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Workshop: MATH-AI: The 3rd Workshop on Mathematical Reasoning and AI

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

Michael Hersche · Francesco Di Stefano · Thomas Hofmann · Abu Sebastian · Abbas Rahimi

Keywords: [ Neural Networks ] [ vector-symbolic architectures ] [ Visual abstract reasoning ] [ Raven's progressive matrices ]


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.

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