References

The papers behind the ideas in hvec, grouped by topic, each with a note on why it matters here. Blog posts and experiment write-ups cite entries from this list by key. To add one, append to docs/_data/references.yml with a resolvable DOI or arXiv link. Definitions of the terms are in the glossary.

Quantization

Least Squares Quantization in PCM
Stuart P. Lloyd. IEEE Transactions on Information Theory 28(2), 1982. doi.org/10.1109/TIT.1982.1056489
The k-means algorithm, which trains every codebook in product quantization. Cite as lloyd1982kmeans.

Vector Quantization
Robert M. Gray. IEEE ASSP Magazine 1(2), 1984. doi.org/10.1109/MASSP.1984.1162229
The tutorial that defined vector quantization as a field, decades before embeddings. Cite as gray1984vq.

Product Quantization for Nearest Neighbor Search
Hervé Jégou, Matthijs Douze, Cordelia Schmid. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(1), 2011. doi.org/10.1109/TPAMI.2010.57
The paper most vector-database quantizers descend from. Introduces product quantization and asymmetric distance computation, the clearest example of homomorphic compression for search. Cite as jegou2011pq.

Iterative Quantization: A Procrustean Approach to Learning Binary Codes for Large-Scale Image Retrieval
Yunchao Gong, Svetlana Lazebnik, Albert Gordo, Florent Perronnin. IEEE Transactions on Pattern Analysis and Machine Intelligence 35(12), 2013. doi.org/10.1109/TPAMI.2012.193
Learns a rotation that makes sign-bit binarisation less lossy. The classic learned binary code. Cite as gong2013itq.

Optimized Product Quantization
Tiezheng Ge, Kaiming He, Qifa Ke, Jian Sun. IEEE Transactions on Pattern Analysis and Machine Intelligence 36(4), 2014. doi.org/10.1109/TPAMI.2013.240
Learns a rotation before splitting into subspaces, cutting PQ error substantially. The usual next step after plain PQ. Cite as ge2014opq.

Additive Quantization for Extreme Vector Compression
Artem Babenko, Victor Lempitsky. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2014. doi.org/10.1109/CVPR.2014.124
Replaces PQ's independent subspaces with sums of codewords. Higher accuracy per byte at higher encoding cost. Cite as babenko2014aq.

Cache locality is not enough: High-Performance Nearest Neighbor Search with Product Quantization Fast Scan
Fabien André, Anne-Marie Kermarrec, Nicolas Le Scouarnec. Proceedings of the VLDB Endowment 9(4), 2015. doi.org/10.14778/2856318.2856324
Shows how to make PQ distance lookups SIMD-friendly. Relevant once hvec cares about throughput, not just error. Cite as andre2015fastscan.

All-but-the-Top: Simple and Effective Postprocessing for Word Representations
Jiaqi Mu, Pramod Viswanath. International Conference on Learning Representations (ICLR), 2018. arxiv.org/abs/1702.01417
Shows that embedding vectors share a large common mean vector and a few dominant directions, and that subtracting them helps. The reason hvec's binary-centred codec exists. Cite as mu2018allbutthetop.

Accelerating Large-Scale Inference with Anisotropic Vector Quantization
Ruiqi Guo, Philip Sun, Erik Lindgren, Quan Geng, David Simcha, Felix Chern, Sanjiv Kumar. International Conference on Machine Learning (ICML), 2020. arxiv.org/abs/1908.10396
Argues that quantization error should be measured by its effect on inner-product ranking, not reconstruction. Exactly the stance hvec takes one level up, at the answer. Cite as guo2020scann.

Matryoshka Representation Learning
Aditya Kusupati, Gantavya Bhatt, Aniket Rege, Matthew Wallingford, Aditya Sinha, Vivek Ramanujan, William Howard-Snyder, Kaifeng Chen, Sham Kakade, Prateek Jain, Ali Farhadi. Advances in Neural Information Processing Systems (NeurIPS), 2022. arxiv.org/abs/2205.13147
Trains embeddings whose leading dimensions are usable alone. Truncation becomes a compression codec with near-zero compute. Cite as kusupati2022mrl.

RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search
Jianyang Gao, Cheng Long. Proceedings of the ACM on Management of Data (SIGMOD), 2024. arxiv.org/abs/2405.12497
A binary quantizer with a provable error bound on estimated distances. A strong modern candidate for the 1-bit codec. Cite as gao2024rabitq.

Sketches and indexes

Extensions of Lipschitz mappings into a Hilbert space
William B. Johnson, Joram Lindenstrauss. Contemporary Mathematics 26, 1984. doi.org/10.1090/conm/026/737400
The Johnson-Lindenstrauss lemma. Random projection preserves pairwise distances within a provable bound, which makes it a homomorphic codec for L2. Cite as johnson1984jl.

Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality
Piotr Indyk, Rajeev Motwani. ACM Symposium on Theory of Computing (STOC), 1998. doi.org/10.1145/276698.276876
Locality-sensitive hashing. Hash collisions as a proxy for similarity. Cite as indyk1998lsh.

Similarity Estimation Techniques from Rounding Algorithms
Moses S. Charikar. ACM Symposium on Theory of Computing (STOC), 2002. doi.org/10.1145/509907.509965
SimHash. Hamming distance between sign bits of random projections estimates the angle between vectors. The theory behind binary quantization of normalised embeddings. Cite as charikar2002simhash.

Efficient and Robust Approximate Nearest Neighbor Search Using Hierarchical Navigable Small World Graphs
Yury A. Malkov, Dmitry A. Yashunin. IEEE Transactions on Pattern Analysis and Machine Intelligence 42(4), 2020. arxiv.org/abs/1603.09320
HNSW, the graph index inside most vector databases. hvec deliberately does not use an index so that codec error is measured alone. Cite as malkov2020hnsw.

ANN-Benchmarks: A Benchmarking Tool for Approximate Nearest Neighbor Algorithms
Martin Aumüller, Erik Bernhardsson, Alexander Faithfull. Information Systems 87, 2020. arxiv.org/abs/1807.05614
The standard recall-versus-throughput benchmark. hvec's bench is the same idea with the chat model added to the loop. Cite as aumuller2020annb.

A Comprehensive Survey on Vector Database: Storage and Retrieval Technique, Challenge
James Jie Pan, Jianguo Wang, Guoliang Li. arXiv:2310.11703, 2023. arxiv.org/abs/2310.11703
A map of the vector-database landscape, including where quantization sits in the storage layer. Cite as pan2023vdbsurvey.

The Faiss library
Matthijs Douze, Alexandr Guzhva, Chengqi Deng, Jeff Johnson, Gergely Szilvasy, Pierre-Emmanuel Mazaré, Maria Lomeli, Lucas Hosseini, Hervé Jégou. arXiv:2401.08281, 2024. arxiv.org/abs/2401.08281
The reference implementation of most quantizers above. Useful for checking that an hvec codec reproduces known numbers. Cite as douze2024faiss.

Homomorphic encryption

Fully Homomorphic Encryption Using Ideal Lattices
Craig Gentry. ACM Symposium on Theory of Computing (STOC), 2009. doi.org/10.1145/1536414.1536440
The first fully homomorphic encryption scheme. The origin of the word "homomorphic" in this project's name. Cite as gentry2009fhe.

Homomorphic Encryption for Arithmetic of Approximate Numbers
Jung Hee Cheon, Andrey Kim, Miran Kim, Yongsoo Song. ASIACRYPT, 2017. eprint.iacr.org/2016/421
CKKS, the scheme that supports approximate arithmetic on real-valued vectors. The natural choice for computing inner products on encrypted embeddings. Cite as cheon2017ckks.

Embeddings and RAG

Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks
Nils Reimers, Iryna Gurevych. Conference on Empirical Methods in Natural Language Processing (EMNLP), 2019. arxiv.org/abs/1908.10084
Made dense sentence embeddings practical for similarity search. Cite as reimers2019sbert.

Dense Passage Retrieval for Open-Domain Question Answering
Vladimir Karpukhin, Barlas Oğuz, Sewon Min, Patrick Lewis, Ledell Wu, Sergey Edunov, Danqi Chen, Wen-tau Yih. Conference on Empirical Methods in Natural Language Processing (EMNLP), 2020. arxiv.org/abs/2004.04906
Dense retrieval for question answering with a learned bi-encoder. The retrieval half of RAG. Cite as karpukhin2020dpr.

Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks
Patrick Lewis, Ethan Perez, Aleksandra Piktus, Fabio Petroni, Vladimir Karpukhin, Naman Goyal, Heinrich Küttler, Mike Lewis, Wen-tau Yih, Tim Rocktäschel, Sebastian Riedel, Douwe Kiela. Advances in Neural Information Processing Systems (NeurIPS), 2020. arxiv.org/abs/2005.11401
Coined "RAG". The pipeline hvec benchmarks. Cite as lewis2020rag.

BEIR: A Heterogeneous Benchmark for Zero-shot Evaluation of Information Retrieval Models
Nandan Thakur, Nils Reimers, Andreas Rücklé, Abhishek Srivastava, Iryna Gurevych. NeurIPS Datasets and Benchmarks, 2021. arxiv.org/abs/2104.08663
Retrieval datasets with relevance judgments. A likely source for hvec's question sets. Cite as thakur2021beir.

C-Pack: Packed Resources For General Chinese Embeddings
Shitao Xiao, Zheng Liu, Peitian Zhang, Niklas Muennighoff. arXiv:2309.07597, 2023. arxiv.org/abs/2309.07597
Introduces the BGE embedding models. hvec's default local embedder is bge-small-en-v1.5. Cite as xiao2023bge.

Text Embeddings Reveal (Almost) As Much As Text
John X. Morris, Volodymyr Kuleshov, Vitaly Shmatikov, Alexander M. Rush. Conference on Empirical Methods in Natural Language Processing (EMNLP), 2023. arxiv.org/abs/2310.06816
Inverts embeddings back to text with high fidelity for short inputs. Evidence that an embedding is a literal compressed representation, not an opaque fingerprint. Cite as morris2023vec2text.

LLMLingua: Compressing Prompts for Accelerated Inference of Large Language Models
Huiqiang Jiang, Qianhui Wu, Chin-Yew Lin, Yuqing Yang, Lili Qiu. Conference on Empirical Methods in Natural Language Processing (EMNLP), 2023. arxiv.org/abs/2310.05736
Compresses the text the model reads, not the vectors it retrieves by. The payload-compression layer, which hvec deliberately leaves out of scope. Cite as jiang2023llmlingua.

Headroom: the context compression layer for AI agents
Headroom Labs. Open-source software, Apache-2.0, 2026. github.com/headroomlabs-ai/headroom
Production payload compression as a proxy, library and MCP server. Compresses what the model reads; hvec compresses what the store searches by and measures both. Cite as headroom2026.

Evaluation

Ragas: Automated Evaluation of Retrieval Augmented Generation
Shahul Es, Jithin James, Luis Espinosa-Anke, Steven Schockaert. arXiv:2309.15217, 2023. arxiv.org/abs/2309.15217
Defines faithfulness, answer relevance and context relevance as LLM-scored metrics. The vocabulary hvec uses for generation-side KPIs. Cite as es2023ragas.

Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena
Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric P. Xing, Hao Zhang, Joseph E. Gonzalez, Ion Stoica. Advances in Neural Information Processing Systems (NeurIPS), 2023. arxiv.org/abs/2306.05685
Evidence for, and known biases of, using a language model to grade answers. Read before trusting an LLM judge in a benchmark. Cite as zheng2023judge.