Summary of Universal Approximation Results For Neural Networks with Non-polynomial Activation Function Over Non-compact Domains, by Ariel Neufeld et al.
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains
by Ariel Neufeld, Philipp Schmocker
First submitted to arxiv on: 18 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE); Classical Analysis and ODEs (math.CA)
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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 explores the capabilities of single-hidden-layer feedforward neural networks in approximating complex functions, particularly in unbounded domains. By assuming non-polynomial activation functions, researchers establish universal approximation results within various function spaces, including L^p-spaces, weighted C^k-spaces, and weighted Sobolev spaces. The findings have implications for tasks such as weighted derivative approximation. Neural networks with non-polynomial activation functions are shown to be capable of approximating functions with sufficiently regular and integrable Fourier transforms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how powerful neural networks can be in approximating complex patterns. It shows that a special type of neural network can approximate many types of functions, even those defined over large or infinite domains. This is important because it means we can use these networks to solve problems that involve big datasets or real-world applications. |
Keywords
» Artificial intelligence » Neural network
