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Summary of Forward-euler Time-discretization For Wasserstein Gradient Flows Can Be Wrong, by Yewei Xu et al.


Forward-Euler time-discretization for Wasserstein gradient flows can be wrong

by Yewei Xu, Qin Li

First submitted to arxiv on: 12 Jun 2024

Categories

  • Main: Machine Learning (stat.ML)
  • Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC)

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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
The paper investigates the limitations of forward-Euler discretization in simulating Wasserstein gradient flows, focusing on the case where the energy functional is defined by the Kullback-Leibler (KL) divergence. Two counter-examples are presented, demonstrating the failure of this discretization for simple probability densities. The authors provide a brief explanation for this limitation.
Low GrooveSquid.com (original content) Low Difficulty Summary
This paper looks at a special way to calculate how things move when we’re trying to make them change in a certain way. It’s like making a plan to get from one place to another, but instead of moving through space, we’re changing what we know about something. The authors show that a common method for doing this doesn’t always work as expected, even with simple situations. They give two examples to illustrate this problem and explain why it happens.

Keywords

» Artificial intelligence  » Probability