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Summary of Neural Optimal Transport with Lagrangian Costs, by Aram-alexandre Pooladian et al.


Neural Optimal Transport with Lagrangian Costs

by Aram-Alexandre Pooladian, Carles Domingo-Enrich, Ricky T. Q. Chen, Brandon Amos

First submitted to arxiv on: 1 Jun 2024

Categories

  • Main: Machine Learning (cs.LG)
  • Secondary: Machine Learning (stat.ML)

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GrooveSquid.com Paper Summaries

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Summary difficulty Written by Summary
High Paper authors High Difficulty Summary
Read the original abstract here
Medium GrooveSquid.com (original content) Medium Difficulty Summary
This paper investigates the optimal transport problem between probability measures, considering a least action principle (Lagrangian cost) that accounts for geometric constraints in physical systems. The authors demonstrate efficient computation of geodesics and spline-based paths, which has not been achieved before even in low-dimensional problems. The formulation also outputs Lagrangian optimal transport maps without requiring an ODE solver, unlike prior work. The paper’s effectiveness is demonstrated on low-dimensional examples from prior research.
Low GrooveSquid.com (original content) Low Difficulty Summary
This paper looks at how to move probability measures between two points in a way that uses the least amount of energy. This is important when studying systems where the movement is affected by obstacles or non-Euclidean shapes. The authors found a way to efficiently calculate these movements, which was not possible before even for simple problems. They also showed how to get the final result without needing special computer programs.

Keywords

» Artificial intelligence  » Probability