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ImplicitSLIM and How it Improves Embedding-based Collaborative Filtering
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Proposes ImplicitSLIM, a closed-form, memory-efficient way to extract embeddings from EASE/SLIM-like item-item models without explicitly computing the I×I weight matrix, and uses them to initialize or regularize embedding-based CF models.
Problem
SLIM-style item-item models give strong collaborative filtering accuracy but have quadratic memory and near-cubic time cost, so they are hard to scale; their learned item-item structure is hard to exploit in embedding-based models.
Approach
Reformulates EASE as the first step of locally linear embedding (LLE) and collapses LLE's two steps into one closed-form, Woodbury-based computation, yielding low-dimensional embeddings that can be used to initialize or regularize existing CF models without ever forming the item-item matrix.
Key results
- ImplicitSLIM applied to RecVAE improves NDCG@100 on MovieLens-20M from 0.442 to 0.447 and H+Vamp(Gated) reaches 0.450, reported as new state of the art on MovieLens-20M and Netflix Prize.
- MF + ImplicitSLIM raises MovieLens-20M NDCG@100 from 0.399 to 0.423 and Million Songs NDCG@100 from 0.314 to 0.366.
- ImplicitSLIM embedding extraction takes about 1.4 to 5.1 seconds at dimension 64 to 1024 on MovieLens-20M, versus roughly 100 seconds for the explicit two-step SLIM-LLE procedure.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply ImplicitSLIM to RecVAE item embeddings | RecVAE · MovieLens-20M | NDCG@100: 0.442 -> 0.447 | Helped |
| Apply ImplicitSLIM to RecVAE item embeddings | RecVAE · Netflix Prize Dataset | NDCG@100: 0.394 -> 0.398 | Helped |
| Apply ImplicitSLIM to RecVAE item embeddings | RecVAE · Million Songs Dataset | NDCG@100: 0.326 -> 0.342 | Helped |
| Apply ImplicitSLIM to H+Vamp(Gated) item embeddings | H+Vamp(Gated) · MovieLens-20M | NDCG@100: 0.445 -> 0.450 | Helped |
| Apply ImplicitSLIM to H+Vamp(Gated) item embeddings | H+Vamp(Gated) · Netflix Prize Dataset | NDCG@100: 0.407 -> 0.410 | Helped |
| Apply ImplicitSLIM to H+Vamp(Gated) item embeddings | H+Vamp(Gated) · Million Songs Dataset | NDCG@100: 0.342 -> 0.347 | Helped |
| Apply ImplicitSLIM to user embeddings | UltraGCN · Yelp2018 | NDCG@20: 0.0561 -> 0.0568 | Helped |
| Apply ImplicitSLIM to user embeddings | UltraGCN · MovieLens-1M | Recall@20: 0.2787 -> 0.2778 | Hurt |
| Apply ImplicitSLIM to item embeddings | UltraGCN · Yelp2018 | NDCG@20: 0.0561 -> 0.0573 | Helped |
| Apply ImplicitSLIM to item embeddings | UltraGCN · MovieLens-1M | NDCG@20: 0.2642 -> 0.2659 | Helped |
| Apply ImplicitSLIM to item embeddings | BERT4Rec · MovieLens-1M, 30 epochs | NDCG@10: 0.511 -> 0.549 | Helped |
| Apply ImplicitSLIM to item embeddings | BERT4Rec · MovieLens-20M, 200 epochs | NDCG@10: 0.790 -> 0.798 | Helped |
Surprising findings
- Using user embeddings from ImplicitSLIM did not improve performance in most strong-generalization experiments.
- Applying ImplicitSLIM as a regularizer during SGD training of VAEs and GCNs did not help compared with periodic embedding updates.
Limitations
- Many hyperparameters (five for ImplicitSLIM plus MF) versus EASE's single hyperparameter.
- Gains over EASE are mostly limited to high embedding dimensions; SLIM-LLE is not scalable and results are limited to low dimensions.
- User-embedding ImplicitSLIM gave no gains in most strong-generalization experiments.
Experimental setup
Datasets: MovieLens-20M Netflix Prize Dataset Million Songs Dataset Yelp2018 MovieLens-1M
Benchmarks: MovieLens-20M Netflix Prize Dataset Million Songs Dataset Yelp2018 MovieLens-1M
Metrics: Recall@k NDCG@k
Baselines: MF WMF CoFactor GRALS SLIM EASE PLRec CDAE MultVAE RaCT RecVAE H+Vamp(Gated)
Builds on: EASE SLIM locally linear embedding RecVAE UltraGCN
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