Minimalist Genetic Programming

2026-06-08

AI Summary

This work addresses the well-known issue of code bloat in traditional genetic programming for symbolic regression, which often impedes stable recovery of the true underlying model. Inspired by the linguistic Minimalist Program, the authors reformulate program induction as a syntactic derivation task, abandoning the conventional evolutionary search paradigm. They propose a Markovian incremental construction mechanism based on a binary MERGE operator that systematically builds symbolic expressions from a lexicon of atomic syntactic objects. This approach reliably and accurately reconstructs ground-truth models on symbolic regression benchmarks where standard genetic programming fails, demonstrating significantly superior performance over traditional methods.

Abstract

Genetic programming (GP) is based on two important insights. First, that any learning task can fundamentally be posed as a program induction problem, where the goal is to construct a symbolic hierarchical model that is expressed as a syntax tree. Second, to pose this task as a search problem, and use evolution to locate the desired model. Since it was proposed, GP has produced notable results in a wide range of tasks and problem domains. This work presents an alternative view by modifying the second core insight of GP, posing the problem as a syntactic derivation task instead. In particular, this paper presents Minimalist Genetic Programming (MGP), an algorithm that like GP is biologically inspired, but instead of evolution it takes inspiration from the Minimalist Program to human language, in which syntax is understood as an optimal solution to the problem of linking two other mental systems. In minimalism, the core computational process is a binary set formation operator called $MERGE$, than can be used to incrementally construct complex syntactic structures using a simple Markovian process. MGP is able to discover the core building blocks of the symbolic expressions, and to incrementally combined them using $MERGE$. The proposed system is benchmarked on symbolic regression tasks that are known to be difficult to solve with standard GP systems because of the propensity for bloat. Results show that when a proper lexicon of atomic syntactic objects are chosen, MGP is able to consistently produce the exact ground truth model on a set of symbolic regression where standard GP struggles to do the same. The insights provided by minimalism are shown to be relevant to the problem of program induction, and should be explored further based on the potential exhibited by MGP in this work.

Problem

• genetic programming
• symbolic regression
• program induction
• bloat
• syntax

Innovation

• Minimalist Genetic Programming
• MERGE operator
• syntactic derivation
• symbolic regression
• program induction