Summary of Provable Convergence and Limitations Of Geometric Tempering For Langevin Dynamics, by Omar Chehab et al.
Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamics
by Omar Chehab, Anna Korba, Austin Stromme, Adrien Vacher
First submitted to arxiv on: 13 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Computation (stat.CO)
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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 soundness of geometric tempering, a popular approach to sampling from challenging multi-modal probability distributions using Langevin dynamics. The authors theoretically analyze the upper and lower bounds of tempered Langevin in both continuous and discrete-time, providing optimal tempering schedules for specific pairs of proposal and target distributions. They also demonstrate that geometric tempering can suffer from poor functional inequalities and slow convergence, even when the target distribution is well-conditioned. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Geometric tempering helps us draw random numbers from complicated probability distributions by mixing two simpler ones together. This paper looks at how well this method works with Langevin dynamics, a common way to generate random numbers in machine learning. The researchers show that geometric tempering can sometimes be helpful, but other times it might not help or even make things worse. |
Keywords
* Artificial intelligence * Machine learning * Multi modal * Probability
