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

arXiv:2608.16621v1 Announce Type: new Abstract: 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.

Abstract: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.

5 pages, 5 figures, 1 table. Accepted and presented at the 2026 International Electronics Symposium (IES), Yogyakarta, Indonesia, August 1-3, 2026 (IEEE technically co-sponsored). Authors' accepted version

Artificial Intelligence (cs.AI); Databases (cs.DB); Information Retrieval (cs.IR)

H.3.3; H.3.1; H.2.4

arXiv:2608.16621 [cs.AI]

(or arXiv:2608.16621v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.16621 arXiv-issued DOI via DataCite (pending registration)

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

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