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

arXiv: https://arxiv.org/abs/2603.16088 · HTML: https://mlsanity.com/paper/2603.16088/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 22 of 22)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [TADAM: Task dependent adaptive metric for improved few-shot learning](https://mlsanity.com/paper/1805.10123/) (2018)
- [Rumor Detection on Social Media with Bi-Directional Graph Convolutional Networks](https://mlsanity.com/paper/2001.06362/) (2020)
- [MeLU: Meta-Learned User Preference Estimator for Cold-Start Recommendation](https://mlsanity.com/paper/1908.00413/) (2019)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [Hierarchically Structured Meta-learning](https://mlsanity.com/paper/1905.05301/) (2019)
- [Virgo: A Preliminary Exploration on Reproducing o1-like MLLM](https://mlsanity.com/paper/2501.01904/) (2025)
- [Enhancing LLM Reasoning with Reward-guided Tree Search](https://mlsanity.com/paper/2411.11694/) (2024)
- [Interpretable Rumor Detection in Microblogs by Attending to User Interactions](https://mlsanity.com/paper/2001.10667/) (2020)
- [MAMO: Memory-Augmented Meta-Optimization for Cold-start Recommendation](https://mlsanity.com/paper/2007.03183/) (2020)
- [User-controllable Recommendation Against Filter Bubbles](https://mlsanity.com/paper/2204.13844/) (2022)
- [MetaSelector: Meta-Learning for Recommendation with User-Level Adaptive Model Selection](https://mlsanity.com/paper/2001.10378/) (2020)
- [Reconciling the accuracy-diversity trade-off in recommendations](https://mlsanity.com/paper/2307.15142/) (2023)
- [Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps](https://mlsanity.com/paper/2110.06983/) (2021)
- [On Practical Diversified Recommendation with Controllable Category Diversity Framework](https://mlsanity.com/paper/2402.03801/) (2024)
- [Enhancing Large Language Models through Structured Reasoning](https://mlsanity.com/paper/2506.20241/) (2025)
- [Rapidly-Exploring Quotient-Space Trees: Motion Planning using Sequential Simplifications](https://mlsanity.com/paper/1906.01350/) (2019)
- [Multilevel Motion Planning: A Fiber Bundle Formulation](https://mlsanity.com/paper/2007.09435/) (2020)
- [Quotient-Space Motion Planning](https://mlsanity.com/paper/1807.09468/) (2018)
- [Alleviating User-Sensitive bias with Fair Generative Sequential Recommendation Model](https://mlsanity.com/paper/2506.19777/) (2025)

## Abstract (arXiv)

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.