# HICF: Hyperbolic Informative Collaborative Filtering

arXiv: https://arxiv.org/abs/2207.09051 · HTML: https://mlsanity.com/paper/2207.09051/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 49 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2110.15114/) (2021)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space](https://mlsanity.com/paper/2107.03767/) (2021)
- [SimpleX: A Simple and Strong Baseline for Collaborative Filtering](https://mlsanity.com/paper/2109.12613/) (2021)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [Latent Relational Metric Learning via Memory-based Attention for Collaborative Ranking](https://mlsanity.com/paper/1707.05176/) (2017)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [Unsupervised Text Generation by Learning from Search](https://mlsanity.com/paper/2007.08557/) (2020)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems](https://mlsanity.com/paper/2105.08908/) (2021)
- [Hyper Meta-Path Contrastive Learning for Multi-Behavior Recommendation](https://mlsanity.com/paper/2109.02859/) (2021)
- [Enhancing Hyperbolic Graph Embeddings via Contrastive Learning](https://mlsanity.com/paper/2201.08554/) (2022)
- [FeatureNorm: L2 Feature Normalization for Dynamic Graph Embedding](https://mlsanity.com/paper/2103.00164/) (2021)
- [Text Revision by On-the-Fly Representation Optimization](https://mlsanity.com/paper/2204.07359/) (2022)
- [Collaborative Translational Metric Learning](https://mlsanity.com/paper/1906.01637/) (2019)

## Built on by (most cited first, 24 of 24)

- [Hyperbolic Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2410.04010/) (2024)
- [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)
- [HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction](https://mlsanity.com/paper/2304.07302/) (2023)
- [Hyperbolic Diffusion Recommender Model](https://mlsanity.com/paper/2504.01541/) (2025)
- [HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.02057/) (2024)
- [Graph Augmentation for Recommendation](https://mlsanity.com/paper/2403.16656/) (2024)
- [Three Revisits to Node-Level Graph Anomaly Detection: Outliers, Message Passing and Hyperbolic Neural Networks](https://mlsanity.com/paper/2403.04010/) (2024)
- [Hyperbolic Graph Representation Learning: A Tutorial](https://mlsanity.com/paper/2211.04050/) (2022)
- [Knowledge-based Multiple Adaptive Spaces Fusion for Recommendation](https://mlsanity.com/paper/2308.15244/) (2023)
- [Hgformer: Hyperbolic Graph Transformer for Recommendation](https://mlsanity.com/paper/2502.15693/) (2024)
- [Large Language Models Enhanced Hyperbolic Space Recommender Systems](https://mlsanity.com/paper/2504.05694/) (2025)
- [Hyperbolic Multimodal Continual Learning](https://mlsanity.com/paper/2608.09572/) (2026)
- [Lorentz Equivariant Model for Knowledge-Enhanced Hyperbolic Collaborative Filtering](https://mlsanity.com/paper/2302.04545/) (2023)
- [Breaking Information Cocoons: A Hyperbolic Framework for Balancing Exploration and Exploitation in Recommender Systems](https://mlsanity.com/paper/2411.13865/) (2024)
- [Minimizing Hyperbolic Embedding Distortion with LLM-Guided Hierarchy Restructuring](https://mlsanity.com/paper/2511.20679/) (2025)
- [Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI](https://mlsanity.com/paper/2609.17969/) (2026)
- [Review-Based Hyperbolic Cross-Domain Recommendation](https://mlsanity.com/paper/2403.20298/) (2024)
- [MixRec: Heterogeneous Graph Collaborative Filtering](https://mlsanity.com/paper/2412.13825/) (2024)
- [Influence Strength Estimation in Hyperbolic Space for Social Influence Maximization](https://mlsanity.com/paper/2502.13571/) (2025)
- [Improving Graph Few-shot Learning with Hyperbolic Space and Denoising Diffusion](https://mlsanity.com/paper/2604.27462/) (2026)
- [Hyperbolic Multimodal Continual Learning: A Closest-Admissible Solution](https://mlsanity.com/paper/2609.29329/) (2026)

## Abstract (arXiv)

Considering the prevalence of the power-law distribution in user-item networks, hyperbolic space has attracted considerable attention and achieved impressive performance in the recommender system recently. The advantage of hyperbolic recommendation lies in that its exponentially increasing capacity is well-suited to describe the power-law distributed user-item network whereas the Euclidean equivalent is deficient. Nonetheless, it remains unclear which kinds of items can be effectively recommended by the hyperbolic model and which cannot. To address the above concerns, we take the most basic recommendation technique, collaborative filtering, as a medium, to investigate the behaviors of hyperbolic and Euclidean recommendation models. The results reveal that (1) tail items get more emphasis in hyperbolic space than that in Euclidean space, but there is still ample room for improvement; (2) head items receive modest attention in hyperbolic space, which could be considerably improved; (3) and nonetheless, the hyperbolic models show more competitive performance than Euclidean models. Driven by the above observations, we design a novel learning method, named hyperbolic informative collaborative filtering (HICF), aiming to compensate for the recommendation effectiveness of the head item while at the same time improving the performance of the tail item. The main idea is to adapt the hyperbolic margin ranking learning, making its pull and push procedure geometric-aware, and providing informative guidance for the learning of both head and tail items. Extensive experiments back up the analytic findings and also show the effectiveness of the proposed method. The work is valuable for personalized recommendations since it reveals that the hyperbolic space facilitates modeling the tail item, which often represents user-customized preferences or new products.