  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.
