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

This paper presents significant advancements in the field of abstract reasoning, particularly for Raven's Progressive Matrices (RPM) and Bongard-Logo problems. We first introduce D2C, a method that redefines concept boundaries in these domains and bridges the gap between high-level concepts and their low-dimensional representations. Leveraging this foundation, we propose D3C, a novel approach for tackling Bongard-Logo problems. D3C estimates the distributions of image representations and measures their Sinkhorn distance to achieve remarkable reasoning accuracy. This innovative method provides new insights into the relationships between images and advances the state-of-the-art in abstract reasoning. To further enhance computational efficiency without sacrificing performance, we introduce D3C-cos. This variant of D3C constrains distribution distances, offering a more computationally efficient solution for RPM problems while maintaining high accuracy. Additionally, we present Lico-Net, a baseline network for RPM that integrates D3C and D3C-cos. By estimating and constraining the distributions of regularity representations, Lico-Net addresses both problem-solving and interpretability challenges, achieving state-of-the-art performance. Finally, we extend our methodology with D4C, an adversarial approach that further refines concept boundaries compared to D2C. Tailored for RPM and Bongard-Logo problems, D4C demonstrates significant improvements in addressing the challenges of abstract reasoning. Overall, our contributions advance the field of abstract reasoning, providing new perspectives and practical solutions to long-standing problems.