TurboQuant-RS

Rust implementation of Google's TurboQuant algorithm for compressing high-dimensional embedding vectors. Achieves 6.2x compression at 384 dimensions with calibration-free, near-optimal distortion guarantees.

use turboquant::{TurboIndex, SearchResult};

let mut index = TurboIndex::create("./my_index", 384, 42, 99)?;
index.insert(0, &embedding)?;

let results: Vec<SearchResult> = index.search(&query, 10);

How It Works

TurboQuant compresses vectors in three steps:

Input vector (384 × f32 = 1,536 bytes)
    │
    ▼
┌───────────────────────────────────────┐
│  Step 1: Random Orthogonal Rotation   │  Spreads energy evenly — each
│  Q × x (deterministic from seed)      │  coordinate → N(0, 1/√d)
└───────────────────┬───────────────────┘
                    │
                    ▼
┌───────────────────────────────────────┐
│  Step 2: Lloyd-Max Scalar Quantize    │  MSE-optimal centroids for
│  b bits per dimension (default b=4)   │  the Gaussian distribution
└───────────────────┬───────────────────┘
                    │ residual = rotated − reconstructed
                    ▼
┌───────────────────────────────────────┐
│  Step 3: QJL Residual Correction      │  sign(S × residual)
│  1-bit sign per dimension             │  → unbiased IP estimator
└───────────────────┬───────────────────┘
                    │
                    ▼
Output: 248 bytes (6.2x compression, 5.17 bits/dim)

The rotation decorrelates coordinates so each follows a known Gaussian. Lloyd-Max finds the provably optimal quantization centroids for this distribution (within 2.7x of information-theoretic lower bound). QJL corrects the residual, making the inner product estimator unbiased.

Interactive demo: Open docs/turbo-quant-visualizer.html in a browser to see the algorithm animate on 3D vectors — step through rotation, quantization, and QJL correction with orbit controls.

Compression Numbers

Measured on 384-dim random unit vectors (from cargo test --test compression_claims):

Config	Bytes/vec	Bits/dim	Compression	Avg Cosine
1-bit Lloyd-Max	104	2.17	14.8x	0.630
2-bit Lloyd-Max	152	3.17	10.1x	0.756
3-bit Lloyd-Max	200	4.17	7.7x	0.818
4-bit Lloyd-Max (default)	248	5.17	6.2x	0.852
6-bit Lloyd-Max	344	7.17	4.5x	0.911

For 10,000 embeddings at 384 dimensions:

• Raw float32: 15.0 MB
• TurboQuant 4-bit: 2.4 MB

Quick Start

As a dependency

[dependencies]
turboquant = { git = "https://github.com/coderjack/turboquant-rs" }

High-level: TurboIndex

Create an index, insert vectors, search:

use turboquant::{TurboIndex, SearchResult};

// Create a persistent index on disk (default: 4-bit Lloyd-Max)
let mut index = TurboIndex::create(
    "./my_index",
    384,  // embedding dimension
    42,   // rotation seed (any u64, deterministic)
    99,   // QJL seed (any u64, deterministic)
)?;

// Or choose a specific bit width: 1–8
let mut index = TurboIndex::create_with_bits("./my_index", 384, 42, 99, 3)?;

// Insert embeddings with unique IDs
index.insert(0, &embedding_vec)?;
index.insert(1, &another_vec)?;

// Search: returns top-k by approximate inner product
let results: Vec<SearchResult> = index.search(&query_vec, 10);
for r in &results {
    println!("id={} score={:.4}", r.id, r.score);
}

// Maintenance
index.delete(1)?;     // soft-delete
index.compact()?;      // rebuild without deleted vectors

// Re-open from disk in another process
let index = TurboIndex::open("./my_index")?;

Low-level: LloydMaxCompressor

For direct access to compression without the index:

use turboquant::{LloydMaxCompressor, PreparedQuery};

let compressor = LloydMaxCompressor::new(
    384,  // dimension
    42,   // rotation seed
    99,   // QJL seed
    4,    // bits per dimension
);

// Compress a vector
let compressed = compressor.compress(&vector);
println!("{} bytes", compressed.byte_size()); // 248

// Decompress (Lloyd-Max reconstruction, no QJL)
let reconstructed = compressor.decompress(&compressed);

// Similarity search: prepare query once, score many candidates
let prepared: PreparedQuery = compressor.prepare_query(&query);
let score = compressor.similarity_prepared(&prepared, &compressed);

prepare_query does the O(d^2) rotation + QJL projection once. Each similarity_prepared call is only O(d).

Examples

Basic index (no external deps)

cargo run -p turboquant --example basic_index

Creates an index with synthetic vectors, inserts, searches, deletes, compacts, and reopens from disk.

Semantic search with a local ONNX model

End-to-end semantic search using all-MiniLM-L6-v2 (384-dim):

# 1. Export the model to ONNX (one-time)
pip install optimum[exporters]
optimum-cli export onnx \
    --model sentence-transformers/all-MiniLM-L6-v2 \
    models/all-MiniLM-L6-v2

# 2. Run the example
cargo run -p turboquant --example semantic_search -- \
    --model-dir models/all-MiniLM-L6-v2

Architecture

turboquant-rs/
  crates/
    turboquant/          Core compression library
      src/
        compression/
          rotation.rs      Step 1: Random orthogonal rotation (Gram-Schmidt)
          lloyd_max.rs     Step 2: Lloyd-Max scalar quantization (default)
          polarquant.rs    Step 2 alt: Polar coordinate quantization
          qjl.rs           Step 3: QJL 1-bit residual correction
        turboquant.rs      Pipeline composition (LloydMaxCompressor + TurboQuantCompressor)
        index.rs           TurboIndex: insert, delete, search, compact
        storage.rs         File-based vector storage
        lib.rs             Public API re-exports
      examples/
        basic_index.rs     Minimal usage example
        semantic_search.rs End-to-end with ONNX embedding model
      tests/
        compression_claims.rs  Property tests + baseline comparisons
        head_to_head.rs        Lloyd-Max vs PolarQuant benchmark

Dependencies

The core library has zero ML dependencies — pure math + compression:

• ndarray — matrix operations
• rand, rand_chacha, rand_distr — deterministic RNG
• serde, bincode — serialization
• thiserror — error types

ONNX Runtime and tokenizers are dev-dependencies only, used by the semantic_search example.

Running Tests

# All tests
cargo test -p turboquant

# With verbose output (shows compression tables, recall numbers)
cargo test -p turboquant --test compression_claims -- --nocapture

# Lloyd-Max vs PolarQuant comparison
cargo test -p turboquant --test head_to_head -- --nocapture

References

This project implements algorithms from:

@article{zandieh2025turboquant,
  title={TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate},
  author={Zandieh, Amir and Daliri, Majid and Hadian, Majid and Mirrokni, Vahab},
  journal={arXiv preprint arXiv:2504.19874},
  year={2025}
}

@article{zandieh2024qjl,
  title={QJL: 1-Bit Quantized JL Transform for KV Cache Quantization with Zero Overhead},
  author={Zandieh, Amir and Daliri, Majid and Han, Insu},
  journal={arXiv preprint arXiv:2406.03482},
  year={2024}
}

@article{han2025polarquant,
  title={PolarQuant},
  author={Han, Insu and Kacham, Praneeth and Karbasi, Amin and Mirrokni, Vahab and Zandieh, Amir},
  journal={arXiv preprint arXiv:2502.02617},
  year={2025}
}

Google Research blog post: TurboQuant: Redefining AI Efficiency with Extreme Compression

License

Licensed under either of

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT License (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.