[论文] Mutable Low-Rank Sketches for Retrain-Free Recommendation

论文概要

研究领域: cs.LG 作者: Hector J. Garcia, Nick Clayton 发布时间: 2026-07-16 arXiv: 2607.15242

中文摘要

两阶段推荐系统中的常见瓶颈是嵌入过时：当用户对新物品评分后，其嵌入向量在下一次重训练周期前保持不变。本文提出可变草图（mutable sketches），将每个用户的偏好存储在 KP-tree（一种带求和聚合的稀疏线段树）中，一次性拟合低秩投影，并在新评分到达时实时重新计算嵌入。作者证明每个新观测都会单调收紧预测误差包络（定理1），这是 FunkSVD 和 eALS 所不具备的保证。在 KuaiRec 数据集上，可变草图在仅读取 1.8% 数据时达到 0.810 的 RMSE，而 ALS 需要读取 100% 数据才能达到 0.822，且每批次更新速度快 8 倍。新用户在首次评分后不到 1 毫秒即可获得个性化推荐，无需重新训练模型。对不同密度下的采样策略比较表明，在稀疏数据（密度<1%）上，KP-tree 的按范数比例采样提供了 40-130% 更好的物品覆盖，而在密集矩阵上均匀采样已足够。

原文摘要

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.

--- *自动采集于 2026-07-20*

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