GEAKG: Generative Executable Algorithm Knowledge Graphs
Summary: arXiv:2603.27922v1 Announce Type: new
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 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 generative (topology and operators are synthesized by a Large Language Model), executable (every node is runnable code), and 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 (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.
Introduction
The advent of Generative Executable Algorithm Knowledge Graphs (GEAKG) marks a significant advancement in the representation of procedural knowledge in algorithm design. Traditional methods have struggled to maintain the integrity of procedural knowledge, often losing critical information between algorithm executions. GEAKG addresses these challenges by enabling the explicit encoding of algorithmic expertise within a structured graph format.
Key Features of GEAKG
- Generative: Utilizes Large Language Models to synthesize topology and operators.
- Executable: Each node in the graph contains runnable code, allowing for direct execution of algorithmic steps.
- Transferable: The knowledge learned can be applied across various domains without the need for re-engineering.
Case Studies
To validate the efficacy of the GEAKG framework, two distinct case studies were conducted:
- Neural Architecture Search: This study involved 70 cross-dataset transfer pairs across two tabular benchmarks, demonstrating the framework’s ability to efficiently search and optimize neural architectures.
- Combinatorial Optimization: Knowledge gained from solving the Traveling Salesman Problem was successfully transferred to scheduling and assignment problems, showcasing the framework’s versatility.
Conclusion
The introduction of GEAKG signifies a pivotal evolution in how procedural knowledge is represented and utilized in algorithmic contexts. By leveraging the capabilities of knowledge graphs and combining them with generative and executable elements, GEAKG not only preserves but also enhances algorithmic expertise. This framework offers promising implications for future research and applications across diverse domains.