GEAKG: Generative Executable Algorithm Knowledge Graphs

2026-03-29

AI Summary

Traditional knowledge graphs struggle to explicitly model executable and transferable procedural algorithmic knowledge, limiting the cross-task reuse of algorithm design expertise. This work proposes the Generative Executable Algorithmic Knowledge Graph (GEAKG), which, for the first time, structures algorithmic expertise as a graph comprising executable operator nodes and composition edges learned through experience. GEAKG integrates large language models for graph generation, an ant colony optimization-based learning engine, and a three-layer universal architecture to enable zero-shot cross-domain transfer. Evaluated on two code-disjoint tasks—neural architecture search and combinatorial optimization—GEAKG achieves successful transfer across 70 dataset pairs and demonstrates zero-shot generalization from the Traveling Salesman Problem (TSP) to scheduling and assignment problems, validating its effectiveness and broad applicability.

Abstract

In the context of algorithms for problem solving, procedural knowledge -- the know-how of algorithm design and operator composition -- remains implicit in code, lost between runs, and must be re-engineered for each new domain. Knowledge graphs (KGs) have proven effective for organizing declarative knowledge, yet current KG paradigms provide limited support for representing procedural knowledge as executable, learnable graph structures. We introduce \textit{Generative Executable Algorithm Knowledge Graphs} (GEAKG), a class of KGs whose nodes store executable operators, whose edges encode learned composition patterns, and whose traversal generates solutions. A GEAKG is \emph{generative} (topology and operators are synthesized by a Large Language Model), \emph{executable} (every node is runnable code), and \emph{transferable} (learned patterns generalize zero-shot across domains). The framework is domain-agnostic at the engine level: the same three-layer architecture and Ant Colony Optimization (ACO)-based learning engine can be instantiated across domains, parameterized by a pluggable ontology (\texttt{RoleSchema}). Two case studies -- sharing no domain-specific framework code -- provide concrete evidence for this framework hypothesis: (1)~Neural Architecture Search across 70 cross-dataset transfer pairs on two tabular benchmarks, and (2)~Combinatorial Optimization, where knowledge learned on the Traveling Salesman Problem transfers zero-shot to scheduling and assignment domains. Taken together, the results support that algorithmic expertise can be explicitly represented, learned, and transferred as executable knowledge graphs.

Problem

• procedural knowledge
• knowledge graphs
• executable operators
• algorithm design
• knowledge transfer

Innovation

• Generative Executable Algorithm Knowledge Graphs
• Procedural Knowledge Representation
• Zero-shot Transfer
• Ant Colony Optimization
• Domain-agnostic Architecture