  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.
