Funny Valen-Tine: Solving visual abstract reasoning problems through defining the solution distribution

Visual abstract reasoning problems hold immense importance in the field of image processing. Both Bongard-Logo and Raven's Progressive Matrices (RPM) belong to this domain, with Bongard-Logo categorized as image clustering reasoning and RPM involving image progression pattern reasoning. This paper introduces Valen, a novel baseline model under probabilistic highlighting models. Valen exhibits remarkable performance in solving both RPM and Bongard-Logo problems, offering a versatile solution. Our investigation delves into the underlying mechanisms of probability-highlighting solvers, realizing they approximate solutions to reasoning problem instances as distributions delineated by primary and auxiliary samples. We propose that the learning objective is not the distribution of correct solutions but one defined by both primary and auxiliary samples. To bridge discrepancies, we introduced the Tine method, an adversarial learning-based approach to assist Valen in estimating a solution distribution closer to the correct one, albeit with issues like unstable training. Reflecting on Tine, we propose modeling the sample distribution of reasoning problems as a mixture of Gaussian distributions, leading to the Funny method. This effectively enables Valen to capture the true form of the correct solution distribution. Furthermore, we designed the SBR method to model the distribution of progressive patterns representation similarly. Overall, the Funny, Tine, and SBR methods significantly improve Valen's performance, providing new ideas and methods for studying visual abstract reasoning problems.