RecBundle: A Next-Generation Geometric Paradigm for Explainable Recommender Systems

2026-03-16

AI Summary

This work addresses the limitations of traditional recommender systems, which employ a single flat representation space and thus struggle to disentangle user topological structures from semantic preferences, leading to structural biases such as filter bubbles that are difficult to trace. To overcome this, the paper introduces fiber bundle theory from differential geometry into recommendation modeling for the first time. User interactions are represented as a base manifold, while dynamic preferences reside in the fiber space. Geometric connections, parallel transport, and holonomy transformations are leveraged to characterize collaborative relationships and content evolution, respectively. This framework achieves a hierarchical disentanglement of structure and preference, offering a quantifiable mechanism to analyze filter bubbles and evolutionary biases, and enabling seamless integration with large language models. Experiments on MovieLens and Amazon Beauty datasets demonstrate significant improvements in recommendation explainability and dynamic adaptability.

Technology Category

• Data Mining & Knowledge Management: Recommender Systems
• Machine Learning: Learning Preferences or Rankings
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

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.

Problem

• recommender systems
• information cocoons
• representation learning
• systemic bias
• geometric paradigm

Innovation

• Fiber Bundle
• Geometric Recommender Systems
• Information Cocoons
• Holonomy
• Differential Geometry