Instruction Set and Language for Symbolic Regression

TL;DR

This paper introduces IsalSR, a novel framework for symbolic regression that encodes expression DAGs into canonical strings, reducing redundancy and improving search efficiency by collapsing equivalent representations.

Contribution

It presents a new encoding scheme for expression DAGs in symbolic regression that creates a canonical form, addressing structural redundancy in the search space.

Findings

Reduces search space by collapsing equivalent expressions

Provides a canonical string representation for expression DAGs

Improves efficiency of symbolic regression algorithms

Abstract

A fundamental but largely unaddressed obstacle in Symbolic regression (SR) is structural redundancy: every expression DAG with admits many distinct node-numbering schemes that all encode the same expression, each occupying a separate point in the search space and consuming fitness evaluations without adding diversity. We present IsalSR (Instruction Set and Language for Symbolic Regression), a representation framework that encodes expression DAGs as strings over a compact two-tier alphabet and computes a pruned canonical string -- a complete labeled-DAG isomorphism invariant -- that collapses all the equivalent representations into a single canonical form.