让神经网络显式处理符号对称性，提升逻辑推理模型的泛化能力。
Symbol-Equivariant Recurrent Reasoning Models
- 通过符号等变层在结构上强制对称性，避免依赖繁琐数据增强。
- 9×9数独任务性能超越此前模型，且可直接推广至4×4到25×25不同规模。
- 仅用200万参数和少量数据，在ARC-AGI任务上表现媲美大模型。
Sudoku和ARC-AGI等推理问题对神经网络仍具挑战。递归推理模型（RRMs）家族，包括层级推理模型（HRM）和微型递归模型（TRM），为大型语言模型提供了紧凑替代方案，但当前仅通过昂贵的数据增强隐式处理符号对称性。本文提出符号等变递归推理模型（SE-RRMs），在架构层面通过符号等变层强制排列等变性，确保符号或颜色置换下的解完全一致。SE-RRMs在9×9数独上优于先前模型，并能从9×9训练直接推广至更小的4×4及更大的16×16、25×25实例，而现有RRMs无法实现外推。在ARC-AGI-1和ARC-AGI-2上，SE-RRMs以极少数据增强和仅200万参数取得与大模型相当的性能，证明显式编码对称性可提升神经推理的鲁棒性与可扩展性。代码已公开于https://github.com/ml-jku/SE-RRM。
原文摘要 · Abstract (English)
Reasoning problems such as Sudoku and ARC-AGI remain challenging for neural networks. The structured problem solving architecture family of Recurrent Reasoning Models (RRMs), including Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM), offer a compact alternative to large language models, but currently handle symbol symmetries only implicitly via costly data augmentation. We introduce Symbol-Equivariant Recurrent Reasoning Models (SE-RRMs), which enforce permutation equivariance at the architectural level through symbol-equivariant layers, guaranteeing identical solutions under symbol or color permutations. SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize from just training on 9x9 to smaller 4x4 and larger 16x16 and 25x25 instances, to which existing RRMs cannot extrapolate. On ARC-AGI-1 and ARC-AGI-2, SE-RRMs achieve competitive performance with substantially less data augmentation and only 2 million parameters, demonstrating that explicitly encoding symmetry improves the robustness and scalability of neural reasoning. Code is available at https://github.com/ml-jku/SE-RRM.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。