Solving the bongard-logo problem by modeling a probabilistic model

Abstract reasoning problems pose challenges to the perception and cognition abilities of AI algorithms, demanding deeper pattern recognition and inductive reasoning beyond mere identification of explicit image features. In this study, we introduce PMoC, a probabilistic model tailored for the Bongard-Logo problem, achieving high reasoning accuracy through the construction of an conditional probabilistic model. Additionally, we have designed the Pose-Transformer, an enhanced Transformer-Encoder specifically crafted for complex abstract reasoning tasks, including Bongard-Logo, RAVEN, I-RAVEN, and PGM. Inspired by the pose matrix in capsule networks, Pose-Transformer strengthens the focus on positional relationships between local features when processing image data. When combined with PMoC, it can further enhance reasoning accuracy. Our Pose-Transformer effectively addresses reasoning difficulties associated with changes in the position of abstract entities, outperforming previous models on RAVEN's OIG, D3$\times$3 subsets, and the PGM dataset. Finally, considering the deployment difficulties arising from the large number of Pose-Transformer parameters, this paper presents a lightweight version, Straw-Pose-Transformer, which maintains performance while significantly reducing the parameter count. This study contributes to enhancing AI capabilities in abstract reasoning and cognitive pattern recognition.