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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| 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
