizes Energy Matching to 3D CT volumes, producing a conservative prior that improves FID and sparse-view reconstruction over pure flow baselines.
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Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
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Born Discrete, Made Smooth: Variational Formulation of Shallow Neural Networks
A λ-convex variational surrogate for shallow NN training yields global well-posedness, almost C³ regularity, and an explicit linear-system solution with 1/α generalization and O(1/N) finite-width rates.
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Kinetic Fokker-Planck Equations with Nonlinear Diffusion
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A Measure-Theoretic Transport Formulation of Galaxy Evolution on the Galaxy Manifold: Geometric Constraints
Galaxy evolution is cast as a geometrically constrained reaction-transport process on probability measures, using Wasserstein distance and CD(K,∞) conditions to enforce energy dissipation and interaction closure.
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Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
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Online Distributional Prediction via Latent Cluster Geometry Under Drift and Corruption
A latent-cluster quasi-Bayesian method with restarted updates yields sublinear cumulative Wasserstein-1 regret for online distributional prediction under drift and adversarial corruption.
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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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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
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On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy
Establishes stability bounds for SHK flows yielding dimension-free controls on log-likelihood ratios and divergences, then applies them to time-dependent Pure-DP and Approximate-DP certificates for exponential-mechanism samplers.
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Energetic characterisation of transient clustering dynamics in aggregation-diffusion systems
Numerical experiments on McKean-Vlasov equations with attractive kernels reveal alternating aggregation-diffusion regimes in transient clustering, with density peak height only partially coupled to energetic mechanisms.