EggMind: LLM-Driven Two-Dimensional Intelligence for Scalable Equality Saturation

Youwei Xiao, Chenyun Yin, Yun Liang

Keywords: Equality saturation, E-graphs, LLM-guided optimization, Strategy synthesis, Domain-specific languages, Code evoluation

Abstract: Equality saturation avoids premature commitment to a single, sub-optimal rewrite path in broad compilation problems, yet its practical adoption is limited by uncontrolled e-graph growth due to blind rewriting decisions. We present the EggMind framework to enable intelligent and scalable equality saturation using large language models (LLMs). EggMind introduces a novel two-dimensional intelligence approach. First, for the phase dimension, EggMind employs LLM-evolved functors to control the equality saturation process and avoid redundancy and suboptimal solutions. Second, for the case dimension, EggMind uses inductive learning over solved cases to transfer successful experience to complex, unsolved ones, reducing blind-exploration effort. Combining these two dimensions of intelligence, EggMind provides a feasible method for next-generation optimizers to achieve both scalability and solution superiority in general target domains.

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Submission Number: 10