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

arXiv: https://arxiv.org/abs/2608.16621 · HTML: https://mlsanity.com/paper/2608.16621/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Placed in

- Retrieval-augmented generation / [Generation and context integration](https://mlsanity.com/rag/generation-and-context-integration/)
- LLM agents and tool use / [Agent memory systems](https://mlsanity.com/agents/agent-memory-systems/)

## Builds on (most cited first, 17 of 17)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [Leveraging Passage Retrieval with Generative Models for Open Domain Question Answering](https://mlsanity.com/paper/2007.01282/) (2020)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [On the Sentence Embeddings from Pre-trained Language Models](https://mlsanity.com/paper/2011.05864/) (2020)
- [A Comprehensive Survey and Experimental Comparison of Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2101.12631/) (2021)
- [Towards Backward-Compatible Representation Learning](https://mlsanity.com/paper/2003.11942/) (2020)
- [A Cluster-based Approach for Improving Isotropy in Contextual Embedding Space](https://mlsanity.com/paper/2106.01183/) (2021)
- [Facts as First Class Objects: Knowledge Objects for Persistent LLM Memory](https://mlsanity.com/paper/2603.17781/) (2026)

## Built on by (most cited first, 2 of 2)

- [RAG Deserves an Index: Why Ingest-Time Compilation Beats Query-Time Interpretation](https://mlsanity.com/paper/2608.20845/) (2026)
- [Ingest-Time Fact Compilation for Cost-Efficient and Reliable Question Answering over Revised Corpora](https://mlsanity.com/paper/2609.29661/) (2026)

## Abstract (arXiv)

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.