Towards Generative Abstract Reasoning: Completing Raven's Progressive Matrix via Rule Abstraction and Selection

Endowing machines with abstract reasoning ability has been a long-term research topic in artificial intelligence. Raven's Progressive Matrix (RPM) is widely used to probe abstract visual reasoning in machine intelligence, where models need to understand the underlying rules and select the missing bottom-right images out of candidate sets to complete image matrices. The participators can display powerful reasoning ability by inferring the underlying attribute-changing rules and imagining the missing images at arbitrary positions. However, existing solvers can hardly manifest such an ability in realistic RPM problems. In this paper, we propose a conditional generative model to solve answer generation problems through Rule AbstractIon and SElection (RAISE) in the latent space. RAISE encodes image attributes as latent concepts and decomposes underlying rules into atomic rules by means of concepts, which are abstracted as global learnable parameters. When generating the answer, RAISE selects proper atomic rules out of the global knowledge set for each concept and composes them into the integrated rule of an RPM. In most configurations, RAISE outperforms the compared generative solvers in tasks of generating bottom-right and arbitrary-position answers. We test RAISE in the odd-one-out task and two held-out configurations to demonstrate how learning decoupled latent concepts and atomic rules helps find the image breaking the underlying rules and handle RPMs with unseen combinations of rules and attributes.