RecBundle: A Next-Generation Geometric Paradigm for Explainable Recommender Systems
Authors: Hui Wang, Tianzhu Hu, Mingming Li, Xi Zhou, Chun Gan, Jiao Dai, Jizhong Han, Songlin Hu, Tao Guo
Organizations: Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · JD.com, Beijing, China · School of Cyberspace Security, University of Chinese Academy of Sciences, Beijing, China
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.
Figures & tables
Figure 1. Simple Diagram of a Principal Fiber Bundle.
Figure 2. Paradigm Shift in Recommender Systems Modeling.
RS Concept
Fiber Bundle Object
Symbol
Practical Meaning & Function
User Set & Topology
Base Space
B(U)
Network topology encoding user cognitive distances.
Preferences Space
Fiber
Fu
Independent semantic spaces for dynamic user interests.
Sequential Interactions
Path on Manifold
γ(t)
Historical interaction trajectories or feedback loops.
Feature Alignment
Connection
ω
Geometric rules for cross-node feature alignment.
Collaborative
Parallel Transport
Pu→v
Projection operators for neighbor feature aggregation.
Local Bias
Connection Curvature
Ω
Spatial distortions during aggregation.
Table 1. Correspondence between Recommender System Concepts and Fiber Bundle Theory
Figure 3. Core geometric operators in RecBundle. (a) Parallel transport aligns heterogeneous neighbor features across the base manifold. (b) Closed feedback loops induce holonomy transformations.
Algorithm Paradigm
Base Manifold Assumption
Curvature Features
Interpretations & Limitations from a Geometric Perspective
Matrix Factorization
Euclidean flat space
Zero curvature
Static space; ignores path dependence and state dynamics.
Graph Neural Networks
Discrete graph manifold
Implicit linear
Linearized transport; over-smooths in high-curvature regions.
Large Language Models
Discrete token sequence
Attention weights
Unconstrained paths; prone to semantic hallucinations.
Sequential recommender systems typically infer user preferences through single-pass encoding of interaction histories without iterative refinement, relying on increasingly deep architectures to capture complex patterns. In this work, we revisit sequential recommendation from a recursive inference perspective: can user preferences be modeled as a persistent latent state that is recursively refined? We propose RecRec (Recursive Recommendation), a lightweight model that maintains a compact latent state and updates it through a shared recursive module conditioned on interaction evidence. Unlike prior recursive models, RecRec introduces an evidence-anchored correction mechanism that stabilizes refinement by grounding each update in the original interaction context, preventing semantic drift during deep recursive reasoning. Experiments on three benchmark datasets under standard evaluation protocols show that RecRec matches or outperforms state-of-the-art sequential, graph-based, and reasoning-enhanced recommenders while using only 3.9M to 14M parameters. Ablation studies demonstrate that both recursive refinement and the evidence-anchored correction gate contribute significantly to performance, highlighting the effectiveness of recursive latent inference as a scalable alternative to deeper or language-based architectures. Code is available at https://anonymous.4open.science/r/RecRec-6B67/README.md.
Bundle recommendation ranks sets of related items rather than isolated items. Its central challenge is to connect user preferences, item interactions, and bundle composition without losing the signals needed to rank bundles. We propose Hypergraph-Enhanced Dual Convolutional Neural Network (HED), which constructs a complete hypergraph containing user--bundle, user--item, and bundle--item interactions together with intra-user and intra-bundle relations. HED couples complete-hypergraph propagation with a user--bundle branch, allowing item-aware higher-order context to inform ranking while preserving recommendation-specific signals. On NetEase, HED-128 improves over the strongest baseline by 5.04--6.97% across the six reported metrics; on Youshu, HED-64 improves by 1.87--4.56%. Ablation results support the contributions of both the user--bundle branch and intra-type relations, and sensitivity analyses identify stable operating ranges for the main hyperparameters. We further quantify the computational trade-off of the complete hypergraph, including its memory cost. The evidence supports HED on the two evaluated bundle-recommendation datasets while making its resource limitations explicit. Code and datasets will be made available upon publication.
Yang Li, Kangbo Liu, Yaoxin Wu +2
Northwestern Polytechnical University, China · Nanyang Technological University, Singapore
Traditional recommender systems (RecSys) primarily infer user preferences from implicit signals (such as clicks, watches, and purchases), often neglecting the rich explicit contextual feedback users provide through verbal text, like comments and reviews. This explicit context feedback captures the nuanced reasons behind user decisions regarding their preferences. In addition, it offers critical heterogeneous information for user preference alignment and more explainable recommendations. Overlooking such signals can lead to misaligned user preferences and further reinforce filter bubbles, as algorithms fail to understand the "semantic context" behind user choices. Recent advances in Large Language Models (LLMs) present new opportunities to harness user-generated content for more accurate and diverse recommendations, yet current LLM-based recommendations still focus on using item meta-data and underutilize this resource. In this paper, we advocate for prioritizing explicit context feedback in the next generation of LLM-based RecSys. We review the evolution of recommendation paradigms, highlight the value of context-rich feedback, call for new benchmarks and metrics, and introduce frameworks for integrating explicit user signals into scalable LLM-driven RecSys. Centering on user-preference modeling, we aim to foster more personalized, transparent, and explainable RecSys online platforms.
Weizhi Zhang, Wooseong Yang, Yuxin Cui +9
University of Illinois Chicago, Chicago, USA · Meta, Menlo Park, USA