On the Translocation of Masses

By L. Kantorovich. 2006

1,540 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Mathematical Optimization

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Citations in the corpus

Unified Scaling Laws for Routed Language Models (2022, methodology): “If 500 billion tokens is a lower bound to the convergence point of 15M, the analysis in Kaplan et al. [2020] would predict needing trillions of tokens to converge 1.”
Model Fusion via Optimal Transport (2019, methodology): “Our method relies on optimal transport (OT) [1, 2], to minimize the transportation cost of neurons present in the layers of individual models, measured by the similarity of activations or incoming weights.”
Theoretical Analysis of Domain Adaptation with Optimal Transport (2016, methodology): “In this section, we first present the formalization of the Monge-Kantorovich [13] optimization problem and show how optimal transportation problem found its application in DA.”
Optimal Transport for Domain Adaptation (2014, background): “The problem reappeared in the middle of the 20th century in the work of Kantorovitch [30] and found recently surprising new developments as a polyvalent tool for several fundamental problems [49].”
Overcoming Negative Transfer: A Survey (2020, methodology): “A relaxation of this assumption is the Kantorovich formulation [72] where we allow the mass at x to be split and move to more than one location.”
Sorting through Search and Matching Models in Economics (2017, background): “This social planner’s problem for the matching literature dates back to the early work by Monge (1781) and Kantorovic (1942) on the mass transportation problem, and to Koopmans and Beckmann (1957) who introduced a pricing system to solve the problem.”
Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm (2018, methodology): “Approximating the OT distance amounts to solving the OT problem (Kantorovich, 1942): where X is transportation plan , C ∈ R n n + is a given ground cost matrix, r, c ∈ R n are given vectors from the probability simplex ∆ n , 1 is the vector of all ones.”
Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces (2018, background): “The problem of optimal transport can be traced back to [30] and [23].”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, background): “In 1942, together with the linear programming problem (Kantorovich [27]), Kantorovich [26] tackled Monge’s problem originally brought up in the study of optimal transport.”
Context Mover's Distance & Barycenters: Optimal transport of contexts for building representations (2018, background): “This allows us to cast ﬁnding distance between entities as an instance of the Optimal Transport problem (Monge, 1781; Kantorovich, 1942; Villani, 2008).”
Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation (2019, methodology): “Kantorovitch [27] proposed a relaxed version of Eq 4, which seeks a transportation plan of a joint probability distribution γ ∈ P(Ω× Ω) such that”