Abstracting Concept-Changing Rules for Solving Raven's Progressive Matrix Problems

TL;DR

This paper introduces CRAB, a deep latent variable model that automatically abstracts concept-changing rules in Raven's Progressive Matrix problems, improving interpretability and performance without auxiliary supervision.

Contribution

CRAB is the first model to learn interpretable concept-changing rules in RPM problems without needing auxiliary annotations or distractors.

Findings

CRAB outperforms unsupervised baselines in answer generation.

CRAB achieves comparable or higher accuracy than supervised models.

CRAB demonstrates interpretability in concept learning and rule abstraction.

Abstract

The abstract visual reasoning ability in human intelligence benefits discovering underlying rules in the novel environment. Raven's Progressive Matrix (RPM) is a classic test to realize such ability in machine intelligence by selecting from candidates. Recent studies suggest that solving RPM in an answer-generation way boosts a more in-depth understanding of rules. However, existing generative solvers cannot discover the global concept-changing rules without auxiliary supervision (e.g., rule annotations and distractors in candidate sets). To this end, we propose a deep latent variable model for Concept-changing Rule ABstraction (CRAB) by learning interpretable concepts and parsing concept-changing rules in the latent space. With the iterative learning process, CRAB can automatically abstract global rules shared on the dataset on each concept and form the learnable prior knowledge of global rules. CRAB outperforms the baselines trained without auxiliary supervision in the arbitrary-position answer generation task and achieves comparable and even higher accuracy than the compared models trained with auxiliary supervision. Finally, we conduct experiments to illustrate the interpretability of CRAB in concept learning, answer selection, and global rule abstraction.