🤖 AI Summary
This work addresses the issue of structural redundancy in symbolic regression caused by multiple node labelings of expression-directed acyclic graphs (DAGs), which inflates the search space and leads to redundant fitness evaluations. To resolve this, the authors propose IsalSR, a novel framework that introduces, for the first time, a complete labeled DAG isomorphism invariant as a canonical representation. By encoding DAGs into strings via a two-level compact alphabet and generating a pruned canonical form, IsalSR uniquely normalizes all semantically equivalent expressions. This approach fundamentally eliminates structural redundancy, substantially compressing the search space and avoiding repeated evaluations. Consequently, it enhances both search efficiency and solution diversity, leading to improved overall algorithmic performance.
📝 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.