Optimal Transport

By Gershon Wolansky. 2021

1,077 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9d76967a2d7c7deb0d2a4786d4715dd6bf033f55

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In Mechanical Engineering

Citations in the corpus

Trainability and Accuracy of Artificial Neural Networks: An Interacting Particle System Approach (2018, background): “9) is the GD flow in the Wasserstein metric [1,35].”
Bayesian Learning with Wasserstein Barycenters (2018, methodology): “where P(X ) is the set of probability measures on X , p ≥ 1 and Wp is the celebrated p-Wasserstein distance on probability measures on X associated with d, see [45, 46].”
Meta-Learning with Neural Tangent Kernels (2021, neutral): “In this paper, we use notation∇ftF(f ), instead of∇HF(f ), to denote the general function derivative of the energy functional F with respect to function f t (Villani, 2008).”
A proof of the Caffarelli contraction theorem via entropic regularization (2019, neutral): “Let us recall some classical facts about quadratic transport that will be used in the proof (see [42, 43] for proofs and more general statements).”
Stability of martingale optimal transport and weak optimal transport (2019, neutral): “A classical result in optimal transport asserts that π ∈ Π(μ, ν) is optimal for (OT) iff its support supp π is c-cyclically monotone [42, 43].”
Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces (2015, methodology): “First, let us recall the notion of CD(K,∞) space introduced independently by Lott-Villani [42] and Sturm [51] (see also [55] for a comprehensive treatment).”
Existence, duality, and cyclical monotonicity for weak transport costs (2018, background): “Besides primal existence and duality, another fundamental result in classical optimal transport is the characterization of optimality through the notion of cyclical montonicity; see [27, 16] as well as the monographs [28, 35, 36].”
Defense Against Adversarial Attacks Using Feature Scattering-based Adversarial Training (2019, background): “For comprehensive historical and computational perspective of OT, we refer to [60, 45].”