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.
Abstract (translated)
在问题求解算法的背景下，过程性知识——即算法设计与操作符组合的实操技能——仍隐含在代码中，在运行间丢失，且必须为每个新领域重新设计。知识图谱（KGs）已被证明能有效组织陈述性知识，但当前KG范式在将过程性知识表示为可执行、可学习的图结构方面支持有限。我们提出了\textit{生成式可执行算法知识图谱}（GEAKG），这是一类KG，其节点存储可执行操作符，边编码习得的组合模式，遍历即可生成解决方案。GEAKG是\textit{生成式}的（拓扑结构与操作符由大语言模型合成）、\textit{可执行}的（每个节点均为可运行代码）且\textit{可迁移}的（习得模式能跨领域零样本泛化）。该框架在引擎层面是领域无关的：相同的三层架构与基于蚁群优化（ACO）的学习引擎可实例化于不同领域，通过可插拔的本体（\texttt{RoleSchema}）进行参数化。两项不共享任何领域特定框架代码的案例研究为该框架假设提供了具体证据：(1) 在两个表格基准测试上进行的跨70个数据集迁移配对的神经架构搜索，以及(2) 组合优化，其中在旅行商问题上学到的知识可零样本迁移至调度与分配领域。综合而言，这些结果支持了算法专长可被显式表示为可执行知识图谱、从中学习并实现迁移的结论。
URL
https://arxiv.org/abs/2603.27922
