用向量符号架构实现可解释的系统性归纳推理，解决瑞文矩阵题
Systematic Abductive Reasoning via Diverse Relation Representations in Vector-symbolic Architecture
- 设计多种原子向量与结构化高维表示，捕捉属性与关系多样性
- 在瑞文矩阵上达到显著性能提升，且对分布外数据泛化能力强
- 适合研究可解释推理、神经符号系统与认知建模的学者
在抽象视觉推理中，传统深度学习模型存在可解释性与泛化能力不足的问题，而现有神经符号方法难以捕捉属性与关系表示的多样性和系统性。为此，我们提出基于向量符号架构（VSA）的系统性归纳推理模型（Rel-SAR），用于求解瑞文渐进矩阵（RPM）任务。为获得具备符号推理潜力的属性表示，我们引入了表示数值、周期和逻辑语义的多种原子向量，并采用结构化高维表示（SHDR）刻画整体网格组件。针对系统性推理，我们提出了新型数值与逻辑关系函数，在统一框架中实现规则归纳与执行。实验表明，Rel-SAR在RPM任务上取得显著性能提升，并展现出强鲁棒性分布外泛化能力。该模型通过高维属性表示与符号推理的协同，实现了兼具可解释性与可计算性的系统性归纳推理。
原文摘要 · Abstract (English)
In abstract visual reasoning, monolithic deep learning models suffer from limited interpretability and generalization, while existing neuro-symbolic approaches fall short in capturing the diversity and systematicity of attributes and relation representations. To address these challenges, we propose a Systematic Abductive Reasoning model with diverse relation representations (Rel-SAR) in Vector-symbolic Architecture (VSA) to solve Raven's Progressive Matrices (RPM). To derive attribute representations with symbolic reasoning potential, we introduce not only various types of atomic vectors that represent numeric, periodic and logical semantics, but also the structured high-dimentional representation (SHDR) for the overall Grid component. For systematic reasoning, we propose novel numerical and logical relation functions and perform rule abduction and execution in a unified framework that integrates these relation representations. Experimental results demonstrate that Rel-SAR achieves significant improvement on RPM tasks and exhibits robust out-of-distribution generalization. Rel-SAR leverages the synergy between HD attribute representations and symbolic reasoning to achieve systematic abductive reasoning with both interpretable and computable semantics.
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