# Thinking inside The Box: Learning Hypercube Representations for Group Recommendation

arXiv: https://arxiv.org/abs/2204.02592 · HTML: https://mlsanity.com/paper/2204.02592/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2022.

## Built on by (most cited first, 11 of 11)

- [Recent Developments in Recommender Systems: A Survey](https://mlsanity.com/paper/2306.12680/) (2023)
- [AlignGroup: Learning and Aligning Group Consensus with Member Preferences for Group Recommendation](https://mlsanity.com/paper/2409.02580/) (2024)
- [Out of the Box Thinking: Improving Customer Lifetime Value Modelling via Expert Routing and Game Whale Detection](https://mlsanity.com/paper/2308.12729/) (2023)
- [A Comprehensive Survey on Self-Supervised Learning for Recommendation](https://mlsanity.com/paper/2404.03354/) (2024)
- [Leveraging Member-Group Relations via Multi-View Graph Filtering for Effective Group Recommendation](https://mlsanity.com/paper/2502.09050/) (2025)
- [When Box Meets Graph Neural Network in Tag-aware Recommendation](https://mlsanity.com/paper/2406.12020/) (2024)
- [Coarse-to-Fine Lightweight Meta-Embedding for ID-Based Recommendation](https://mlsanity.com/paper/2501.11870/) (2025)
- [Collaborative Interest-aware Graph Learning for Group Identification](https://mlsanity.com/paper/2506.14826/) (2025)
- [Stochastic Deep Graph Clustering for Practical Group Formation](https://mlsanity.com/paper/2511.02879/) (2025)
- [DALI: LLM-Agent Enhanced Dual-Stream Adaptive Leadership Identification for Group Recommendations](https://mlsanity.com/paper/2603.19909/) (2026)
- [AgentGR: Semantic-aware Agentic Group Decision-Making Simulator for Group Recommendation](https://mlsanity.com/paper/2605.10367/) (2026)

## Abstract (arXiv)

As a step beyond traditional personalized recommendation, group recommendation is the task of suggesting items that can satisfy a group of users. In group recommendation, the core is to design preference aggregation functions to obtain a quality summary of all group members' preferences. Such user and group preferences are commonly represented as points in the vector space (i.e., embeddings), where multiple user embeddings are compressed into one to facilitate ranking for group-item pairs. However, the resulted group representations, as points, lack adequate flexibility and capacity to account for the multi-faceted user preferences. Also, the point embedding-based preference aggregation is a less faithful reflection of a group's decision-making process, where all users have to agree on a certain value in each embedding dimension instead of a negotiable interval. In this paper, we propose a novel representation of groups via the notion of hypercubes, which are subspaces containing innumerable points in the vector space. Specifically, we design the hypercube recommender (CubeRec) to adaptively learn group hypercubes from user embeddings with minimal information loss during preference aggregation, and to leverage a revamped distance metric to measure the affinity between group hypercubes and item points. Moreover, to counteract the long-standing issue of data sparsity in group recommendation, we make full use of the geometric expressiveness of hypercubes and innovatively incorporate self-supervision by intersecting two groups. Experiments on four real-world datasets have validated the superiority of CubeRec over state-of-the-art baselines.