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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.
Summary
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.
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.
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