Systematic Abductive Reasoning via Diverse Relation Representations in Vector-symbolic Architecture
🤖 AI Summary
Existing large models exhibit weak generalization and poor interpretability on abstract visual reasoning tasks (e.g., Raven’s Progressive Matrices), while neural-symbolic approaches suffer from limited relational representation capacity.
Method: We propose the first abductive reasoning framework based on Vector Symbolic Architecture (VSA), featuring Structured High-Dimensional Representation (SHDR)—a grid-based high-dimensional encoding scheme—integrated with multi-semantic atomic vectors (numerical, periodic, and logical). A unified numerical-logical relational function enables joint rule abduction and execution. Symbol-vector co-reasoning orchestrates symbolic manipulation and vector-space computation.
Contribution/Results: Our framework achieves state-of-the-art performance on RPM benchmarks, demonstrates strong out-of-distribution generalization, and ensures full interpretability of inference steps alongside semantically grounded, computable representations—bridging the gap between neural scalability and symbolic rigor.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Abstract Thinking
Complex Pattern Recognition
Adaptability in Raven's Matrices
Innovation
Methods, ideas, or system contributions that make the work stand out.
Rel-SAR Model
Abstract Reasoning
Raven's Progressive Matrices
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