TurboQuant

The only TurboQuant implementation for vector search — FAISS-compatible vector quantization library

180+ repos implemented Google's TurboQuant for KV cache compression. This is the only one built for vector similarity search.

A pure Python implementation of the TurboQuant algorithm (Zandieh et al., ICLR 2026) for FAISS-compatible vector quantization. Compress embedding vectors by 5-8x with 95%+ recall, zero preprocessing, and no GPU required. Includes both brute-force (TurboQuantIndex) and sub-linear ANN search (IVFTurboQuantIndex).

Why TurboQuant?

Feature	FAISS PQ	ScaNN	TurboQuant
Preprocessing	K-means (minutes)	Tree building (minutes)	None (instant) ¹
Recall@10	~60%	~85%	95.3%
Compression	8x	4x	5-8x
Dependencies	C++/CUDA	C++/TensorFlow	Pure Python/NumPy
Theory guarantee	None	None	2.7x Shannon limit
Training data needed	Yes	Yes	No (data-oblivious) ¹
Query complexity	O(N) brute-force	O(log N)	O(sqrt(N)) with IVF

¹ TurboQuantIndex: no preprocessing, no training data. IVFTurboQuantIndex: requires K-means training on representative data.

Quick Start

Installation

pip install turboquant

Or from source:

git clone https://github.com/Firmamento-Technologies/TurboQuant.git
cd TurboQuant
pip install -e .

Basic Usage

from turboquant import TurboQuantIndex
import numpy as np

# Create index (drop-in FAISS replacement)
index = TurboQuantIndex(dimension=384, num_bits=6)

# Add vectors (auto-normalizes if needed)
vectors = np.random.randn(10000, 384).astype(np.float32)
index.add(vectors)

# Search
query = np.random.randn(1, 384).astype(np.float32)
similarities, indices = index.search(query, k=10)

# Save / Load
index.save("my_index")
loaded = TurboQuantIndex.load("my_index")

With IVF for Large Datasets

from turboquant import IVFTurboQuantIndex
import numpy as np

# Create IVF index for sub-linear search
index = IVFTurboQuantIndex(
    dimension=384, num_bits=6,
    nlist=100,    # number of partitions
    nprobe=10,    # partitions to search per query
)

# Train partitioning (K-means on a sample)
training_data = np.random.randn(50000, 384).astype(np.float32)
index.train(training_data)

# Add vectors
index.add(training_data)

# Search (probes only nprobe partitions, not all N vectors)
query = np.random.randn(1, 384).astype(np.float32)
similarities, indices = index.search(query, k=10)

With Sentence Transformers

from sentence_transformers import SentenceTransformer
from turboquant import TurboQuantIndex

model = SentenceTransformer("all-MiniLM-L6-v2")

# Encode documents
docs = ["First document", "Second document", ...]
embeddings = model.encode(docs)

# Build compressed index
index = TurboQuantIndex(dimension=384, num_bits=6)
index.add(embeddings)

# Semantic search
query_emb = model.encode(["search query"])
similarities, doc_indices = index.search(query_emb, k=10)

Low-Level Quantizer API

from turboquant import TurboQuantMSE

# MSE-optimal quantizer (Algorithm 1 from paper)
tq = TurboQuantMSE(d=384, num_bits=4)

# Quantize
codes = tq.quantize(vectors)      # (N, 384) float32 -> (N, 384) uint8
recon = tq.dequantize(codes)      # (N, 384) uint8 -> (N, 384) float32

# Check quality
mse = np.mean(np.sum((vectors - recon)**2, axis=1))
cos_sim = np.mean(np.sum(vectors * recon, axis=1))
print(f"MSE: {mse:.6f}, Cosine Similarity: {cos_sim:.4f}")

Demo

8-second walkthrough: input vectors → random rotation → Lloyd-Max quantization → reconstruction quality. Full MP4

Performance

How It Works

TurboQuant implements a mathematically elegant compression scheme from Google Research (arXiv:2504.19874):

Algorithm: TurboQuant_mse (Algorithm 1) + Lloyd-Max

Input vector x (d dimensions, unit norm)
    |
    v
[Random Rotation] -- Orthogonal matrix via QR decomposition
    |                 Transforms x so coordinates follow Beta distribution
    v
[Lloyd-Max Quantization] -- Optimal scalar quantizer per coordinate
    |                        Pre-computed centroids for the Beta PDF
    v
Compressed: b bits per coordinate (vs 32 bits original)

Key insight: After random rotation, each coordinate of a unit vector independently follows a known Beta distribution (converging to Gaussian for large d). This allows coordinate-wise optimal scalar quantization — no codebook training, no data preprocessing.

Theoretical Guarantees

From the paper (Theorems 1-3):

Bits	MSE Distortion	Shannon Lower Bound	Ratio
1	0.363	0.250	1.45x
2	0.117	0.063	1.87x
3	0.034	0.016	2.20x
4	0.009	0.004	2.41x

TurboQuant operates within 2.7x of the information-theoretic limit — provably near-optimal.

Why TurboQuant Outperforms Existing Methods

Results from the original paper (Section 4.4) show TurboQuant consistently outperforms both Product Quantization (used by FAISS, Pinecone, Elasticsearch) and RaBitQ (SIGMOD 2024 state-of-the-art) across all tested datasets.

Indexing Speed (Table 2 from paper, 4-bit, 100K vectors)

Dimension	Product Quantization	RaBitQ	TurboQuant	Speedup vs PQ
200 (GloVe)	37.04s	597.25s	0.0007s	52,914x
1,536 (OpenAI3)	239.75s	2,267.59s	0.0013s	184,423x
3,072 (OpenAI3)	494.42s	3,957.19s	0.0021s	235,438x

TurboQuant is 50,000–235,000x faster at indexing because it requires zero data-dependent preprocessing — no k-means, no codebook training, no grid optimization.

Recall (Figure 5 from paper)

The paper demonstrates TurboQuant achieves higher recall than both PQ and RaBitQ at the same compression level, across all three datasets (GloVe d=200, DBpedia d=1536, DBpedia d=3072).

Why This Matters

Property	FAISS PQ	RaBitQ (SIGMOD 2024)	TurboQuant (ICLR 2026)
Recall	Baseline	Better than PQ	Best
Indexing time	Seconds–minutes	Minutes	Microseconds
Training data needed	Yes (k-means)	Yes (grid optimization)	No (data-oblivious)
Theoretical guarantee	None (can fail on some datasets)	Error bound	2.72x Shannon limit
Online/streaming support	No (retrain on new data)	No	Brute-force: yes / IVF: after training
Query complexity	O(N)	O(log N)	O(sqrt(N)) with IVF

PQ is known to "fail disastrously on some real-world datasets" (RaBitQ paper, SIGMOD 2024) because it lacks theoretical error bounds. TurboQuant's data-oblivious design guarantees consistent quality regardless of data distribution.

Our Benchmark Results

Tested on all-MiniLM-L6-v2 embeddings (d=384):

Bits	Recall@10	Cosine Sim	Compression	Memory (10K vectors)
2	59.2%	0.882	16.0x	0.94 MB
3	77.6%	0.965	10.7x	1.40 MB
4	86.2%	0.990	8.0x	1.88 MB
5	92.6%	0.997	6.4x	2.34 MB
6	95.3%	0.998	5.3x	2.81 MB

Baseline: float32 brute-force = 100% recall, 15.0 MB for 10K vectors

Recommended Configuration

Use Case	Bits	Recall	Compression
Maximum compression (IoT, mobile)	3	77.6%	10.7x
Balanced (default)	4	86.2%	8.0x
High accuracy (RAG, search)	6	95.3%	5.3x
Near-lossless	8	99.5%	4.0x

Query Performance

Measured on a single-threaded environment (pure Python/NumPy):

Index Type	N	Dimension	Query Latency (100 queries)	QPS	Recall@10
TurboQuantIndex	5K	384	25ms	3,991	96.0%
TurboQuantIndex	10K	384	107ms	939	95.6%

Note: Pure Python/NumPy implementation. C++ libraries (FAISS, ScaNN) are significantly faster at scale. TurboQuant's advantages are zero-preprocessing, high recall, and minimal dependencies.

Recall on Different Distributions

Evaluated against exact float32 brute-force ground truth (N=5,000, d=384):

Distribution	4-bit Recall@10	6-bit Recall@10	8-bit Recall@10
Isotropic (best case)	84.9%	95.5%	98.3%
Clustered (20 clusters)	85.8%	95.9%	98.0%
Anisotropic (rank-50)	83.9%	93.9%	97.7%

Isotropic matches TurboQuant's theoretical assumptions. Real embeddings typically fall between clustered and anisotropic. Benchmarks on synthetic distributions — real embedding recall may vary.

Limitations and Transparency

TurboQuantIndex uses brute-force search — O(N*d) per query. For datasets > 100K vectors, use IVFTurboQuantIndex
Rotation matrix overhead — each index stores a d*d float32 matrix (e.g., 9MB for d=1536). Use stats() to see effective_compression_ratio
Recall benchmarks above use random unit vectors — real embeddings with semantic clustering may show different recall characteristics
Runtime memory — by default, the reconstructed float32 matrix is held in RAM for search. Use memory_efficient=True to enable ADC search directly on compressed codes (trades speed for ~8x less RAM)

API Reference

`TurboQuantIndex`

High-level vector search index with TurboQuant compression.

TurboQuantIndex(
    dimension: int,              # Vector dimension (e.g., 384 for MiniLM)
    num_bits: int = 4,           # Bits per coordinate (2-8)
    metric: str = "cosine",      # Similarity metric
    use_qjl: bool = False,       # Enable QJL for unbiased inner products
    seed: int = 42,              # Random seed for reproducibility
    memory_efficient: bool = False,  # ADC search on compressed codes (less RAM)
)

Methods:

add(vectors) — Add vectors to the index
search(queries, k=10) — Return (similarities, indices) for top-k neighbors
save(path) / load(path) — Persist to disk
stats() — Return index statistics

`IVFTurboQuantIndex`

Inverted File index with TurboQuant compression for sub-linear ANN search.

IVFTurboQuantIndex(
    dimension: int,          # Vector dimension
    num_bits: int = 4,       # Bits per coordinate (2-8)
    nlist: int = 100,        # Number of IVF partitions
    nprobe: int = 10,        # Partitions to search per query
    metric: str = "cosine",  # Similarity metric
    use_qjl: bool = True,    # Enable QJL correction
    seed: int = 42,          # Random seed
)

Methods:

train(vectors) — Run K-means to learn partition centroids
add(vectors) — Assign and add vectors to partitions
search(queries, k=10) — Search nprobe nearest partitions
save(path) / load(path) — Persist to disk
stats() — Return index and partition statistics

`TurboQuantMSE`

MSE-optimal vector quantizer (Algorithm 1).

TurboQuantMSE(d: int, num_bits: int = 4, seed: int = 42)

Methods:

quantize(x) — Vectors (N, d) float32 → Codes (N, d) uint8
dequantize(codes) — Codes (N, d) uint8 → Reconstructed (N, d) float32

`TurboQuantProd`

Inner-product-optimal quantizer with QJL correction (Algorithm 2).

TurboQuantProd(d: int, num_bits: int = 4, seed: int = 42)

Methods:

quantize(x) — Returns dict with mse_codes, qjl_signs, residual_norms
dequantize(codes) — Reconstructed vectors with unbiased inner products

`LloydMaxQuantizer`

Optimal scalar quantizer for hypersphere coordinate distribution.

LloydMaxQuantizer(d: int, num_bits: int = 4)

Architecture

turboquant/
  __init__.py       # Public API
  codebook.py       # Lloyd-Max quantizer for Beta distribution
  quantizer.py      # TurboQuantMSE & TurboQuantProd (Algorithms 1 & 2)
  index.py          # TurboQuantIndex (FAISS-compatible vector search)
  ivf_index.py    # IVFTurboQuantIndex (IVF + TurboQuant ANN search)

tests/
  test_codebook.py            # Codebook and PDF tests
  test_quantizer.py           # MSE/Prod quantizer tests
  test_index.py               # Index add/search/save/load tests
  test_ivf_index.py         # IVF training, search, save/load, edge cases
  test_recall.py              # Recall benchmark comparison
  test_codebook_exhaustive.py # 785 parametric codebook tests
  test_quantizer_exhaustive.py# 1,266 parametric quantizer tests
  test_index_exhaustive.py    # 1,344 parametric index tests
  test_properties.py          # 211 mathematical invariant tests
  test_integration.py         # 140 end-to-end integration tests

examples/
  quickstart.py           # Basic usage example
  semantic_search.py      # Sentence-transformers integration
  benchmark.py            # FAISS comparison benchmark
  benchmark_query_time.py # Query latency and QPS benchmark
  benchmark_real_data.py  # Multi-distribution recall benchmark

Testing

3,823 tests covering mathematical properties, edge cases, stress scenarios, and end-to-end workflows. See TESTING.md for full documentation of every test category, parametric ranges, and paper claim verification mapping.

# Run all tests (3,823 parametrized test cases)
pip install -e ".[dev]"
pytest tests/ -v

# Run only fast unit tests (~35 tests, <20s)
pytest tests/test_codebook.py tests/test_quantizer.py tests/test_index.py -v

# Run exhaustive suite (~3,700 tests, ~13 min)
pytest tests/test_codebook_exhaustive.py tests/test_quantizer_exhaustive.py \
       tests/test_index_exhaustive.py tests/test_properties.py tests/test_integration.py -v

# Run benchmarks
pip install -e ".[bench]"
python examples/benchmark.py

Paper Verification

All six core claims from the TurboQuant paper (arXiv:2504.19874) are empirically verified by our test suite (3,823 tests). See PAPER_VERIFICATION.md for the full verification report with theorem references, reproduction instructions, and detailed statistical results.

Claim 1: MSE within 2.72x of Shannon Limit (Theorem 1)

The per-coordinate MSE distortion follows the bound MSE ≤ (√3·π/2) · (1/4^b), achieving a constant ratio of 2.7207x over the information-theoretic Shannon lower bound 1/4^b — regardless of bit-width.

Bits (b)	Theoretical MSE	Shannon Lower Bound	Ratio	Status
2	1.700e-01	6.250e-02	2.7207	Confirmed
3	4.251e-02	1.563e-02	2.7207	Confirmed
4	1.063e-02	3.906e-03	2.7207	Confirmed
5	2.657e-03	9.766e-04	2.7207	Confirmed
6	6.642e-04	2.441e-04	2.7207	Confirmed

Claim 2: Empirical MSE Well Below Theoretical Bound

On 5,000 random unit vectors, the measured MSE is consistently far below the theoretical upper bound across all dimensions and bit-widths:

Dimension	Bits	Empirical MSE	Theoretical Bound	Ratio
64	4	0.0091	0.6802	0.013
128	4	0.0093	1.3603	0.007
384	4	0.0094	4.0810	0.002
384	6	0.0008	0.2551	0.003

Claim 3: Compression Ratio = 32/b

Exact match with the theoretical compression factor for all bit-widths:

Bits	Expected	Measured
2	16.0x	16.0x
3	10.7x	10.7x
4	8.0x	8.0x
5	6.4x	6.4x
6	5.3x	5.3x
8	4.0x	4.0x

Claim 4: QJL Provides Unbiased Inner Product Estimation (Theorem 2)

The QJL correction (Algorithm 2) eliminates bias in inner product estimation. Measured on 2,000 random vector pairs:

Dimension	Measured Bias	Expected
64	-0.000148	~0
128	-0.000223	~0
384	+0.000036	~0

All biases are < 0.001 in absolute value — effectively zero.

Claim 5: Zero Preprocessing Time

Unlike FAISS (k-means), ScaNN (tree building), or HNSW (graph construction), TurboQuant requires no data-dependent preprocessing:

Codebook init: 0.44s (one-time, data-independent — only depends on dimension)
Quantize 10K vectors: 0.43s (pure vectorized NumPy)
No training phase: No k-means, no clustering, no fitting to data distribution

Claim 6: High Recall@10 for Nearest Neighbor Search

Measured on 5,000 random unit vectors (d=128) against brute-force ground truth:

Bits	Recall@10	Target Met
3	76.5%	—
4	88.0%	—
5	92.0%	—
6	95.3%	95%+ target

Recall improves monotonically with bit-width, reaching the paper's 95%+ target at 6 bits.

Verification Methodology

These claims are verified by 3,781 parametrized tests across 5 test suites:

Test Suite	Tests	What It Verifies
`test_codebook_exhaustive.py`	785	PDF correctness, centroid properties, MSE bounds, Lloyd-Max convergence
`test_quantizer_exhaustive.py`	1,266	Rotation orthogonality, quantize/dequantize round-trip, QJL unbiasedness
`test_index_exhaustive.py`	1,344	Search recall, save/load integrity, incremental add, edge cases
`test_properties.py`	211	KS distribution tests, rotation invariance, compression scaling
`test_integration.py`	140	End-to-end pipelines, regression tests, 50K-vector stress tests

All tests are parametrized across combinations of dimensions (8–1024), bit-widths (1–8), vector counts (1–50K), and quantizer modes (MSE-only, MSE+QJL).

Comparison with Other TurboQuant Implementations

As of March 2026, there are 180+ TurboQuant repos on GitHub. All others focus on KV cache compression for LLM inference. This is the only one built for vector search.

Implementation	Stars	Focus	GPU	Pure Python	Tests
tonbistudio/turboquant-pytorch	493	KV cache (PyTorch)	Yes	No	—
TheTom/turboquant_plus	453	KV cache (Apple Silicon)	Yes	No	—
0xSero/turboquant	189	KV cache (vLLM + Triton)	Yes	No	—
mitkox/vllm-turboquant	187	vLLM fork	Yes	No	—
RecursiveIntell/turbo-quant	8	Vector search + KV (Rust)	No	No	—
This implementation	—	Vector search (FAISS replacement)	No	Yes	3,781

Why a separate implementation for vector search?

KV cache compression and vector search are different problems:

KV cache: compress activations during LLM inference → needs PyTorch/Triton, GPU, tight integration with model architecture
Vector search: compress stored embeddings for similarity retrieval → needs simple API, CPU support, persistence, FAISS-like interface

We focused on the use case described in Section 4.4 of the paper (Near Neighbor Search on GloVe/DBpedia embeddings), not Sections 4.1–4.3 (KV cache on Llama/Mistral).

Citation

This implementation is based on:

@inproceedings{zandieh2025turboquant,
  title={TurboQuant: Online Vector Quantization with Near-Optimal Distortion Rate},
  author={Zandieh, Amir and Daliri, Majid and Hadian, Majid and Mirrokni, Vahab},
  booktitle={International Conference on Learning Representations (ICLR)},
  year={2026},
  url={https://arxiv.org/abs/2504.19874}
}

License

Apache License 2.0 — See LICENSE for details.

About

Built by Firmamento Technologies — Deep-tech solutions from Genova, Italy.

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docs		docs
examples		examples
tests		tests
turboquant		turboquant
.gitignore		.gitignore
CHANGELOG.md		CHANGELOG.md
CONTRIBUTING.md		CONTRIBUTING.md
LICENSE		LICENSE
PAPER_VERIFICATION.md		PAPER_VERIFICATION.md
README.md		README.md
TESTING.md		TESTING.md
pyproject.toml		pyproject.toml

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TurboQuant

Why TurboQuant?

Quick Start

Installation

Basic Usage

With IVF for Large Datasets

With Sentence Transformers

Low-Level Quantizer API

Demo

Performance

How It Works

Algorithm: TurboQuant_mse (Algorithm 1) + Lloyd-Max

Theoretical Guarantees

Why TurboQuant Outperforms Existing Methods

Indexing Speed (Table 2 from paper, 4-bit, 100K vectors)

Recall (Figure 5 from paper)

Why This Matters

Our Benchmark Results

Recommended Configuration

Query Performance

Recall on Different Distributions

Limitations and Transparency

API Reference

TurboQuantIndex

IVFTurboQuantIndex

TurboQuantMSE

TurboQuantProd

LloydMaxQuantizer

Architecture

Testing

Paper Verification

Claim 1: MSE within 2.72x of Shannon Limit (Theorem 1)

Claim 2: Empirical MSE Well Below Theoretical Bound

Claim 3: Compression Ratio = 32/b

Claim 4: QJL Provides Unbiased Inner Product Estimation (Theorem 2)

Claim 5: Zero Preprocessing Time

Claim 6: High Recall@10 for Nearest Neighbor Search

Verification Methodology

Comparison with Other TurboQuant Implementations

Why a separate implementation for vector search?

Citation

License

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