Systematic Abductive Reasoning via Diverse Relation Representations in Vector-Symbolic Architecture

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 attribute 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 high-dimensional (HD) encodings that capture numeric, periodic, and logical semantics, but also the structured HD representation (SHDR) for the overall grid component. For systematic reasoning, we further propose novel numerical and logical relation functions and perform rule abduction and execution in a unified framework built upon these relation representations. Experimental results demonstrate that Rel-SAR achieves significant performance improvements on RPM tasks. By synergistically combining HD attribute representations with symbolic reasoning, Rel-SAR enables systematic abductive reasoning with both interpretable and computable semantics.