# Projection and Quantisation: A Unifying View of Learning to Hash, from Random Projections to the RAG Era

arXiv: https://arxiv.org/abs/2510.04127 · HTML: https://mlsanity.com/paper/2510.04127/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Generation and context integration, one of 15 directions in Retrieval-augmented generation.
- First posted on arXiv 5 Oct 2025.

## Placed in

- Retrieval-augmented generation / [Generation and context integration](https://mlsanity.com/rag/generation-and-context-integration/)

## Abstract (arXiv)

Approximate nearest-neighbour search underpins large-scale retrieval and retrieval-augmented generation, yet its methods are studied in communities that seldom read one another. We argue that they form one field with three design choices. We develop the projection-quantisation-organisation lens: every method places its projections, places its quantisation thresholds, and organises the resulting codes for search. We test the lens with a reproducible measurement, released as the open BitBudget benchmark, and report three findings. First, the quantisation axis delivers the largest memory savings: a one-bit code with full-precision re-ranking matches uncompressed quality for six of seven embedders, the scanned code one thirty-second of the float's size. Second, the orderings the lens anticipates, including a learned-embedding regime where binary codes overtake an inverted-file product quantiser at a matched byte budget, recur as the embedding is enlarged. Third, given class labels, an eight-byte supervised code more than doubles the retrieval quality of the two-kilobyte task-agnostic float it replaces. We also recast the semantic identifiers of generative retrieval as quantisation codes. The main contribution is a single, tested account of compact-code search, from random projections to the retrieval-augmented era.