Summary of Score-based Generative Models Break the Curse Of Dimensionality in Learning a Family Of Sub-gaussian Probability Distributions, by Frank Cole et al.
Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions
by Frank Cole, Yulong Lu
First submitted to arxiv on: 12 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 delves into the mathematical foundations of score-based generative models (SGMs) and analyzes their approximation and generalization capabilities. Specifically, it introduces a notion of complexity for probability distributions based on their relative density with respect to the standard Gaussian measure. The authors prove that if the log-relative density can be locally approximated by a neural network with suitably bounded parameters, then the distribution generated by empirical score matching approximates the target distribution in total variation at a dimension-independent rate. The theory is illustrated through examples involving certain mixtures of Gaussians. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks into how well computer programs called score-based generative models (SGMs) can create new images that are realistic and similar to real-life pictures. SGMs have done really well in making big images, but we still don’t fully understand why they work so well. This paper helps us figure out why by looking at the math behind how these programs make predictions. It shows that if we can make a simple computer program approximate certain measurements of an image, then the SGM will be able to create new pictures that are close to real-life ones. The authors also give some examples of this working with different types of images. |
Keywords
* Artificial intelligence * Generalization * Neural network * Probability
