Solving the bongard-logo problem by modeling a probabilistic model

Abstract reasoning problems challenge the perceptual and cognitive abilities of AI algorithms, demanding deeper pattern discernment and inductive reasoning beyond explicit image features. This study introduces PMoC, a tailored probability model for the Bongard-Logo problem, achieving high reasoning accuracy by constructing independent probability models. Additionally, we present Pose-Transformer, an enhanced Transformer-Encoder designed for complex abstract reasoning tasks, including Bongard-Logo, RAVEN, I-RAVEN, and PGM. Pose-Transformer incorporates positional information learning, inspired by capsule networks' pose matrices, enhancing its focus on local positional relationships in image data processing. When integrated with PMoC, it further improves reasoning accuracy. Our approach effectively addresses reasoning difficulties associated with abstract entities' positional changes, outperforming previous models on the OIG, D3$\times$3 subsets of RAVEN, and PGM databases. This research contributes to advancing AI's capabilities in abstract reasoning and cognitive pattern recognition.