D4C glove-train: solving the RPM and Bongard-logo problem by distributing and Circumscribing concepts

This paper achieves significant progress in the field of abstract reasoning, particularly in addressing Raven's Progressive Matrices (RPM) and Bongard-Logo problems. We propose the D2C approach, which redefines conceptual boundaries in these domains and bridges the gap between high-level concepts and their low-dimensional representations. Based on this, we further introduce the D3C method that handles Bongard-Logo problems and significantly improves reasoning accuracy by estimating the distribution of image representations and measuring their Sinkhorn distance. To enhance computational efficiency, we introduce the D3C-cos variant, which provides an efficient and accurate solution for RPM problems by constraining distribution distances. Additionally, we present Lico-Net, a network that combines D3C and D3C-cos to achieve state-of-the-art performance in both problem-solving and interpretability. Finally, we extend our approach to D4C, employing adversarial strategies to further refine conceptual boundaries and demonstrate notable improvements for both RPM and Bongard-Logo problems. Overall, our contributions offer a new perspective and practical solutions to the field of abstract reasoning.