Research map / Learning theory and algorithms / Matrix and tensor methods
A Geometric Approach to Personalized Recommendation with Set-Theoretic Constraints Using Box Embeddings
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Formulates personalized recommendation with set-theoretic queries (intersection, negation) as matrix completion and uses Gumbel box embeddings to represent users and attributes, outperforming vector-based MF/NeuMF/LightGCN baselines on compositional queries.
Problem
Standard vector-embedding matrix factorization struggles to answer personalized recommendation queries that involve set-theoretic compositions such as intersection and negation of attributes (e.g., comedy and action but not romance) under sparse data.
Approach
Represent users, attributes, and items as Gumbel-smoothed axis-parallel boxes so that set operations (intersection, set difference via inclusion-exclusion) can be computed geometrically on the embeddings, giving a set-theoretic inductive bias that vectors lack.
Key results
- Box-Geometric achieves 46.1 HR@50 on the U∩A1∩A2 query on MovieLens-1M-style set-theoretic evaluation, versus 27.5 for the best vector-based MF-Filter, and the paper reports about 30% average improvement over the best vector model on HR@50.
- Box-Geometric has the smallest generalization spectrum gap (26.4%) on U∩A1∩A2 queries, compared with 35.9% to 95.6% for vector methods.
- On Last-FM, Box-Geometric reaches 83.1 HR@50 on U∩A1∩A2 versus 80.7 for LGCN-Product.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use box embeddings with geometric set operations instead of the strongest vector-based method | Personalized set-theoretic recommendation · Last-FM, U ∩ A₁ ∩ ¬A₂ | Hit Rate@50 (%): 27.6 -> 60.0 | Helped |
| Use box embeddings with geometric set operations instead of the strongest vector-based method | Personalized set-theoretic recommendation · MovieLens-1M, U ∩ A₁ ∩ A₂ | Hit Rate@50 (%): 43.5 -> 46.1 | Helped |
| Use box embeddings with geometric set operations instead of the strongest vector-based method | Personalized set-theoretic recommendation · NYC-R, U ∩ A₁ ∩ A₂ | Hit Rate@50 (%): 35.1 -> 39.2 | Helped |
| Use geometric operations on box embeddings rather than score multiplication (ablation) | Box recommendation model · Last-FM, U ∩ A₁ ∩ ¬A₂ | Hit Rate@50 (%): 60.3 -> 60.0 | No clear effect |
| Use geometric operations on box embeddings rather than score multiplication (ablation) | Box recommendation model · MovieLens-1M, U ∩ A₁ ∩ A₂ | Hit Rate@50 (%): 34.2 -> 46.1 | Helped |
| Use geometric operations on box embeddings rather than score multiplication (ablation) | Box recommendation model · NYC-R, U ∩ A₁ ∩ A₂ | Hit Rate@50 (%): 37.3 -> 39.2 | Helped |
| Use box geometric query composition rather than vector addition and subtraction | MF geometric query composition · MovieLens-1M, U ∩ A₁ ∩ A₂ | Hit Rate@50 (%): 0.8 -> 46.1 | Helped |
| Increase the number of negative samples from 5 to 20 | Box embeddings training · Training hyperparameter selection | selected negative samples: 5 -> 20 | No clear effect |
Surprising findings
- Geometric vector operations (addition/subtraction) for intersection and difference perform much worse than all other vector-based methods, e.g., MF-Geometric reaches 0.8 HR@50 on the hardest MovieLens-1M query.
- Threshold-based Filter aggregation performs competitively only at HR@10 and degrades as k increases.
Limitations
- Evaluation uses a fixed set of datasets and attribute-based queries limited to two-attribute intersection and negation.
- Gumbel soft min/max approximations are used in training; hard operators at inference are suggested but not evaluated.
- Authors' own draft notes claim of faithful set-theoretic support is not fully demonstrated by experiments.
Experimental setup
Datasets: MovieLens 1M MovieLens-20M Last-FM NYC-R
Benchmarks: MovieLens 1M MovieLens-20M Last-FM NYC-R
Metrics: Hit Rate@10 Hit Rate@20 Hit Rate@50 NDCG
Baselines: MF NeuMF LightGCN
Builds on: Gumbel box embeddings matrix factorization NeuMF LightGCN
Closest papers by meaning
- Recommendations with Sparse Comparison Data: Provably Fast Convergence for Nonconvex Matrix Factorization (ICML 2025 · similarity 0.87)
- FACE: A General Framework for Mapping Collaborative Filtering Embeddings into LLM Tokens (NeurIPS 2025 · similarity 0.85)
- On the Embedding Collapse when Scaling up Recommendation Models (ICML 2024 · similarity 0.84)
- Learning Multiple User Distributions for Recommendation via Guided Conditional Diffusion (AAAI 2025 · similarity 0.84)
- UxSID: Semantic-Aware User Interests Modeling for Ultra-Long Sequence (NeurIPS 2026 · similarity 0.84)
- Improving LLMs for Recommendation with Out-Of-Vocabulary Tokens (ICML 2025 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.