  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.
