Probabilistic Abduction for Visual Abstract Reasoning via Learning Rules in Vector-symbolic Architectures

TL;DR

This paper introduces Learn-VRF, a novel method that learns rule formulations in vector-symbolic architectures to solve visual abstract reasoning tasks like Raven's matrices efficiently, accurately, and with interpretability.

Contribution

It presents a new approach that learns rule formulations directly from data in VSA, outperforming existing connectionist models and maintaining transparency.

Findings

High accuracy on I-RAVEN in-distribution data

Strong out-of-distribution generalization to unseen attribute-rule pairs

Outperforms large language models and pure connectionist baselines

Abstract

Abstract reasoning is a cornerstone of human intelligence, and replicating it with artificial intelligence (AI) presents an ongoing challenge. This study focuses on efficiently solving Raven's progressive matrices (RPM), a visual test for assessing abstract reasoning abilities, by using distributed computation and operators provided by vector-symbolic architectures (VSA). Instead of hard-coding the rule formulations associated with RPMs, our approach can learn the VSA rule formulations (hence the name Learn-VRF) with just one pass through the training data. Yet, our approach, with compact parameters, remains transparent and interpretable. Learn-VRF yields accurate predictions on I-RAVEN's in-distribution data, and exhibits strong out-of-distribution capabilities concerning unseen attribute-rule pairs, significantly outperforming pure connectionist baselines including large language models. Our code is available at https://github.com/IBM/learn-vector-symbolic-architectures-rule-formulations.