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Instruction Set and Language for Symbolic Regression
cs.CLcs.AIcs.PL Ezequiel Lopez-Rubio, Mario Pascual-Gonzalez · Mar 23, 2026

Symbolic regression search spaces suffer from structural redundancy: expression DAGs with $k$ internal nodes admit $\Theta(k!)$ distinct node-numberings that encode the same mathematical expression. This paper proposes IsalSR, a representation framework that computes a pruned canonical string—a complete labeled-DAG isomorphism invariant—to collapse all equivalent forms into a single canonical representation. The approach promises to reduce effective search space size by $O(k!)$ and can be integrated into any existing SR algorithm as a preprocessing step.

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.
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