# Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation

arXiv: https://arxiv.org/abs/2108.06468 · HTML: https://mlsanity.com/paper/2108.06468/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2021.

## Built on by (most cited first, 30 of 38)

- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [COSTA: Covariance-Preserving Feature Augmentation for Graph Contrastive Learning](https://mlsanity.com/paper/2206.04726/) (2022)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [A Survey of Trustworthy Federated Learning with Perspectives on Security, Robustness, and Privacy](https://mlsanity.com/paper/2302.10637/) (2023)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [Graph-adaptive Rectified Linear Unit for Graph Neural Networks](https://mlsanity.com/paper/2202.06281/) (2022)
- [Learning Weakly Supervised Audio-Visual Violence Detection in Hyperbolic Space](https://mlsanity.com/paper/2305.18797/) (2023)
- [Shrinking Embeddings for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2306.02199/) (2023)
- [Deep Structural Knowledge Exploitation and Synergy for Estimating Node Importance Value on Heterogeneous Information Networks](https://mlsanity.com/paper/2402.12411/) (2024)
- [Hyperbolic Diffusion Recommender Model](https://mlsanity.com/paper/2504.01541/) (2025)
- [Hyperbolic Graph Diffusion Model](https://mlsanity.com/paper/2306.07618/) (2023)
- [Think Rationally about What You See: Continuous Rationale Extraction for Relation Extraction](https://mlsanity.com/paper/2305.03503/) (2023)
- [DP-DGAD: A Generalist Dynamic Graph Anomaly Detector with Dynamic Prototypes](https://mlsanity.com/paper/2508.00664/) (2025)
- [Heterogeneous Social Event Detection via Hyperbolic Graph Representations](https://mlsanity.com/paper/2302.10362/) (2023)
- [Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks](https://mlsanity.com/paper/2303.01724/) (2023)
- [Knowledge-based Multiple Adaptive Spaces Fusion for Recommendation](https://mlsanity.com/paper/2308.15244/) (2023)
- [Hyperbolic Contrastive Learning with Model-augmentation for Knowledge-aware Recommendation](https://mlsanity.com/paper/2505.08157/) (2025)
- [Lorentz Equivariant Model for Knowledge-Enhanced Hyperbolic Collaborative Filtering](https://mlsanity.com/paper/2302.04545/) (2023)
- [FedHGN: A Federated Framework for Heterogeneous Graph Neural Networks](https://mlsanity.com/paper/2305.09729/) (2023)
- [Graph Neural Networks with a Distribution of Parametrized Graphs](https://mlsanity.com/paper/2310.16401/) (2023)
- [Treatment-Aware Hyperbolic Representation Learning for Causal Effect Estimation with Social Networks](https://mlsanity.com/paper/2401.06557/) (2024)
- [InBox: Recommendation with Knowledge Graph using Interest Box Embedding](https://mlsanity.com/paper/2403.12649/) (2024)
- [KG4RecEval: Does Knowledge Graph Really Matter for Recommender Systems?](https://mlsanity.com/paper/2404.03164/) (2024)
- [Breaking Information Cocoons: A Hyperbolic Framework for Balancing Exploration and Exploitation in Recommender Systems](https://mlsanity.com/paper/2411.13865/) (2024)
- [EHGCN: Hierarchical Euclidean-Hyperbolic Fusion via Motion-Aware GCN for Hybrid Event Stream Perception](https://mlsanity.com/paper/2504.16616/) (2025)

## Abstract (arXiv)

Aiming to alleviate data sparsity and cold-start problems of traditional recommender systems, incorporating knowledge graphs (KGs) to supplement auxiliary information has recently gained considerable attention. Via unifying the KG with user-item interactions into a tripartite graph, recent works explore the graph topologies to learn the low-dimensional representations of users and items with rich semantics. However, these real-world tripartite graphs are usually scale-free, the intrinsic hierarchical graph structures of which are underemphasized in existing works, consequently, leading to suboptimal recommendation performance. To address this issue and provide more accurate recommendation, we propose a knowledge-aware recommendation method with the hyperbolic geometry, namely Lorentzian Knowledge-enhanced Graph convolutional networks for Recommendation (LKGR). LKGR facilitates better modeling of scale-free tripartite graphs after the data unification. Specifically, we employ different information propagation strategies in the hyperbolic space to explicitly encode heterogeneous information from historical interactions and KGs. Our proposed knowledge-aware attention mechanism enables the model to automatically measure the information contribution, producing the coherent information aggregation in the hyperbolic space. Extensive experiments on three real-world benchmarks demonstrate that LKGR outperforms state-of-the-art methods by 3.6-15.3% of Recall@20 on Top-K recommendation.