Recommender systems are inherently dynamic feedback loops where prolonged local interactions accumulate into macroscopic structural degradation such as information cocoons. Existing representation learning paradigms are universally constrained by the assumption of a single flat space, forcing topologically grounded user associations and semantically driven historical interactions to be fitted within the same vector space. This excessive coupling of heterogeneous information renders it impossible for researchers to mechanistically distinguish and identify the sources of systemic bias. To overcome this theoretical bottleneck, we introduce Fiber Bundle from modern differential geometry and propose a novel geometric analysis paradigm for recommender systems. This theory naturally decouples the system space into two hierarchical layers: the base manifold formed by user interaction networks, and the fibers attached to individual user nodes that carry their dynamic preferences. Building upon this, we construct RecBundle, a framework oriented toward next-generation recommender systems that formalizes user collaboration as geometric connection and parallel transport on the base manifold, while mapping content evolution to holonomy transformations on fibers. From this foundation, we identify future application directions encompassing quantitative mechanisms for information cocoons and evolutionary bias, geometric meta-theory for adaptive recommendation, and novel inference architectures integrating large language models (LLMs). Empirical analysis on real-world MovieLens and Amazon Beauty datasets validates the effectiveness of this geometric framework.

翻译：推荐系统本质上是动态反馈循环，其中长期的局部交互会累积形成宏观结构退化，如信息茧房。现有的表示学习范式普遍受限于单一平坦空间的假设，迫使基于拓扑结构的用户关联与语义驱动的历史交互被强行拟合在同一向量空间中。这种异质信息的过度耦合使研究者无法从机制上区分和识别系统性偏差的来源。为克服这一理论瓶颈，我们引入现代微分几何中的纤维丛概念，提出一种新颖的推荐系统几何分析范式。该理论自然地将系统空间解耦为两个层次：由用户交互网络构成的基础流形，以及附着于个体用户节点、承载其动态偏好的纤维。基于此，我们构建了面向下一代推荐系统的框架RecBundle，该框架将用户协作形式化为基础流形上的几何联络与平行移动，同时将内容演化映射为纤维上的和乐变换。在此基础上，我们指出了未来的应用方向，包括信息茧房与演化偏差的量化机制、自适应推荐的几何元理论，以及融合大语言模型（LLMs）的新型推理架构。在真实世界MovieLens和Amazon Beauty数据集上的实证分析验证了这一几何框架的有效性。