Summary of Optimal Neural Network Approximation For High-dimensional Continuous Functions, by Ayan Maiti et al.
Optimal Neural Network Approximation for High-Dimensional Continuous Functions
by Ayan Maiti, Michelle Michelle, Haizhao Yang
First submitted to arxiv on: 4 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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 The paper presents a neural network architecture that achieves super approximation properties for continuous functions on high-dimensional spaces. The authors develop a neural network with a specific width and depth, utilizing an elementary universal activation function, which requires only a fixed number of neurons to approximate arbitrary accuracy. The construction leverages the Kolmogorov Superposition Theorem and achieves the super approximation property using at most 10,889d + 10887 unique nonzero parameters. This is compared to other approximation methods that may require exponentially growing parameters with increasing input dimension. The paper’s findings have implications for the number of neurons or parameters required in neural networks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research creates a special kind of artificial intelligence network that can get really good at approximating certain types of functions, even if those functions are very complex and operate on many variables. To do this, the researchers use a unique combination of mathematical formulas and computer code to create a network with a specific structure. This allows the network to learn and become more accurate without needing to use too much computational power or memory. The study shows that this type of network can be very efficient and effective at achieving good results, which could lead to breakthroughs in fields like science, medicine, and technology. |
Keywords
» Artificial intelligence » Neural network
