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

TL;DR

This paper introduces Rel-SAR, a neuro-symbolic model using diverse vector representations within VSA to improve systematic abductive reasoning and generalization in visual IQ tests like Raven's Progressive Matrices.

Contribution

It develops a novel framework combining various atomic vectors and structured high-dimensional representations for symbolic reasoning in visual tasks.

Findings

Significant improvement on RPM tasks

Robust out-of-distribution generalization

Enhanced interpretability and reasoning capabilities

Abstract

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.