On the Generalization Bounds of Symbolic Regression with Genetic Programming
Symbolic regression (SR) with genetic programming (GP) aims to discover interpretable mathematical expressions directly from data. Despite its strong empirical success, the theoretical understanding of why GP-based SR generalizes beyond the training data remains limited. In this work, we provide a learning-theoretic analysis of SR models represented as expression trees. We derive a generalization bound for GP-style SR under constraints on tree size, depth, and learnable constants. Our result decomposes the generalization gap into two interpretable components: a structure-selection term, reflecting the combinatorial complexity of choosing an expression-tree structure, and a constant-fittin...
| Authors | Masahiro Nomura, Ryoki Hamano, Isao Ono |
|---|---|
| Primary category | cs.LG |
| Published | 19 April 2026 |
| Last updated at source | 12 June 2026 |
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