Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energies

arXiv:2609.27008 · math.AP, cs.LG, math.OC · Submitted 2026-09-22 · Read on arXiv

math.AP, cs.LG, math.OC

Submitted: 2026-09-22

Updated: 2026-09-22

Terminology

• Gradient Flow — 30× in this paper · explained in 2 episodes
• Transformer — 9× in this paper · explained in 2 episodes
• Aggregation — 4× in this paper · explained in 1 episode
• Clustering — 4× in this paper · explained in 2 episodes
• Transformer Models — 4× in this paper · explained in 2 episodes
• Initial Data — 3× in this paper · explained in 2 episodes
• American Mathematical Society — 2× in this paper
• Degeneracy — 2× in this paper · explained in 3 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Adversarial Training — 1× in this paper · explained in 1 episode
• Distribution Matching — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Mean-Field Dynamics — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes

Sources

• Propagation of Chaos in Contextual Flow Maps
• Quantitative Clustering in Mean-Field Transformer Models
• Quantitative Convergence of Wasserstein Gradient Flows of Kernel Mean Discrepancies
• Wasserstein gradient flows for Coulomb discrepancies
• Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels

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