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 yet precise solution. Furthermore, we propose the D2C method, redefining conceptual 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 conceptual 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's Progressive Matrices（RPM）与Bongard-Logo挑战。首先，我们引入Lico-Net这一新型基线模型，以卓越的准确率解决RPM问题。基于此，我们进一步提出D3C方法，主张通过分布来表示抽象推理问题中的潜在概念。该视角同时提升了Lico-Net以及在Bongard-Logo任务中表现出色的基线模型的性能。为提升D3C的计算效率，我们提出其精简变体D3C-cos，在保持精确性的同时实现高效求解。此外，我们提出D2C方法，重新定义了这些领域内的概念边界，并弥合了高层抽象与其低维对应物之间的鸿沟。最后，我们将方法论扩展至D4C，通过对抗技术进一步优化概念边界，并在RPM与Bongard-Logo挑战中均展示了显著的性能提升。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。