Summary of On the Growth Of the Parameters Of Approximating Relu Neural Networks, by Erion Morina and Martin Holler
On the growth of the parameters of approximating ReLU neural networks
by Erion Morina, Martin Holler
First submitted to arxiv on: 21 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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 paper investigates fully connected feedforward ReLU neural networks as they approximate smooth functions. Unlike previous studies on universal approximation properties, this work focuses on the asymptotic growth of parameters in approximating networks. The results have implications for error analysis and consistency in training neural networks. Specifically, the study shows that, for state-of-the-art approximation error, the realizing parameters grow polynomially with respect to a normalized network size. This rate is compared to existing results, showing superiority in most cases, especially for high-dimensional inputs. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how neural networks can get close to perfecting a given function. Instead of just looking at how big the network needs to be to approximate any function, this study focuses on how many parameters are needed to achieve a certain level of accuracy. The main finding is that, for highly accurate approximations, the number of parameters grows slowly and steadily with the size of the network. This has important implications for understanding how neural networks work and how they can be trained. |
Keywords
» Artificial intelligence » Relu
