arXiv:2608.16621cs.AIcs.DB2026-08中稿 · and presented at t…被引 1

动态更新语义底座,成本随变化量增长而非文档总量。

Cost Scales with Change, Not Corpus Size: Incrementally Maintaining an Evolving Semantic Substrate

  • 增量低秩更新技术,仅处理新增/修改内容
  • 更新成本仅为全量重算的1/33.7,精度损失可忽略
  • 适合需要长期维护知识库的智能问答系统

检索增强与代理式问答系统越来越倾向于在查询时重新推导语料意义。理想情况是:文档到达时一次性编译其语义,后续只需查询,如同编译器而非解释器。另一种方案是在摄入时将语义编译为紧凑可查询的语义底座,并随语料演进持续维护。传统顾虑在于维护成本——每次变更都需重建截断奇异值分解(SVD),模型更新更需全量重嵌入。本文实证表明:维护成本实际与变化量相关,而非语料规模。在控制性合成实验中(维度256,秩32,文档数从3000增至9000,共50次更新),增量低秩更新单次成本仅为全量重算的1/33.7,累计节省23.8倍;增量子空间与全量重算的主角角度漂移低于1e-11度,召回率@10达1.0。通过正交普鲁斯特虚拟轴更新,仅重嵌入约10%语料,即可达到0.95平均余弦相似度,逼近全量重嵌结果。结果支持持续维护而非反复重建语义底座。

原文摘要 · Abstract (English)

Retrieval-augmented and agentic question-answering systems increasingly re-derive the meaning of a corpus at query time. Put plainly, instead of re-deriving what a corpus means on every question, the work is done once when a document arrives and is thereafter merely consulted -- a compiler, not an interpreter, of meaning. An alternative is to compile that meaning once, at ingest time, into a compact, queryable semantic substrate and maintain it as the corpus evolves. The central objection is maintenance cost: rebuilding a truncated singular value decomposition (SVD) on every change appears prohibitive, and a change of embedding model seems to force a full re-embedding. We argue and show empirically that maintenance cost scales with the amount of change, not corpus size. On a controlled synthetic pilot (dimension 256, rank 32, a corpus grown from 3,000 to 9,000 documents over 50 update events), incremental low-rank updates were 33.7 times cheaper per update than full re-SVD and 23.8 times cheaper cumulatively, while the incremental subspace tracked the full recomputation to within floating-point precision (maximum principal-angle drift below 1e-11 degrees; recall@10 = 1.0). An orthogonal Procrustes virtual axis update recovered 0.95 mean cosine to truly re-embedded vectors by re-embedding only about 10 percent of the corpus. The results support maintaining, rather than repeatedly reconstructing, a semantic substrate.

语义底座增量学习知识库维护SVD

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