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Hgformer: Hyperbolic Graph Transformer for Collaborative Filtering
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Proposes Hgformer, a fully hyperbolic graph transformer for collaborative filtering that combines a parameter-free hyperbolic graph convolution (LHGCN) with a linear-complexity hyperbolic cross-attention to capture local and global user-item structure.
Problem
Graph-neural-network collaborative filtering struggles with long-tail items because of local-only message passing and distortion from embedding user-item graphs in Euclidean space; existing hyperbolic CF methods and hyperbolic graph transformers lack a fully hyperbolic, scalable global attention for
Approach
Perform LightGCN-style parameter-free convolution directly via hyperbolic centroids (LHGCN) and add a user-item-only hyperbolic cross-attention whose softmax kernel is approximated with hyperbolic positive random features, reducing complexity from O(MN) to O(M+N) with an approximation error bound.
Key results
- On Amazon Book, Hgformer reaches Recall@10 0.0901 vs 0.0766 for the second-best HICF (about 17.6% relative gain).
- On Amazon CD, relative improvements over HICF are 18.3% (Recall@10) and 15.9% (NDCG@10).
- Removing the hyperbolic transformer lowers Recall@10 by 11.6% on Amazon Book, and removing LHGCN causes the largest drop in the ablation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Hgformer instead of HICF | Collaborative filtering · Amazon Book | Recall@10: 0.0766 -> 0.0901* | Helped |
| use Hgformer instead of HICF | Collaborative filtering · Amazon CD | Recall@10: 0.0826 -> 0.0977* | Helped |
| use Hgformer instead of HRCF | Collaborative filtering · Amazon Movie | Recall@10: 0.0761 -> 0.0803* | Helped |
| use Hgformer instead of HICF | Collaborative filtering · Douban Book | Recall@10: 0.1388 -> 0.1462* | Helped |
| use Hgformer instead of HRCF | Collaborative filtering · Douban Movie | NDCG@10: 0.1342 -> 0.1322* | Hurt |
| use Hgformer instead of HICF | Collaborative filtering · Douban Music | Recall@10: 0.1276 -> 0.1386* | Helped |
| add Hyperbolic Transformer (ablation) | Hgformer · Amazon Book | Recall@10: 0.0796 -> 0.0901* | Helped |
| add LHGCN (ablation) | Hgformer · Amazon Book | Recall@10: 0.0422 -> 0.0901* | Helped |
| replace HGCF with LHGCN (ablation) | Hgformer with Hyperbolic Transformer · Amazon Book | Recall@10: 0.0821 -> 0.0901* | Helped |
| replace HGCF with LHGCN (ablation) | Hgformer with Hyperbolic Transformer · Douban Book | Recall@10: 0.1412 -> 0.1462* | Helped |
Surprising findings
- Transformers alone without the LHGCN graph convolution perform poorly, so the transformer works best as a supplementary module to GNN message passing.
- Graph transformers designed for node classification (SGFormer, NodeFormer, Hypformer) perform worse than GNN baselines on CF, attributed to attention over all same-type node pairs.
Limitations
- Ablation shows the model relies on LHGCN; the transformer alone is insufficient.
- Approximation error bound depends on feature norms and curvature, so accuracy requires normalization or more random features.
- Performance optimal layer count differs between Amazon and Douban datasets, requiring dataset-specific tuning.
Experimental setup
Datasets: Amazon Book Amazon CD Amazon Movie Douban Book Douban Movie Douban Music
Benchmarks: Amazon Book Amazon CD Amazon Movie Douban Book Douban Movie Douban Music
Metrics: Recall@10 Recall@20 NDCG@10 NDCG@20 tail recall@10 tail percentage
Baselines: BPR NGCF LightGCN HMLET HGCF HRCF HICF SGFormer NodeFormer Hypformer
Builds on: LightGCN HGCF HICF Hypformer NodeFormer
Closest papers by meaning
- Revisiting Graph Based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach (AAAI 2020 · similarity 0.91)
- Hyperbolic Graph Neural Networks at Scale: A Meta Learning Approach (NeurIPS 2023 · similarity 0.89)
- Semantic Enhanced Heterogeneous Hypergraph Network for Collaborative Filtering (AAAI 2025 · similarity 0.87)
- Beyond Graph Convolution: Multimodal Recommendation with Topology-aware MLPs (AAAI 2025 · similarity 0.86)
- LGMRec: Local and Global Graph Learning for Multimodal Recommendation (AAAI 2024 · similarity 0.86)
- Residual Hyperbolic Graph Convolution Networks (AAAI 2024 · similarity 0.86)
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