Summary of Universal Approximation Theorem For Vector- and Hypercomplex-valued Neural Networks, by Marcos Eduardo Valle et al.
Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks
by Marcos Eduardo Valle, Wington L. Vital, Guilherme Vieira
First submitted to arxiv on: 4 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Neural and Evolutionary Computing (cs.NE)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| 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 research paper presents an extension to the universal approximation theorem for a wide range of vector-valued neural networks. Building on existing work, the authors demonstrate that neural networks with one hidden layer can approximate continuous functions on compact sets with any desired precision, even when operating on complex and hypercomplex values. The findings support the use of neural networks in various applications, including regression and classification tasks. By introducing the concept of non-degenerate algebra, the paper provides a framework for understanding the universal approximation theorem’s applicability to vector-valued models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper shows that special kinds of computer programs called neural networks can get really good at learning and making predictions. It says that these networks can approximate any continuous function, which means they can make very accurate guesses about things like how tall someone might be based on their height when they were 10 years old. The researchers are exploring ways to use these networks with special kinds of math called complex numbers and quaternions, which could help them learn even more things. This is important because it could lead to new discoveries in areas like medicine and self-driving cars. |
Keywords
* Artificial intelligence * Classification * Precision * Regression
