发表机构
HUN-REN Wigner Research Centre for Physics; Corvinus University of Budapest（HUN-REN维格纳物理研究中心; 布达佩斯考文纽斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出含概念图与程序图的知识空间结构框架，明确问题求解相关表征操作，确定抽象等的表征前提，为弱求解器设定给出显式成败条件。
AI 中文摘要
学习与问题求解高度依赖内部表征的结构。尽管许多现代数据驱动的人工智能系统能实现出色的预测性能，但其学习得到的表征往往缺乏用于表达抽象、不变性及任务相关规则的显式结构。我们提出了一个极简结构框架，其中与问题求解相关的表征操作（如语境形成、不变性识别、表征选择、抽象及程序复用）均被显式定义。核心概念是「语境」，其形式化为底层状态空间子集的划分，它确定了问题可被提出的区分、粒度与形式。在此设定下，不变性识别与表征选择被视为基础表征操作。该框架实现为知识空间（Knowledge Space），由两个耦合图结构构成：承载构建与优化概念的概念图（Concept Graph），以及编码表征上类型化操作的程序图（Procedure Graph）。这些结构共同提供了一个极简认知表征代数，用于对表征进行操作，且无需假设复杂的推理、学习、控制、感知或运动机制。通过简单示例与有限弱求解器演示，我们表明，即便问题求解由固定且有限的求解器执行，恰当的表征组织仍可简化可接受规则的形式与范围。本文的贡献是结构性而非算法性的：它确定了问题求解中抽象、不变性与程序复用的表征前提，并阐明了弱求解器设定下的显式成功与失败条件。
英文摘要
Learning and problem solving depend critically on the structure of internal representations. While many modern data-driven artificial systems achieve strong predictive performance, their learned representations often lack explicit structure for expressing abstraction, invariance, and task-relevant regularities. We propose a minimal structural framework in which representational operations relevant to problem solving, such as context formation, invariance recognition, representative selection, abstraction, and procedural reuse, are made explicit. The central notion is that of a \emph{context}, formalized as a partition of a subset of an underlying state space, which fixes the distinctions, granularity, and form in which a problem can be posed. Within this setting, invariance recognition and representative selection are treated as fundamental representational operations. The framework is realized as a Knowledge Space composed of two coupled graph structures: a Concept Graph that hosts constructed and refined concepts, and a Procedure Graph that encodes typed operations over representations. Together, these structures provide a minimal cognitive-representational algebra for operating on representations without assuming sophisticated inference, learning, control, perception, or motor mechanisms. Using simple illustrative examples and a finite weak-solver demonstration, we show that appropriate representational organization can simplify the form and scope of admissible regularities, even when problem solving is carried out by a fixed and limited solver. The contribution of the paper is structural rather than algorithmic: it identifies representational prerequisites for abstraction, invariance, and procedural reuse in problem solving, and states explicit success and failure conditions for the weak-solver setting.
Comments41 pages, 1 figure
