This paper achieves noteworthy progress in the realm of abstract reasoning, particularly in addressing Raven's Progressive Matrices (RPM) and Bongard-Logo challenges. Initially, we introduce Lico-Net, a novel baseline model that resolves RPM problems with remarkable accuracy. Leveraging this foundation, we advance with the D3C approach, which advocates representing the underlying concepts in abstract reasoning problems through distributions. This perspective enhances the performance of both Lico-Net and a baseline model excelling in Bongard-Logo tasks. To bolster the computational efficiency of D3C, we present the D3C-cos variant, offering a streamlined solution. Furthermore, we propose the D2C method, redefining concept boundaries within these domains and bridging the divide between high-level abstractions and their lower-dimensional counterparts. Finally, we extend our methodology to D4C, employing adversarial techniques to refine concept boundaries further and demonstrate substantial improvements in both RPM and Bongard-Logo challenges. Overall, our contributions present a fresh outlook and practical advancements in the field of abstract reasoning.

翻译：本文在抽象推理领域取得了显著进展，尤其针对Raven渐进矩阵（RPM）和Bongard-Logo挑战问题。首先，我们提出Lico-Net——一种具有卓越精度的新型基线模型，用于解决RPM问题。在此基础上，我们推进D3C方法，主张通过分布来表示抽象推理问题中的潜在概念。这一视角同时提升了Lico-Net及在Bongard-Logo任务中表现优异的基线模型的性能。为增强D3C的计算效率，我们提出其变体D3C-cos，提供了一种精简的解决方案。此外，我们提出D2C方法，重新定义这些领域中的概念边界，并弥合高层抽象与低维对应物之间的鸿沟。最后，我们将方法扩展至D4C，采用对抗技术进一步细化概念边界，并在RPM和Bongard-Logo挑战中均展现出实质性改进。总体而言，我们的贡献为抽象推理领域提供了全新视角与实践性进展。