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.

翻译：本文在抽象推理领域取得重大进展，特别针对瑞文推理矩阵（RPM）和Bongard-Logo问题。我们首先提出D2C方法，该方法重新定义了上述领域中的概念边界，并弥合了高层概念与其低维表示之间的鸿沟。基于这一基础，我们提出D3C方法，这是一种解决Bongard-Logo问题的新颖方法。D3C通过估计图像表示的分布并计算其Sinkhorn距离，实现了卓越的推理精度。该创新方法为理解图像间关系提供了新视角，推动了抽象推理领域的前沿发展。为在不牺牲性能的前提下进一步提升计算效率，我们引入D3C-cos变体。该方法通过约束分布距离，在保持高精度的同时为RPM问题提供了更具计算效率的解决方案。此外，我们提出Lico-Net基线网络，该网络集成了D3C与D3C-cos方法。通过估计并约束规律性表示的分布，Lico-Net同时解决了问题求解与可解释性挑战，达到了最先进性能。最后，我们通过D4C方法扩展方法论，该对抗性方法相较于D2C进一步精炼了概念边界。针对RPM与Bongard-Logo问题定制的D4C方法，在应对抽象推理挑战方面展现出显著改善。总体而言，我们的贡献推动了抽象推理领域的发展，为长期存在的问题提供了全新视角与实用解决方案。