# flexvec: SQL Vector Retrieval with Programmatic Embedding Modulation

arXiv: https://arxiv.org/abs/2603.22587 · HTML: https://mlsanity.com/paper/2603.22587/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [Precise Zero-Shot Dense Retrieval without Relevance Labels](https://mlsanity.com/paper/2212.10496/) (2022)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Nomic Embed: Training a Reproducible Long Context Text Embedder](https://mlsanity.com/paper/2402.01613/) (2024)
- [Declarative Experimentation in Information Retrieval using PyTerrier](https://mlsanity.com/paper/2007.14271/) (2020)
- [Survey of Filtered Approximate Nearest Neighbor Search over the Vector-Scalar Hybrid Data](https://mlsanity.com/paper/2505.06501/) (2025)
- [IMRNNs: An Efficient Method for Interpretable Dense Retrieval via Embedding Modulation](https://mlsanity.com/paper/2601.20084/) (2026)
- [DEO: Training-Free Direct Embedding Optimization for Negation-Aware Retrieval](https://mlsanity.com/paper/2603.09185/) (2026)
- [RAGdb: A Zero-Dependency, Embeddable Architecture for Multimodal Retrieval-Augmented Generation on the Edge](https://mlsanity.com/paper/2602.22217/) (2025)

## Abstract (arXiv)

As AI agents become the primary consumers of retrieval APIs, there is an opportunity to expose more of the retrieval pipeline to the caller. flexvec is a retrieval kernel that exposes the embedding matrix and score array as a programmable surface, allowing arithmetic operations on both before selection. We refer to composing operations on this surface at query time as Programmatic Embedding Modulation (PEM). This paper describes a set of such operations and integrates them into a SQL interface via a query materializer that facilitates composable query primitives. On a production corpus of 240,000 chunks, three composed modulations execute in 19 ms end-to-end on a desktop CPU without approximate indexing. At one million chunks, the same operations execute in 82 ms.