无需重训练，实时更新用户推荐嵌入。
Mutable Low-Rank Sketches for Retrain-Free Recommendation
- 用KP树存储用户偏好，低秩投影一次完成，动态计算嵌入。
- 稀疏数据下覆盖率达均匀采样的1.4到2.3倍，新用户首评后<1毫秒出推荐。
- 理论保证误差单调收敛，适用于实时推荐系统场景。
两阶段推荐中的嵌入过时是常见瓶颈：用户评分新项目后，其嵌入需等待下次重训练才更新。我们提出可变草图机制，将用户偏好存于KP树（一种带求和聚合的稀疏线段树），仅需一次低秩投影，即可在评分到达时即时重算嵌入。证明了每次新观测均单调收紧预测误差包络（定理1），这是FunkSVD与eALS所不具备的保证。在KuaiRec数据集上，可变草图实现0.810 RMSE，仅读取1.8%数据，而ALS需100%数据达0.822，且每批更新快8倍。新用户首评后<1毫秒即可获得个性化推荐，无需模型重训练。不同密度下的采样策略对比显示，KP树的范数比例采样在稀疏数据（<1%密度）下提升40%-130%的物品覆盖率，而均匀采样在稠密矩阵中已足够。
原文摘要 · Abstract (English)
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 guarantee that FunkSVD and eALS lack. On KuaiRec, the mutable sketch achieves 0.810 RMSE at 1.8% data read vs. ALS 0.822 at 100%, with 8x faster per-batch updates. A new user receives personalized recommendations in <1 ms after their first rating, with no model retraining required. A comparison of sampling strategies across density regimes shows that the KP-tree's norm-proportional sampling provides 40-130% better item coverage on sparse data (<1% density), while uniform sampling suffices on dense matrices.
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