发表机构
California Institute of Technology（加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过幺半群世界上的约束学习任务，发现标准训练无法传播全局约束，而组合训练显著提升泛化，为理解世界模型中的全局理解提供了形式化框架。
AI 中文摘要
人工智能系统常常显得脆弱且碎片化。大型语言模型（LLM）可能正确解释一个概念却无法应用它，或者在一个情境中遵循安全指令而在另一个情境中却不遵循。这种行为表明，将局部信息提升为全局理解方面存在普遍失败。为了获得根本性洞见，我们将“理解”定义为学习约束并传播其后果。我们在幺半群世界（monoid worlds）上构建学习任务，这些世界是由动作转换连接的状态集合，其中观察到的训练转换和一个未见的约束共同决定保留的转换。测量泛化能力可以测试模型是否能从局部转换中学习全局约束并传播其后果。我们考虑了与空间和语义结构相关的逆、交换、组合和周期性约束。在注意力、循环和状态空间架构中，下一步状态训练能拟合数据但无法传播非平凡约束。组合训练（compositional training）使用相同路径但隐藏输入中的中间状态，在逆、交换和组合约束上跨架构达到96%的准确率，并在具身环境训练的世界模型的几何泛化以及维基数据微调的LLM的关系泛化中带来相应改进。当推断一个未见事实可能依赖于先推断其他事实时，模型能传播多远？我们定义了保留转换的证明深度d，即推断该转换所需的最小推理轮数，并发现模型泛化随证明深度急剧下降。增加组合路径长度T可改善泛化。这些结果为研究语言和世界模型中的全局理解提供了一种形式化方法，并证明组合训练能促进信息传播与整合。
英文摘要
AI systems often feel brittle and fragmented. A large language model (LLM) may correctly explain a concept but fail to apply it, or follow safety instructions in one context but not another. This behavior suggests a general failure to lift local information to a global understanding. To gain fundamental insight, we frame "understanding" as learning constraints and propagating their consequences. We construct learning tasks on monoid worlds, sets of states connected by action transitions, where observed training transitions and an unseen constraint jointly determine held-out transitions. Measuring generalization tests whether models can learn global constraints from local transitions and propagate their consequences. We consider inverse, commutativity, composition, and periodicity constraints relevant to spatial and semantic structure. Across attention, recurrent, and state-space architectures, next-state training fits the data but fails to propagate non-trivial constraints. Compositional training, which uses identical paths but hides intermediate states from the input, achieves 96% accuracy on inverse, commutativity, and composition constraints across architectures, yields corresponding improvements in geometric generalization of world models trained on embodied environments and relational generalization in Wikidata-finetuned LLMs. How far do models propagate constraints when inferring an unseen fact may depend on first inferring others? We define proof depth d of a held-out transition, measuring the minimum number of inference rounds to infer the transition, and find that model generalization decreases sharply with proof depth. Increasing compositional path length T improves generalization. These results provide a formal way to investigate global understanding in language and world models and demonstrate that compositional training promotes information propagation and integration.
Comments16 pages, 8 figures
