cs.AIAug 17, 2026

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

Authors: Yusuke Takahashi, Kyle Wild, Asako Uraki

Organizations: Asia AI Institute, Faculty of Data Science Musashino University Tokyo, Japan

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.

Explore similar work

Aug 21, 2026

RAG Deserves an Index: Why Ingest-Time Compilation Beats Query-Time Interpretation

Nearly every retrieval-augmented question-answering system in production ships with a hidden interpreter: on each query a language model re-derives the meaning of raw corpus text and then throws that work away. Cheaper models do not close the gap: per-token prices have fallen by orders of magnitude while inference spend has risen, because context volume grows faster than prices fall. This is the modern equivalent of the full-table scan, and the remedy is the one databases found fifty years ago: do the expensive work once, at write time, into a maintained structure that makes reads cheap. A corpus whose read pattern is known before it ever meets a user can and should be indexed too. We call the paradigm ingest-time semantic compilation (ISC): compile a corpus's meaning into a queryable substrate with two coupled layers - incrementally maintained embeddings, and atomic claims whose provenance is validated at compile time - and treat that substrate as a first-class database object with its own DDL, maintenance contract, migration contract, and cost model. Two existence proofs support it. Substrate upkeep scales with change rather than corpus size: incremental updates run 33.7x cheaper than reconstruction while tracking it to floating-point precision. And on a held-out sample of 500 broadcast-interview transcripts, compiled claims as the retrieval payload win all 32 budget-by-model cells: 85.2% correct from roughly 2.2k reader tokens against 72.5% from 16.3k for the best chunk configuration anywhere. The only baseline that keeps pace is a contextualized-chunk pipeline with hybrid retrieval and reranking, statistically indistinguishable from compiled claims at roughly twenty-one times the query-path tokens - and it reaches that parity, we argue, precisely because it has itself begun to compile. We close with the systems agenda this opens, from compilation planners to read planning.
Aug 29, 2026

Ingest-Time Fact Compilation for Cost-Efficient and Reliable Question Answering over Revised Corpora

Most agentic question answering (QA) systems do an important part of their semantic work at the worst possible time: every time someone asks a question. When a corpus contains revisions, drafts, revocations, deletions, and sources with different levels of authority, the model must reconstruct the governed current state on every read - then throw that work away and repeat it on the next query. This is a bit like a database that rebuilds a materialized view every time someone reads from it. We present ingest-time fact compilation, an architecture that performs this work when corpus data is ingested or changed. Raw passages are rephrased into self-contained facts; rules governing revisions, deletions, effective dates, and source trust are resolved once; and the resulting state is stored as typed records carrying source and revision provenance. At query time, an inexpensive model reads the compiled record instead of reconstructing it from noisy candidates. In a controlled synthetic experiment across five seeds, the same low-cost model produced the correct value, source, and revision in only one of 30 trials under query-time reconstruction, but in all 30 trials from the compiled substrate, at 12.89 times lower mean read cost per question. On simpler revision questions both architectures were exact, but the compiled path used 21.6 times fewer tokens. A separate test found that fact rephrasing roughly halved verbose Federal Reserve dialogue while preserving high source entailment, but left concise Wikipedia prose essentially unchanged. These results support a narrow but practical claim: resolving a corpus state once can make subsequent QA cheaper and more reliable for inexpensive models. We release the open source, MIT-licensed implementation and experimental artifacts.
Jul 29, 2026

BM25 Wins at Scale: A Scaling Study of Retrieval-Augmented Generation Paradigms

Retrieval-augmented generation (RAG) spans lexical and dense retrieval, graph-based indexing, and agentic search, but these paradigms are usually evaluated on different benchmarks at one corpus size, leaving their accuracy-cost scaling unclear. To bridge this gap, we present a controlled study that varies corpus size along 28 strictly nested tiers spanning roughly 450-fold, while holding questions and a fixed bedrock of relevant and adversarial documents unchanged. Under one reader model and one judging protocol, we measure official accuracy, construction and query tokens, and latency. The results reveal a scale-dependent crossover rather than an unconditional winner. File-System Agent leads at the smallest shared tiers, but its sequential exploration costs 39 times more query tokens at the bedrock and becomes less effective as the search space grows. Around 10 million corpus tokens, BM25 overtakes it and leads at every larger shared tier, with a margin approaching 20 points at full scale. BM25 also anchors the low-cost end of the Pareto frontier without LLM-based construction. Dense retrieval remains efficient but less accurate, whereas graph-based RAG encounters construction walls before deployment scale and its scalable variants remain below BM25 at shared tiers. Overall, corpus growth increasingly favors global candidate ranking: lexical retrieval is the strongest scalable default, while agentic reasoning works best after ranked discovery rather than in place of it.