snapvec 0.3.0

Fast compressed ANN search via randomized Hadamard transform and optimal Gaussian scalar quantization. Pure NumPy, no heavy dependencies.

snapvec

Fast compressed approximate nearest-neighbor search. Pure NumPy. No heavy dependencies.

snapvec implements the TurboQuant compression pipeline — randomized Hadamard transform followed by optimal Gaussian scalar quantization (Lloyd-Max) — as a self-contained Python library for embedding vector search. It achieves ~6× / ~8× / ~12× compression at 4-bit / 3-bit / 2-bit (disk and RAM match, thanks to tight bit-packing) with >0.92 recall@10 against float32 brute-force, using only NumPy.

pip install snapvec

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Quick start

import numpy as np
from snapvec import SnapIndex

# Build index
idx = SnapIndex(dim=384, bits=4)          # 4-bit, ~6x compression
# ⚠ pass float32 arrays — see "Input dtype" below
embeddings = np.asarray(embeddings, dtype=np.float32)
idx.add_batch(ids=list(range(N)), vectors=embeddings)

# Query
results = idx.search(query_vector.astype(np.float32), k=10)  # [(id, score), ...]

# Persist
idx.save("my_index.snpv")
idx2 = SnapIndex.load("my_index.snpv")   # atomic save, v1/v2/v3 compatible

Input dtype: pass np.float32

add_batch, add, and search accept any array-like input but cast internally to float32. If you pass float64 (the NumPy default), a full-size temporary copy is allocated during the cast — for add_batch(1M × 384) that's a transient 1.5 GB allocation on top of your input array, gone only after quantization completes.

To avoid this:

# Models that return float32 directly (most modern embeddings)
embeddings = model.encode(texts)             # already float32 → no copy
idx.add_batch(ids, embeddings)

# Arrays from np.array([...]) default to float64 — cast explicitly
embeddings = np.asarray(my_list, dtype=np.float32)   # cast once upfront
idx.add_batch(ids, embeddings)

# Loading from disk — respect the original dtype or force float32
embeddings = np.load("vecs.npy").astype(np.float32, copy=False)

The cast is a correctness convenience, not a design choice — the whole pipeline (normalize, RHT, quantize) operates in float32.

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Technical background

The problem: embedding vectors are expensive

Modern embedding models produce float32 vectors of dimension d ∈ {384, 768, 1536}. Storing N vectors requires 4·N·d bytes; brute-force search costs O(N·d) per query. For N = 1M, d = 384: 1.5 GB RAM, with inner products dominating inference time.

Product Quantization (PQ) splits vectors into M sub-vectors and quantizes each independently. It is effective but requires training a K-means codebook per dataset. Random Binary Quantization (RaBitQ, 1-bit) is fast but coarse.

TurboQuant (Zandieh et al., ICLR 2026, arXiv:2504.19874) achieves near-optimal distortion at b bits per coordinate without training codebooks, by first rotating the space with a randomized Hadamard transform to make coordinates approximately Gaussian, then quantizing each coordinate independently with the optimal scalar quantizer for N(0,1).

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Algorithm

Step 1 — Normalize

Given a raw embedding v ∈ ℝᵈ, compute the unit vector v̂ = v / ‖v‖ and store ‖v‖ separately (float32, 4 bytes per vector).

Step 2 — Randomized Hadamard Transform (RHT)

Pad v̂ to the next power of 2 (d' = 2^⌈log₂ d⌉), then apply:

x = (1/√d') · H · D · v̂

where:

• D = diag(σ₁, …, σ_d') — diagonal matrix of i.i.d. ±1 random signs (seed-deterministic)
• H — unnormalized Walsh-Hadamard matrix (butterfly pattern)

By the Johnson-Lindenstrauss lemma, each coordinate xᵢ ≈ N(0, 1/d'). After rescaling x̃ = x · √d', the coordinates are approximately N(0,1) regardless of the original distribution of v.

Complexity: O(d log d) — no matrix multiplication, no codebook training.

Step 3 — Lloyd-Max scalar quantization

The optimal scalar quantizer for N(0,1) at b bits partitions ℝ into 2^b intervals and assigns each the conditional mean as reconstruction value. These boundaries and centroids are precomputed and hardcoded in snapvec._codebooks (no scipy required at runtime):

bits	levels	distortion (MSE)	bytes/coord
2	4	0.1175	0.25
3	8	0.0311	0.375
4	16	0.0077	0.50

The quantized vector is stored as a uint8 index matrix, tightly bit-packed to b/8 bytes per coordinate both on disk and in RAM. For 3-bit this means packing 8 indices into 3 bytes (24 bits); for 2-bit and 4-bit the packing is byte-aligned (4 per byte, 2 per byte respectively).

Step 4 — Approximate inner product

At search time the query q is rotated (not quantized) and the approximate cosine similarity is computed as:

score(q, v) = (1/d') · Σᵢ centroid[idx_qᵢ] · centroid[idx_vᵢ]

This is a single float16 matrix–vector product against the cached centroid expansions.

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TurboQuant_prod: unbiased estimator with QJL correction

The MSE quantizer introduces a small systematic downward bias. The use_prod=True mode corrects this using a Quantized Johnson-Lindenstrauss (QJL) residual:

Build time (per stored vector):

1. Quantize at (b-1) bits MSE, compute residual r = x̃ - x̃_MSE
2. Store sign(S·r) as a 1-bit vector (int8 ±1 in practice), where S ∈ ℝ^(d'×d') is a fixed random Gaussian matrix
3. Store ‖r‖ / √d' (one float32 per vector)

Query time (correction term):

correctionᵢ = √(π/2) / d' · ‖rᵢ‖ · dot(S·q̂, sign(S·rᵢ))
final_scoreᵢ = mse_scoreᵢ + correctionᵢ

This follows from Lemma 4 of Zandieh et al. (2025): E[sign(S·r)] = √(2/π) · S·r / ‖S·r‖, giving an unbiased estimate of ⟨r, q̂⟩.

When to use use_prod=True:

• When you need accurate inner product magnitudes (KV-cache, attention approximation)
• Not recommended for pure ranking/NNS — the added QJL variance degrades recall@k relative to MSE-only at equal total bits

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Compression ratios

Measured on d = 384 (BGE-small); the RHT pads to the next power of 2 so padded_dim = 512. All per-vector byte counts below include the padded dimensions — they are the numbers you actually pay in RAM and on disk. The trailing + 4 is the float32 norm; in normalized=True mode it is still persisted (as 1.0) to keep the on-disk layout stable across modes.

Backend	Bytes/vec (disk)	Bytes/vec (RAM, idle)	Disk ratio	RAM ratio
float32	1 536	1 536	1.0×	1.0×
4-bit snapvec	256 + 4	256 + 4	5.9×	5.9×
3-bit snapvec	192 + 4	192 + 4	7.8×	7.8×
2-bit snapvec	128 + 4	128 + 4	11.6×	11.6×
int8 (naïve)	384 + 4	384 + 4	4.0×	4.0×

RAM = disk: indices are tightly bit-packed in both. The same byte layout is used everywhere, so save / load copy bytes directly without an intermediate unpack/repack step. This halves indices RAM vs the pre-v0.2 behaviour (which stored uint8 in RAM and only packed on disk).

Bit-packing scheme:

• 4-bit (0.5 bytes/coord): 2 indices per byte (byte-aligned).
• 3-bit (0.375 bytes/coord): 8 indices → 3 bytes, cross-byte tight packing (v3 file format; v1/v2 files are read transparently via the legacy byte-aligned decoder).
• 2-bit (0.25 bytes/coord): 4 indices per byte (byte-aligned).

Unpacking happens when the float16 centroid cache is built (cached full-scan path — once, off the hot matmul) or per-chunk/per-query in chunk_size / filter_ids modes.

Search cache: a lazy float16 centroid expansion of shape (N, padded_dim) is materialised on first query for fast matmul (~5 ms at N = 100 k). It is evicted on writes and can be avoided entirely via chunk_size for memory-constrained deployments.

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Recall benchmarks

Measured on synthetic unit-sphere vectors (d=384, N=10 000, 100 queries). Baseline: exact cosine float32 brute-force.

bits	recall@1	recall@10	recall@50
2	0.72	0.83	0.91
3	0.81	0.91	0.96
4	0.86	0.93	0.95

Recall improves with clustered (real-world) data. On BGE-small-en embeddings from mixed document corpora, 4-bit achieves recall@10 ≈ 0.95.

Note on published results: The TurboQuant paper (Zandieh et al., 2025) reports recall up to 0.99, measured against HNSW graph navigation (not brute-force float32), on GloVe d=200 data, using recall@1 with large k_probe. These conditions differ from the above; both results are correct under their respective definitions.

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File format (.snpv)

Offset  Size   Field
──────────────────────────────────────────────────
0       4 B    magic: "SNPV"
4       4 B    version: uint32 (1, 2, or 3)
8       4 B    dim: uint32  — original embedding dimension
12      4 B    bits: uint32 — total bits (2, 3, or 4)
16      4 B    seed: uint32 — rotation seed
20      4 B    n: uint32    — number of stored vectors
24      4 B    flags: uint32 — bit-0: use_prod, bit-1: normalized  [v2/v3 only]
──────────────────────────────────────────────────
28      4 B    packed_len: uint32
32      *      indices: bit-packed uint8 MSE indices
       n×4 B   norms: float32 per-vector original norms
[prod only]
       n×d' B  qjl_signs: int8 sign(S·r) per vector
       n×4 B   rnorms: float32 ‖r‖/√d per vector
──────────────────────────────────────────────────
       n×(2+L) ids: uint16-length-prefixed UTF-8 strings

Saves are atomic on POSIX: writes to .snpv.tmp then os.replace(). Backward compatible: v1 (mse-only, pre-flags), v2 (flags + byte-aligned 3-bit), and v3 (tight 3-bit packing) files all load correctly — the reader dispatches the 3-bit decoder on version.

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API reference

SnapIndex(dim, bits=4, seed=0, use_prod=False, chunk_size=None, normalized=False)

Parameter	Type	Default	Description
dim	int	—	Embedding dimension
bits	int	4	Bits per coordinate: 2, 3, or 4
seed	int	0	Rotation seed — must be consistent across build and query
use_prod	bool	False	Enable QJL unbiased estimator (requires bits ≥ 3)
chunk_size	int | None	None	Stream search in chunks without the float16 cache (for N > 500k)
normalized	bool	False	Skip norm computation: trust that input vectors are unit-length

Methods

idx.add(id, vector)                           # Add one vector
idx.add_batch(ids, vectors)                   # Add N vectors (~50x faster than loop)
idx.delete(id) -> bool                        # Remove by id, O(1) lookup
idx.search(query, k=10, filter_ids=None)      # [(id, score), ...] descending
idx.save(path)                                # Atomic binary save to .snpv
SnapIndex.load(path)                          # Load from .snpv file
idx.stats() -> dict                           # Compression / memory diagnostics
len(idx)                                      # Number of stored vectors
repr(idx)                                     # SnapIndex(dim=384, bits=4, mode=mse, n=1000)

All vector inputs should be np.float32. Passing float64 triggers a full-size temporary cast inside add_batch / search (see "Input dtype" in Quick start). Most embedding models already return float32; only ad-hoc arrays built from Python lists via np.array(...) default to float64.

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Relation to TurboQuant / PolarQuant

snapvec implements the core compression pipeline from:

Zandieh, A., Daliri, M., Hadian, A., & Mirrokni, V. (2025). TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate. ICLR 2026. arXiv:2504.19874

The same algorithm was published concurrently as "PolarQuant" at AISTATS 2026. Both names were already taken on PyPI; snapvec = Hadamard + Lloyd-Max, named after its two core operations.

Key contributions of this implementation over the reference:

• No scipy — codebooks hardcoded, numpy is the only runtime dependency
• Batch WHT — single O(n·d·log d) call for bulk inserts (~50x faster than loop)
• Float16 cache — centroid expansions in half precision, ~2x faster matmul
• Packed RAM indices — 2/4-bit indices stored bit-packed in RAM (2× less memory), unpacked lazily when the float16 cache is built — zero impact on warm query latency
• Pre-filtering — filter_ids restricts search to a subset with O(|filter| · d) cost
• Chunked streaming search — chunk_size avoids the float16 cache for large N
• O(1) delete — _id_to_pos dict + position compaction
• Atomic saves — .snpv.tmp → os.replace() pattern
• Versioned format — v1/v2/v3 all loadable, forward-compatible flags field, legacy 3-bit decoder kept around for pre-v0.3 indices

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Roadmap

The current implementation comfortably hits the 10–20 ms interactive budget for N ≤ 200 k, d ∈ {384, 768}, with p50 warm-query latency of ~5 ms at N=100 k, d=384. The float16 centroid cache carries ~77% of that time as a BLAS-bound gemv; the remaining 23% is Python glue (RHT, normalization, argpartition, result assembly).

Future work is scoped around this measured profile — we don't optimize what's already fast.

Pure-Python improvements (no new dependencies)

• Quantized norms on disk — store per-vector norms as uint8 with a (min, max) header. Saves 3 bytes/vec on disk with <0.1% precision loss.
• Typed ID storage — persist integer IDs as fixed-width uint32/uint64 instead of UTF-8 strings when all IDs are numeric. Saves ~3 bytes/vec on disk for sequential integer IDs.
• Positional-ID fast path — when IDs are 0..N-1, skip _ids list and _id_to_pos dict entirely; position is the ID. Saves ~23 bytes/vec of Python object overhead.

Previously planned and now shipped: Tight 3-bit packing (v0.3.0); vectorized FWHT (v0.3.0, ~25× faster per query in isolation, ~10% E2E).

Hybrid Python + Rust core (opt-in accelerator)

The following phases would ship as an optional snapvec-core wheel. The pure-Python path remains fully functional — Rust is detected at import time and used automatically when available.

Phase 1 — Cold-start / cache build (highest ROI)

• Move centroid expansion + float16 conversion to Rust with SIMD.
• Target: cold first-query 150 ms → ~20 ms on N=100 k, d=384.
• Smallest API surface; trivial Python fallback.

Phase 2 — LUT-based scan (eliminates the float16 cache)

• Implement PQ-style Asymmetric Distance Computation: per-query LUT (16 entries × pdim) + SIMD gather over packed indices.
• Target: warm query 5 ms → ~1.5–2 ms; cache RAM: 102 MB → 0.
• Enables N > 500 k with flat RAM growth.

Phase 3 — Batch RHT + quantization

• Rust FWHT + searchsorted for add_batch.
• Target: add_batch(100k, d=384) 2.5 s → ~200 ms.
• Lowest priority — indexing is typically amortized offline.

Non-goals

• Trained codebooks (PQ / OPQ / RaBitQ-trained). Keeps the "no training required" guarantee; the data-agnostic Lloyd-Max tables make snapvec safe to use without a representative training sample.
• Graph indices (HNSW / NSG). Different trade-off space; snapvec targets flat indices where compression and predictable latency matter more than sub-linear scan.
• GPU acceleration. The cache-matmul path is memory-bound on modern CPUs; GPU would help only at very large N where network/transfer cost already dominates.

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Changelog

See CHANGELOG.md for the per-release history. Recent highlights:

• v0.3.0 — Tight 3-bit packing (5.9× → 7.8× compression for 3-bit), vectorised FWHT (~24× faster single-query RHT), file format v3 with transparent v1/v2 backward-compat.
• v0.2.0 — RAM-packed indices for 2/4-bit (idle RAM cut in half), normalized=True flag, measured-accurate compression docs.

Installation

pip install snapvec

Requirements: Python >= 3.10, NumPy >= 1.24. No other runtime dependencies.

For development:

git clone https://github.com/stffns/snapvec
cd snapvec
pip install -e .
pytest tests/ -v

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License

MIT © 2025 Jayson Steffens.

The TurboQuant algorithm is described in arXiv:2504.19874 by Zandieh et al. (Google Research / ICLR 2026). This package is an independent implementation.