Summary of Universal Approximation Of Operators with Transformers and Neural Integral Operators, by Emanuele Zappala and Maryam Bagherian
Universal Approximation of Operators with Transformers and Neural Integral Operators
by Emanuele Zappala, Maryam Bagherian
First submitted to arxiv on: 1 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 paper explores the capabilities of transformers and neural integral operators in processing complex mathematical operations. Specifically, it demonstrates that the transformer architecture can universally approximate integral operators between Hölder spaces. Additionally, it shows that modified versions of these architectures, incorporating Gavurin integrals or Leray-Schauder mappings, can universally approximate arbitrary operators between Banach spaces. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how transformers and neural integral operators work with big mathematical ideas. It finds that the transformer is good at mimicking certain types of math problems involving Hölder spaces. The researchers also make new versions of these tools, using Gavurin integrals or Leray-Schauder mappings, which can help solve a wide range of math problems. |
Keywords
» Artificial intelligence » Transformer
