mlsanityData to 14 Oct 2026

Interaction-Force Transport Gradient Flows

arXiv 2405.17075 ↗First posted 27 May 2024cs.LG math.AP stat.MLcited by 9

Not on the map. Why?

Abstract (arXiv)

This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by reproducing kernels. Using a precise connection between the Hellinger geometry and the maximum mean discrepancy (MMD), we propose the interaction-force transport (IFT) gradient flows and its spherical variant via an infimal convolution of the Wasserstein and spherical MMD tensors. We then develop a particle-based optimization algorithm based on the JKO-splitting scheme of the mass-preserving spherical IFT gradient flows. Finally, we provide both theoretical global exponential convergence guarantees and improved empirical simulation results for applying the IFT gradient flows to the sampling task of MMD-minimization. Furthermore, we prove that the spherical IFT gradient flow enjoys the best of both worlds by providing the global exponential convergence guarantee for both the MMD and KL energy.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 23 of its 58 references that are in the map. First posted on arXiv 27 May 2024.

Builds on

23 of 58 references.

References · 23

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 507
  3. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 364
  4. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 337
  5. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 291
  6. 2015Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measurescited by 139
  7. 2019Maximum Mean Discrepancy Gradient Flowcited by 127
  8. 2019On the geometry of Stein variational gradient descentcited by 82
  9. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
  10. 2021Kernel Stein Discrepancy Descentcited by 57
  11. 2019Sparse Optimization on Measures with Over-parameterized Gradient Descentcited by 50
  12. 2017Multilevel Clustering via Wasserstein Meanscited by 49
11 more
  1. 2019Accelerating Langevin Sampling with Birth-deathcited by 45
  2. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
  3. 2023Generative Sliced MMD Flows with Riesz Kernelscited by 37
  4. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  5. 2023Learning Gaussian Mixtures Using the Wasserstein-Fisher-Rao Gradient Flowcited by 27
  6. 2015Provable Bayesian Inference via Particle Mirror Descentcited by 23
  7. 2015Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filteringcited by 22
  8. 2020Estimating Barycenters of Measures in High Dimensionscited by 18
  9. 2024Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spacescited by 15
  10. 2020MMD-Regularized Unbalanced Optimal Transportcited by 8
  11. 2022A blob method for inhomogeneous diffusion with applications to multi-agent control and samplingcited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 2; 2026: 5.

9 papers.

  1. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flowscited by 12
  2. 2024Stein transport for Bayesian inferencecited by 11
  3. 2024Kernel Approximation of Fisher-Rao Gradient Flowscited by 7
  4. 2025Hellinger-Kantorovich Gradient Flows: Global Exponential Decay of Entropy Functionalscited by 7
  5. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 2
  6. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  7. 2026Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimizationcited by 0
  8. 2026Kernel-based External Validity of Experimental Studiescited by 0
  9. 2026On the Optimisation Landscape of Overparameterised Weighted MMDcited by 0