Summary of Interpolation with Deep Neural Networks with Non-polynomial Activations: Necessary and Sufficient Numbers Of Neurons, by Liam Madden
Interpolation with deep neural networks with non-polynomial activations: necessary and sufficient numbers of neurons
by Liam Madden
First submitted to arxiv on: 22 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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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 minimum number of neurons required for feedforward neural networks to interpolate input-output pairs from high-dimensional spaces. It shows that a surprisingly small number of neurons, proportional to the square root of the input dimension and the number of data points, is sufficient for successful interpolation. This result holds regardless of the activation function used, as long as it’s real analytic at a point and not polynomial. The study has implications for choosing suitable activation functions for specific problems without sacrificing interpolation power. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about how many neurons are needed in artificial intelligence to create a special type of network that can accurately predict new data based on old data. It turns out that surprisingly few neurons are needed, and the number depends on the size of the input data and the number of training examples. The good news is that this result applies to most types of activation functions used in these networks. |
