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Artificial Intelligence
arXiv (cs.LG) · July 16, 2026

Mutable Low-Rank Sketches for Retrain-Free Recommendation

Hector J. Garcia, Nick Clayton

Recommender systems have an annoying lag. You rate a new movie, but your taste profile (your embedding) stays frozen until the next full retrain, which might be hours or days away. This paper updates that profile the moment a rating arrives, no retraining needed. It stores each user's preferences in a specialized tree, fits a low-rank projection once, and recomputes the embedding on the fly.

There's a real guarantee behind it: they prove each new rating can only tighten the error bound, never loosen it, which some classic methods don't promise. On the KuaiRec dataset they report slightly better accuracy than a standard method while reading under 2% of the data and updating batches about eight times faster, and a brand-new user gets personalized picks within a millisecond of their first rating. On very sparse data their norm-based sampling covers far more items than plain uniform sampling.

These are the abstract's numbers on one dataset, so see the paper for the theorem's assumptions and how it behaves elsewhere.

From the arXiv (cs.LG) abstract

A common bottleneck in two-stage recommendation is embedding staleness: when a user rates a new item, their embedding remains fixed until the next retrain cycle. We propose mutable sketches, which store each user's preferences in a KP-tree (a sparse segment tree with sum aggregation), fit a low-rank projection once, and recompute embeddings on-the-fly as ratings arrive. We prove that each new observation monotonically tightens the prediction error envelope (Theorem 1), a…


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