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Deterministic evidence about embedding spaces and vector indexes: hubness, collapse, ANN recall
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{
"mcpServers": {
"vecscope": {
"command": "uvx",
"args": [
"vecscope",
"mcp"
]
}
}
}Führe das in deinem Terminal aus
claude mcp add vecscope -- uvx vecscope mcpIn .cursor/mcp.json in deinem Projekt oder in ~/.cursor/mcp.json einfügen
{
"mcpServers": {
"vecscope": {
"command": "uvx",
"args": [
"vecscope",
"mcp"
]
}
}
}Dein Browser fragt, ob er die App öffnen darf, dann zeigt die App die Einstellungen und bittet dich um Bestätigung. Schlüsselwerte bleiben leer, damit du sie selbst einträgst.
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{
"servers": {
"vecscope": {
"type": "stdio",
"command": "uvx",
"args": [
"vecscope",
"mcp"
]
}
}
}Dein Browser fragt, ob er die App öffnen darf, dann zeigt die App die Einstellungen und bittet dich um Bestätigung. Schlüsselwerte bleiben leer, damit du sie selbst einträgst.
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English · 한국어
Before an agent trusts a vector index, let it see the space it is searching.
Quick start · What it measures · Queries and clusters · Index sweep · Compare two embeddings · Retrieval quality and the fix order · Vector stores · Use with an agent · Use in CI · Input formats · Real embeddings · FAQ
pip install vecscope
Agents build RAG pipelines, semantic search and recommendation retrieval every day, but they cannot see the embedding space they are searching.
When retrieval goes wrong it rarely looks like a bug. It looks like:
Each of those failures has a known, deterministic diagnostic in the literature. vecscope turns them into one command and one JSON:
ok / warn / fail verdictsIt runs locally on NumPy, needs no model or network, and reports the same numbers every time.
vecscope diagnoses the vector search implementation: the geometry the model produced, the hygiene of the corpus, the distance metric, the index and the query pipeline.
It does not measure relevance. Whether the right documents come back for a question needs labeled queries, and a clean audit is evidence that search is not sabotaging retrieval, not proof that retrieval is good.
pip install vecscope
vecscope reads a file with one embedding vector per row: the (n, dim) array a model's encode returns, saved as .npy, .parquet, .jsonl, .json or .csv (all formats).
import numpy as np
embeddings = model.encode(texts) # shape (n, dim), e.g. (3000, 128) np.save("embeddings.npy", embeddings)
No embeddings at hand? Generate three synthetic matrices (healthy, anisotropic, collapsed):
python -c "import urllib.request as u; u.urlretrieve('https://raw.githubusercontent.com/076923/vecscope/main/examples/make_examples.py', 'make_examples.py')"
python make_examples.py
vecscope audit embeddings.npy
vecscope x.y.z n=3000 dim=128 k=10 verdict=FAIL
[ok ] hubness skewness=1.1661 (ok < 2, warn >= 2, fail >= 4) k-occurrence skewness 1.17; top 1% of items take 3.9% of all neighbor slots (max N_k=51, expected 10). [WARN] antihubs antihub_excess=0.0523 (ok < 0.05, warn >= 0.05, fail >= 0.2) 5.2% of items are never anyone's neighbor (random data at k=10 would give 0.0%); the excess is unreachable through k-NN retrieval. try: inspect a sample of never-retrieved items; drop empty inputs, then apply the hubness fix [FAIL] anisotropy mean_random_cosine=0.8732 (ok < 0.5, warn >= 0.5, fail >= 0.85) random pairs have mean cosine 0.873 (isotropic ~0); mean unit vector has norm 0.93; centering would bring the cosine to -0.000. try: subtract the corpus mean vector and re-normalize, applying the same transform to queries; details.mean_random_cosine_after_centering shows the expected result [ok ] effective_rank effective_rank_ratio=0.5407 (ok >= 0.1, warn < 0.1, fail < 0.05) effective rank 69.2 of 128 attainable (128 dims; 54.1%); low values mean most dimensions carry nothing. [ok ] collapse near_duplicate_ratio=0.0000 (ok < 0.02, warn >= 0.02, fail >= 0.1) 0.0% of items have a neighbor with cosine >= 0.99 or an exact copy (exact duplicates 0.0%); no row has a near-duplicate. [ok ] rogue_dimensions top1_dim_variance_ratio=1.3070 (ok < 10, warn >= 10, fail >= 50) dimension 94 alone holds 1.0% of variance, 1.3x the uniform share of 0.78%; top 3 dims hold 3.0%. Rogue dimensions dominate cosine. [ok ] norms norm_cv=0.0000 (ok < 0.1, warn >= 0.1, fail >= 0.3) vector norms vary with CV 0.000 (median 1.000, range 1.000-1.000); 0.00% are zero vectors. Unequal norms bias inner-product search toward long vectors. [ok ] metric_mismatch topk_overlap=1.0000 (ok >= 0.9, warn < 0.9, fail < 0.7) cosine and inner-product top-10 share 100.0% of neighbors; 100.0% of items get identical lists. Low overlap means the index metric changes the results. [ok ] distance_concentration contrast_over_noise=2.2784 (ok >= 1.4, warn < 1.4, fail < 1.1) on 3000 rows a random item is 3.27x farther than the nearest neighbor (random distance 0.127); isotropic noise at 128-d and the same rows would give 1.44x, so the contrast is 2.28x that of noise. On all rows the contrast is 3.27x (median NN distance 0.039). Near 1.0 means distances carry no signal. [ok ] outliers outlier_ratio=0.0030 (ok < 0.01, warn >= 0.01, fail >= 0.05) 0.30% of items have no neighbor within cosine distance 0.050 (median 0.039); see details.sample_ids. Typically junk, empty or foreign-language content. [ok ] connectivity island_ratio=0.0000 (ok < 0.01, warn >= 0.01, fail >= 0.1) 0.00% of items sit in 0 small island(s) of the k-NN graph (fewer than 15 items; 60 components in total). Graph-based ANN (HNSW) attaches islands to the wrong region or never reaches them.
verdict: the worst verdict among the findings.ok, and a sentence saying what the number means for retrieval. Findings that are not ok add a try: line with the smallest change to test first.1 on FAIL, so the same command works as a CI gate.--json to get the same evidence as JSON for an agent or a script.| Finding | Metric | ok | warn | fail | What it means when it fails |
|---|---|---|---|---|---|
hubness | skewness of the k-occurrence distribution | < 2.0 | 2.0 to 4.0 | ≥ 4.0 | a few items appear in everyone's k-NN list and will top every query |
antihubs | share of items never retrieved as a neighbor, above the random baseline e^-k | < 5% | 5 to 20% | ≥ 20% | part of the corpus is unreachable through k-NN |
anisotropy | mean cosine of random pairs | < 0.85 | 0.85 to 0.95 | ≥ 0.95 | vectors crowd into a narrow cone, so scores compress into a band; good retrievers sit well below this without losing nDCG, so only extreme values are flagged |
effective_rank | participation ratio of the covariance spectrum / attainable rank (dim, or rows − 1 when rows do not exceed dims) | ≥ 0.10 | 0.05 to 0.10 | < 0.05 | most dimensions carry nothing |
collapse | share of rows with a neighbor at cosine ≥ 0.99 or an exact copy (zero vectors included); details give the duplicate groups and sample pairs | < 2% | 2 to 10% | ≥ 10% | top-k is spent on copies of the same item |
ann_recall | recall@k of ANN neighbors vs exact k-NN, counted by distance so that exact ties (duplicates) are interchangeable; the tie slack is 1e-6 + 2e-6 x distance, two to three times float32 rounding | ≥ 0.95 | 0.85 to 0.95 | < 0.85 | the index, not the model, is losing results |
rogue_dimensions | variance of the largest dimension as a multiple of the uniform 1/dim share | < 10x | 10 to 50x | ≥ 50x | a few coordinates decide every cosine score |
norms | coefficient of variation of vector norms | < 0.10 | 0.10 to 0.30 | ≥ 0.30 | inner-product search favors long vectors; zero vectors are reported too |
metric_mismatch | top-k overlap between cosine and inner product | ≥ 0.90 | 0.70 to 0.90 | < 0.70 | the index metric changes which results come back |
distance_concentration | relative contrast (random distance / nearest-neighbor distance) divided by that of isotropic noise at the same dimension and row count | ≥ 1.4 | 1.1 to 1.4 | < 1.1 | the nearest neighbor is barely closer than a random item; 1.0 is pure noise |
outliers | share of items with an abnormally far nearest neighbor | < 1% | 1 to 5% | ≥ 5% | junk, empty or foreign items; ids are listed in details |
connectivity | share of items in small k-NN graph islands | < 1% | 1 to 10% | ≥ 10% | self-contained groups too small to be clusters; HNSW attaches them badly or never reaches them |
query_gap | median query-to-corpus nearest distance divided by the median corpus-to-corpus nearest distance | < 2.6 | 2.6 to 3.0 | ≥ 3.0 | queries and corpus do not share a space, typically queries embedded by a different model (5 to 10). Pipelines that reproduce published nDCG@10 sit at 0.94 to 2.52; a missing query prefix does not reliably move it |
query_shift | share of queries farther from the corpus than the median + 3 MAD of a reference query set (needs a baseline) | < 20% | 20 to 30% | ≥ 30% | the query pipeline moved since the reference: another model or version, or traffic on topics the corpus does not cover. Healthy query sets score 0 to 9% |
ood_queries | deprecated, read query_gap: share of queries farther from the corpus than 99% of corpus items are from each other | < 50% | 50 to 80% | ≥ 80% | same question as query_gap, but it counts the normal distance between short queries and long passages too (good models score 0 to 65% on BEIR) and false-alarmed on 4 of 18 reproduced pipelines |
query_hubness | skewness of corpus k-occurrence over query results | < 4.0 | 4.0 to 10.0 | ≥ 10.0 | the same few items answer most queries; the value tracks nDCG@10 across models (Spearman −0.5 to −0.9), wrong-language models score 11 to 30. It grows with corpus size: good English models score 1.5 to 3.4 up to 26k documents and 4.0 to 4.8 on 58k, so on large corpora compare against a baseline |
Every finding in the JSON carries its healthy_range, warn_at and fail_at, plus a details block with the raw numbers. For anisotropy that block includes the cosine the same vectors would have after centering, so the agent can see whether centering alone fixes the problem.
Some findings appear only when you pass their inputs:
ann_recall: an ANN neighbor file with --annquery_gap, query_hubness and ood_queries: query embeddings with --queriesquery_shift: query embeddings, and --baseline also pointing at an earlier audit run with queriesEach finding also carries likely_causes, suggested_action and verify_by. They are hypotheses, not prescriptions:
The agent skill spells out that lo
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