Summary of Towards An Algebraic Framework For Approximating Functions Using Neural Network Polynomials, by Shakil Rafi et al.
Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials
by Shakil Rafi, Joshua Lee Padgett, Ukash Nakarmi
First submitted to arxiv on: 1 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Neural and Evolutionary Computing (cs.NE); Combinatorics (math.CO); Numerical Analysis (math.NA)
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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 proposed research aims to establish the foundations for a novel neural network calculus by exploring the concept of neural network objects. Building upon existing work presented in Chapter 2, the study demonstrates that neural networks can approximate real-number polynomials, exponentials, sine, and cosine functions, subject to certain parameter limitations (q and ε). The research highlights the polynomial growth of parameters and depth for achieving a desired level of accuracy (defined as a 1-norm difference over the reals), thereby showing that this approach is not entirely intractable. By doing so, the authors provide a framework for understanding neural networks with structural properties similar to those of the functions they approximate. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Neural networks are powerful tools used in machine learning and artificial intelligence. In this research, scientists aim to make it possible to use these networks to solve problems that were previously too hard or impossible. They want to show that neural networks can be used to approximate real-world functions like polynomials, exponentials, sine, and cosine, as long as certain conditions are met. This would allow developers to create more efficient and effective AI systems. |
Keywords
* Artificial intelligence * Machine learning * Neural network
