Reproduce “All elementary functions from a single binary operator” on OpenResearch
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About this paper
Andrzej Odrzywołek
The paper defines EML, a two-input operator, and shows it represents the 36-entry scientific-calculator basis using only EML and constant 1. It also tests optimizing parameterized EML trees to recover expressions from examples. Random-start recovery was 100% at depth 2 and about 25% at depths 3–4, a proof of concept rather than a general symbolic-regression result.
Key insights
- A single binary operator can serve as a functionally complete primitive for all elementary functions in continuous mathematics, revealing a deeper, simpler underlying structure.
- This operator allows for a completely uniform representation of all elementary function expressions as binary trees, analogous to digital circuits built from NAND gates.
- The uniform binary tree structure of expressions facilitates a novel approach to symbolic regression, enabling gradient-based methods to discover exact closed-form elementary functions from numerical data.
Summary by alphaXiv.
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