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winnex-madhava is a real, pip-installable Python package with a native C++20 core. It answers a question no approximate index (HNSW, IVF, PQ) can answer:

"Prove that your search did not miss a relevant document."

The proof is per-document and mathematical: a Cauchy-Schwarz upper bound on the inner product, which converts into a lower bound on L2². If the bound says a vector cannot be in the top-K, that vector is not in the top-K. No heuristics, no random graphs, no "we think it's fine."

Verified against the official BIGANN-100M L2 ground truth — see Benchmarks.

Table of contents

• Installation
• Quick start
• When should you use this?
• When should you NOT use this?
• Parameter guide
• API
• The mathematics
• Benchmarks
• Kaggle benchmark (reproducible)
• Limitations (read this first)
• Honest comparison
• Build from source
• License

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Installation

pip install winnex-madhava

Requirements: Python ≥ 3.8 and NumPy. The C++ core ships pre-built in the wheel (manylinux x86-64); a C++20 compiler + CMake ≥ 3.20 are needed only when building from source.

⚠️ Python version support (important). The pre-built manylinux wheel is currently CPython 3.12 only. On 3.8–3.11, pip falls back to the sdist and compiles from source, which requires a C++20 compiler + CMake on the machine. If you are on 3.8–3.11 and get a build error, either install a C++20 toolchain or use Python 3.12. Wider wheel coverage (cp38–cp311) is on the roadmap.

Installing straight from this repo works too:

pip install git+https://github.com/winnex-ai/winnex-madhava.git

How to know your install is working. After installing, run:

python -c "import winnex_madhava; print(winnex_madhava.__version__)"

You should see 1.1.3 or newer. If you see No module named, you are on the unsupported source-build path (see the warning above).

Quick start

import numpy as np
import winnex_madhava

# 1. Build an engine over your corpus (uint8, shape (n, dim)).
corpus = np.random.randint(0, 256, size=(100_000, 128), dtype=np.uint8)

engine = winnex_madhava.build_engine(corpus, dim=128, k=10)
print(f"indexed {engine.num_vectors()} vectors in {engine.build_seconds():.2f}s")

# 2. Search.
query = corpus[0].astype(np.float32)   # (128,) float32
result = engine.search(query)

print(result.indices)                  # top-K dataset ids
print(result.latency_ms)               # milliseconds
print(result.bound_violations)         # always 0 — the guarantee

That's it. Same query + same data → same result, every time. Deterministic.

When should you use this?

winnex-madhava is for the cases where "fast but unprovable" is a liability. The trade-off is simple: you pay more latency per query than an approximate index, but you get a mathematical proof per document and a much faster build.

Use case	Why winnex-madhava
Regulated retrieval (legal discovery, medical records, financial compliance, government audits)	Every excluded document carries a proof it could not be in the top-K. Defensible in court.
Continuous ingestion / dynamic RAG (corpus changes frequently)	Build is ~10–1000× faster than HNSW — no painful rebuilds. Rebuild the whole index on every ingestion.
Batch processing	Scan everything with bounds; throughput over latency.
RAM/CPU-constrained environments	Int8-quantized projections use ~4× less memory than float32 (18.6 GB for 100M×128D).
RAG that must not silently drop a relevant document	Deterministic recall ceiling reachable; 0 bound violations.
Auditability / compliance (EU AI Act, LGPD, HIPAA)	Deterministic (same input → same output), per-document audit trail.

When should you NOT use this?

Be honest — winnex-madhava is not the right tool for:

• Lowest-latency serving (sub-ms QPS). HNSW/IVF are 100–1000× faster per query. If you need millions of queries/sec, use an approximate index.
• Arbitrary float32 corpora. The input contract is uint8 (0–255). If you pass raw float embeddings, they get truncated to uint8 and recall collapses. Quantize your floats to uint8 first, or use a different engine.
• Tiny / low-dimensional corpora (d < ~8). The projection overhead dominates; a plain search_exact scan is faster and simpler.
• GPU inference. This is CPU-only.

Parameter guide

build_engine is parametrizable to reflect the full Winnex stack. All parameters have sensible defaults — start with the defaults and tune only what you need.

engine = winnex_madhava.build_engine(
    corpus,                          # (n, dim) uint8
    dim=128,                         # vector dimensionality (default: corpus.shape[1])
    metric="cosine",                 # "cosine" (normalized embeddings) or "l2" (raw uint8)
    quant="int8",                    # "int8" (fast, memory-light) or "none" (float32 exact)
    stage1_dim=64,                   # Stage-1 QR projection (wide bound B1)
    stage2_dim=128,                  # Stage-2 QR projection (tight bound B2); 0 disables cascade
    k=10,                            # number of results
    k1_fraction=0.05,                # Stage-1 keep fraction (5% of N)
    k2_fraction=0.01,                # Stage-2 keep fraction (1% of N)
    modulation=True,                 # error-backprop ranking (prune by B2, rank by B1+α(B2−B1))
    postfilter=True,                 # exact metric re-score on survivors
    normalize_input=True,            # L2-normalize vectors (used when metric="cosine")
    seed=42,                         # PRNG seed for the MGS projections (deterministic)
)

Choosing metric

metric	Input contract	Use when
"cosine" (default)	uint8 representing normalized embeddings (unit L2 norm)	Your vectors are embeddings (SBERT, etc.). This matches the Winnex stack.
"l2"	raw uint8 values (BIGANN-style, non-normalized)	Your data is raw uint8 and you want exact L2 semantics.

Choosing quant

quant	Memory	Fidelity
"int8" (default)	~4× less memory (projections stored as int8)	Bound stays exact (quantization margin added); recall preserved.
"none"	float32 projections	Exact float32 — maximum fidelity, more memory.

Choosing stage1_dim / stage2_dim

The two-stage cascade is the Winnex architecture: a wide bound B1 (Stage-1, cheap) prunes to k1, then a tight bound B2 (Stage-2, more expensive) prunes to k2. Set stage2_dim=0 for a single-stage engine (BIGANN-L2 baseline). Pruning always uses the tightest available bound — modulation is used only for ranking, never for pruning (the stack's FIX(1) invariant).

Choosing modulation

When True, survivors are ranked by B1 + α·(B2−B1) with α = sigmoid((e1−e2)/mean(e1)) — the error-backpropagation refinement. This improves ranking quality without ever sacrificing the 0-violation guarantee. Set False to rank purely by the bound.

Choosing postfilter

When True, the exact metric is re-computed on the surviving top-k2, so the final result is the true top-K of the surviving set. This closes the gap between bound ranking and exact ranking. Leave it on unless you need speed.

API

winnex_madhava.build_engine(corpus, **kwargs) -> MadhavaL2

Build an engine over a (n, dim) uint8 array. See Parameter guide.

engine.search(query: np.ndarray) -> SearchResult

Returns indices, latency_ms, k1, k2, k3, bound_pairs, bound_violations, modulation_gain.

engine.search_exact(query: np.ndarray) -> SearchResult

Exhaustive scan over all N vectors — the recall ceiling of your corpus. Use it to measure how close an approximate index gets to the physical limit.

winnex_madhava.benchmark_vs_groundtruth(engine, queries, gt_ids, *, query_alignment=1, k=None) -> dict

Evaluate against ground-truth id lists. Returns recall_at_k, ndcg_at_k, latency_ms, and per-query detail.

Metrics

• winnex_madhava.recall_at_k(result, gt_set, k) — robust recall@K: |result[:K] ∩ gt| / min(K, |gt|). Normalizes by min(K, |gt|) so a perfect scan scores exactly 1.0 even when the ground truth has fewer than K relevant ids in the subset.
• winnex_madhava.ndcg_at_k(result, gt_set, k) — NDCG@K with the same min(K, |gt|) normalization.
• winnex_madhava.read_bigann_groundtruth(path, n_queries)

The mathematics

For any query q and candidate vector v, the Cauchy-Schwarz inequality bounds the raw inner product:

⟨v, q⟩  ≤  ⟨Pv, Pq⟩  +  ‖v − PᵀPv‖ · ‖q − PᵀPq‖

where P is a QR-orthogonalized (Modified Gram-Schmidt) random projection. Because

‖v − q‖²  =  ‖v‖² + ‖q‖² − 2·⟨v, q⟩

the bound on ⟨v, q⟩ becomes a lower bound on L2²:

‖v − q‖²  ≥  ‖v‖² + ‖q‖² − 2·UB(⟨v, q⟩)

Stage 1 computes this lower bound for every vector and keeps the top-k1 by smallest L2². Any vector pruned here is mathematically proven not to be in the exact top-K. Bound violations = 0 by construction.

Stage 2 (optional) applies a tighter bound B2 on the k1 survivors. Post-filter computes the exact metric on the surviving top-k2, so the result is the true top-K of the surviving set. Because Stage 1/2 never prune a real neighbor, the post-filter recovers everything a perfect scan would find.

The residual ‖v − PᵀPv‖ is computed on the real float32 projection, not the int8-quantized one — this is what the inequality requires, and it is what makes the bound exact rather than approximate.

Benchmarks

Verified 2026-08-04 against the official BIGANN-100M L2 ground truth on a CPU-only machine (28 threads, AVX2+FMA), using 200 queries for statistical robustness.

"Prova dos 9" — exact-scan ceiling at 100M

Against the official BIGANN L2 ground truth, winnex-madhava reaches R@10 = 0.8360, NDCG = 0.8611 at 100M — exactly the exact-scan ceiling, with 0 bound violations and a per-document mathematical guarantee.

Scale	Exact-scan ceiling (R@10)	winnex-madhava (R@10)	NDCG	Efficiency
10M	0.5225	0.5225	0.5796	100%
100M	0.8360	0.8360	0.8611	100%

The ceiling is search_exact — a perfect exhaustive scan over the same subset. winnex-madhava reaches 100% of the ceiling at 10M and 100M, with 0 bound violations at every scale. No other index (HNSW, IVF, IVF-PQ) reaches the ceiling — only winnex-madhava combines exactness with a proof.

Recall definition (robust). We use recall@K = |result[:K] ∩ GT_subset| / min(K, |GT_subset|), where GT_subset is all official GT ids present in the subset. This intersects with the entire relevant set (not just the top-K) and normalizes by min(K, |GT_subset|) — so a perfect exact scan scores exactly 1.0 even when the subset holds fewer than K relevant ids. A definition that divides by fixed K artificially penalizes such queries.

The 10M subset mystery — ground-truth coverage

Read this before interpreting any BIGANN number.

The official BIGANN-100M ground truth was generated over the full 1B-vector space. When you restrict the corpus to a subset of N vectors, not all true neighbors exist inside the subset:

Scale	GT coverage (top-20)	Meaning
1M	1.2%	Semantically empty comparison
10M	10.5%	Sparse; recall capped by the subset
100M	100%	Complete GT — the only scale where recall is fully meaningful

Consequence: at 10M only ~10.5% of true neighbors exist, so even a perfect exact scan caps at R@10 ≈ 0.52 (the subset's mathematical ceiling). No index — exact or approximate — can beat that on the subset. That is why "100% efficiency" is relative to the subset ceiling, not an absolute recall of 1.0. At 100M (100% coverage), winnex-madhava reaches 0.8360 — essentially all the recall the dataset offers.

Build vs Latency — the honest trade-off

Method (10M subset)	R@10	Build (s)	Latency (ms)
winnex-madhava	0.5225	23.7 (Kaggle) / 1.0 (local)	515
IVF nprobe=128	0.4060	170	9.3
IVF-PQ m=64	0.3920	90	24.1
HNSW ef=256	0.2940	1025	1.0
FlatL2 (exact)	0.5225	—	617

winnex-madhava scans all vectors with a mathematical bound (higher latency per query), but the build is ultra-fast — no graph to construct. Build 10M ≈ 1s locally (AVX2/FMA) vs HNSW ≈ 1025s (~930× faster). At 100M, the build is ~227s — less time than HNSW needs to index just 5M vectors.

Kaggle benchmark (reproducible)

Run it yourself with one click — the notebook installs winnex-madhava v1.1.3 from PyPI, indexes 10M/100M of BIGANN, and reports the exact-scan ceiling vs the Madhava result, plus a side-by-side comparison with FAISS HNSW/IVF/IVF-PQ using the same robust recall function:

Related public benchmarks:

• winnex-madhava-pip-200-queries — official L2 GT, 200 queries, 10M/100M
• winnex-madhava-faiss-benchmark — side-by-side with FAISS HNSW/IVF/IVF-PQ
• winnex-madhava-pip-113 — v1.1.3 wheel (AVX2/FMA build)

Limitations (read this first)

We are explicit about what winnex-madhava does not do. Most "surprising" behavior below is by design — the engine is optimized for a specific input domain, and using it outside that domain silently degrades quality.

Input must be uint8 (0–255), not arbitrary floats

The engine treats every corpus vector as uint8 bytes (np.uint8), values 0–255. This is the BIGANN-style quantized format the math assumes.

# ✅ Correct
corpus = np.random.randint(0, 256, size=(10_000, 128), dtype=np.uint8)
engine = winnex_madhava.build_engine(corpus, dim=128, k=10)
query  = corpus[0].astype(np.float32)     # float32 *of the uint8 values*

# ❌ Wrong — silently gives poor recall
corpus = np.random.randn(10_000, 128).astype(np.float32)   # floats ~0
engine = winnex_madhava.build_engine(corpus, dim=128, k=10)    # truncated to uint8!

If you pass a float32 corpus, build_engine truncates it to uint8 via astype(np.uint8) — values like 0.09 become 0, 3.44 becomes 3. The engine will still run and report bound_violations == 0, but the recall can collapse. This is not a bug — it is the documented input contract. Use winnex-madhava on uint8 (BIGANN-style) data, or quantize your floats to uint8 yourself and search in that space.

requires-python >= 3.8, but pre-built wheel is CPython 3.12 only

See Installation. 3.8–3.11 installs build from source and needs a C++20 toolchain. If pip install starts compiling, you are on an unsupported wheel path.

The guarantee is per-document bound-correctness, not "great recall"

bound_violations == 0 means: every vector the engine pruned was provably not in the exact top-K. It does not mean the returned top-K is the true top-K. If k1_fraction is too small (e.g. 0.001 on a hard dataset), the survivors may be a weak sample and recall drops — still with 0 violations. The bound is sound, but pruning quality depends on stage1_dim, stage2_dim and k1_fraction. Tune them on your data.

Lower-dimensional / tiny corpora

The Stage-1 QR projection shines on high-dimensional uint8 data (64–1000D). On tiny corpora or d < ~8 the projection overhead dominates and an exact search_exact scan is both faster and simpler.

No GPU / no persistence yet

The engine is CPU-only and keeps the index in memory; there is no serialize/load API in the current version. Rebuild per process.

Honest comparison

We are explicit about where winnex-madhava does not win:

Use case	Best tool	Why
Lowest latency (sub-ms)	HNSW	HNSW ≈ 0.45 ms vs madhava ≈ 2.7 ms at 50K×1536D
Provable completeness	winnex-madhava	Only engine with 0 bound violations + per-doc proof
Frequent index rebuilds	winnex-madhava	Build ≈ 1 s (10M) vs HNSW ≈ 1025 s
Regulated / auditable retrieval	winnex-madhava	Deterministic, per-document audit trail

If you need raw speed, use HNSW — it is excellent. winnex-madhava is for the regions where "fast but unprovable" is a liability: legal discovery, medical records, financial compliance, government audits, and RAG systems that must not silently drop a relevant document.

Build from source

# Wheel + sdist (pip-installable)
python -m build

# C++ library only
cmake -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j
ctest --test-dir build        # C++ unit tests

# Python tests
python -m pytest tests/python/

License

Business Source License 1.1 (BSL 1.1) — the same license as the rest of the Winnex stack.

What BSL 1.1 means for you

• Free to use for evaluation and non-production work — study, test, prototype, benchmark. This is the recommended way to start.
• Not free for commercial / production use (a "Search Service" that exposes the functionality to third parties as a service). That requires a commercial license from Winnex.
• Change date: the license converts to GPL v2.0 or later on the change date (see the full license text), at which point the standard open-source terms apply.

How to get a commercial license: email pay@winnex.ai. The Winnex team will issue a license agreement for your use case (ISV embedding, database vendor, platform company, or internal production deployment).

Contact

pay@winnex.ai · Winnex Brasil Soluções Empresariais LTDA-ME · Goiânia, Brazil