成本随变化量而非语料库规模变化：增量式维护演化中的语义基底
Cost Scales with Change, Not Corpus Size: Incrementally Maintaining an Evolving Semantic Substrate
AI总结：
该研究提出语义基底维护成本随变化量而非语料库规模变化，通过增量低秩更新等方法，以远低于完整重构的成本实现语义基底的高效维护，且精度满足要求。
AI中文摘要：
检索增强与智能体问答系统日益在查询时重新推导语料库的含义。简单来说，系统并非针对每个问题重新推导语料库的含义，而是在文档到达时完成一次推导，之后仅需参考即可——这是一种意义的编译器，而非解释器。另一种方案是在摄入时将含义一次性编译为紧凑、可查询的语义基底，并在语料库演化过程中对其进行维护。核心争议在于维护成本：每次变化后重建截断奇异值分解（SVD）的成本似乎过高，且嵌入模型的变更似乎会强制要求对全部语料库重新嵌入。本文论证并通过实验证明，维护成本随变化量而非语料库规模变化。在受控合成试点中（维度256、秩32，语料库经50次更新事件从3000篇增长至9000篇），增量式低秩更新的单次更新成本比完整重新SVD低33.7倍，累计成本低23.8倍，同时增量子空间跟踪完整重新计算的精度达到浮点级别（最大主角度漂移低于1e-11度；召回@10=1.0）。正交Procrustes虚拟轴更新通过仅重新嵌入约10%的语料库，使平均余弦相似度恢复至真正重新嵌入向量的0.95。这些结果支持维护而非重复重构语义基底的思路。
英文摘要：
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.
