Summary of On the Optimal Approximation Of Sobolev and Besov Functions Using Deep Relu Neural Networks, by Yunfei Yang
On the optimal approximation of Sobolev and Besov functions using deep ReLU neural networks
by Yunfei Yang
First submitted to arxiv on: 2 Sep 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Numerical Analysis (math.NA)
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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 explores the efficient approximation of functions in Sobolev spaces and Besov spaces by deep ReLU neural networks. The authors investigate how the error measured in the L^p norm is affected by network width W and depth L when approximating functions from these spaces. Building on previous works, the study generalizes the results to show that the approximation rate O((WL)^{-2s/d}) holds under certain conditions. This rate is known to be optimal up to logarithmic factors. The proof relies on a novel encoding of sparse vectors using deep ReLU networks with varied width and depth, which may have independent interest. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how well computer models can copy real functions. It looks at special kinds of computer models called neural networks that are really good at copying certain types of patterns in data. The researchers want to know how these models do when trying to copy more complicated patterns, like those found in special math spaces called Sobolev and Besov spaces. They find a way to make the models work better by using a new trick to simplify complex information. This could be useful for people who need to model real-world data that has lots of different patterns. |
Keywords
» Artificial intelligence » Relu
