Summary of Approximation Error and Complexity Bounds For Relu Networks on Low-regular Function Spaces, by Owen Davis et al.
Approximation Error and Complexity Bounds for ReLU Networks on Low-Regular Function Spaces
by Owen Davis, Gianluca Geraci, Mohammad Motamed
First submitted to arxiv on: 10 May 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 The paper explores the approximation capabilities of ReLU neural networks in approximating large classes of bounded functions, without relying on strong regularity assumptions. The authors demonstrate that the approximation error can be upper-bounded by a quantity proportional to the uniform norm of the target function and inversely proportional to the product of network width and depth. This result is inherited from Fourier features residual networks, which utilize complex exponential activation functions. The proof is constructive and involves a careful analysis of the complexity associated with approximating a Fourier features residual network using a ReLU network. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how neural networks called ReLU networks can be used to approximate certain types of functions. It shows that these networks are good at this job, as long as they have enough layers and neurons. This is important because it means we can use ReLU networks for many different tasks, such as image recognition or speech recognition. |
Keywords
» Artificial intelligence » Relu » Residual network
