Invariant Representation of Mathematical Expressions

TL;DR

This paper introduces a structural encoding method for mathematical expressions that remains invariant to superficial differences, improving comparison accuracy over traditional string-based methods in machine learning tasks.

Contribution

The paper proposes a novel, structure-sensitive encoding technique for mathematical expressions that is invariant to superficial variations, enhancing semantic comparison capabilities.

Findings

The method effectively captures the structural properties of mathematical expressions.

It outperforms traditional string comparison methods on mathematical data.

The encoding is invariant to superficial differences in expressions.

Abstract

While there exist many methods in machine learning for comparison of letter string data, most are better equipped to handle strings that represent natural language, and their performance will not hold up when presented with strings that correspond to mathematical expressions. Based on the graphical representation of the expression tree, here we propose a simple method for encoding such expressions that is only sensitive to their structural properties, and invariant to the specifics which can vary between two seemingly different, but semantically similar mathematical expressions.