Funny-Valen-Tine: Planning Solution Distribution Enhances Machine Abstract Reasoning Ability

The importance of visual abstract reasoning problems in the field of image processing cannot be overstated. Both Bongard-Logo problems and Raven's progressive matrices (RPM) belong to the domain of visual abstract reasoning tasks, with Bongard-Logo categorized as image clustering reasoning and RPM involving image progression pattern reasoning. This article introduces a novel baseline model, visual abstraction learning network (Valen), which falls under the umbrella of probability-highlighting models. Valen demonstrates remarkable performance in solving both RPM and Bongard-Logo problems, offering a versatile solution for these reasoning tasks. Our investigation extends beyond the application of Valen, delving into the underlying mechanisms of probability-highlighting solvers. In revisiting how these solvers handle RPM and Bongard-Logo tasks, we realize that they approximate the solution to each reasoning problem as a distribution in which primary samples are compliant while auxiliary samples are not. This prompts us to propose that the learning objective of probability-highlighting solvers is not the distribution of correct solutions but rather one jointly delineated by primary and auxiliary samples. To bridge the discrepancies, we introduced the Tine method, an adversarial learning-based approach that helps Valen estimate a distribution close to that of the correct solutions. However, adversarial training in Tine suffers from instability. Motivated by this limitation, we model the sample distribution of reasoning problems as a mixture of Gaussian distributions, enabling Valen to capture the correct solution distribution more efficiently. This nonadversarial methodology leads to the development of the framework utilizing neural networks for yielding (Funny) method. Building on a similar Gaussian-mixture paradigm, we further propose the supervised representation distribution planning method (SBR) method to plan the distribution of progressive pattern representations. Overall, this article contends that the key to enhancing solvers' ability to address visual abstract reasoning problems lies in explicitly planning the distribution of predicted solutions to approach the correct solution distribution. Codes are available in: https://github.com/Yuanbeiming/Funny-Valen-Tine-Planning-Solution-Distribution-Enhances-Machine-Abstract-Reasoning-Ability.