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Equality graph-assisted symbolic regression.

Fabricio Olivetti de França1, Gabriel Kronberger2

  • 1CMCC, Universidade Federal do ABC, Santo André, São Paulo, Brazil.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|April 9, 2026
PubMed
Summary
This summary is machine-generated.

Symbolic regression (SR) using genetic programming (GP) can be inefficient due to redundant calculations. A new algorithm, SymRegg, uses equality graphs (e-graphs) to avoid re-evaluating equivalent expressions, improving search efficiency in SR.

Keywords:
equality graphsequation discoverysymbolic regression

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Area of Science:

  • Computational mathematics
  • Artificial intelligence

Background:

  • Genetic programming (GP) is a key algorithm for symbolic regression (SR), known for accuracy.
  • GP's effectiveness stems from navigating neutral search spaces, but this involves significant redundant computations (up to 60%).

Purpose of the Study:

  • To introduce SymRegg, a novel SR search algorithm designed to enhance computational efficiency.
  • To leverage equality graphs (e-graphs) for compact storage and retrieval of equivalent mathematical expressions.

Main Methods:

  • SymRegg utilizes e-graphs to store and group equivalent expressions, preventing redundant computations.
  • The algorithm perturbs solutions from the e-graph and inserts novel or equivalent expressions back into the e-graph.

Main Results:

  • SymRegg significantly improves the efficiency of symbolic regression searches.
  • The algorithm maintains high accuracy across diverse datasets.
  • SymRegg requires a minimal set of hyperparameters for effective operation.

Conclusions:

  • SymRegg offers a more efficient approach to symbolic regression by intelligently managing expression evaluation.
  • The e-graph structure is a powerful tool for optimizing search processes in SR.
  • This method presents a promising advancement for SR applications, particularly in physical sciences.