Incorrect results when storing cosine distance in a column

[rsomani95]

When I query for cosine distances to return the distance in a new column, I get back unordered results.

Here's a reproducible script for how I'm setting up my dataset: https://gist.github.com/rsomani95/dfc1006fb63fbf861bb389cae894b97f

And this is the erroneous query:

SET diskann.query_search_list_size=100;

-- EXPLAIN ANALYZE
WITH distances AS (
    SELECT
        segment.id, segment.category,
        embedding <=> '[0.048492431640625,0.004207611083984375,0.020538330078125,-0.06622314453125,-0.009918212890625,0.0819091796875,-0.0247344970703125,-0.01090240478515625,0.0679931640625,-0.040924072265625,-0.0034122467041015625,0.072021484375,0.0008335113525390625,-0.006832122802734375,0.00824737548828125,-0.03314208984375,0.025909423828125,0.04852294921875,-0.0171661376953125,0.0048370361328125,-0.0230712890625,-0.01190185546875,-0.0043792724609375,0.01007080078125,-0.052276611328125,0.0180816650390625,-0.00858306884765625,0.0078582763671875,-0.050811767578125,0.007328033447265625,0.0712890625,0.033416748046875,-0.03240966796875,-0.0029735565185546875,-0.0399169921875,-0.07537841796875,-0.0631103515625,-0.02191162109375,-0.0292510986328125,0.063232421875,0.093017578125,0.022674560546875,-0.0186920166015625,0.0041046142578125,-0.0300140380859375,-0.0941162109375,0.038970947265625,0.036651611328125,-0.0223388671875,0.002079010009765625,0.00818634033203125,-0.0187225341796875,0.031982421875,-0.01050567626953125,-0.00460052490234375,-0.0517578125,-0.0269317626953125,-0.038055419921875,0.007781982421875,0.038482666015625,-0.05145263671875,0.00878143310546875,0.021575927734375,0.053375244140625,0.0005512237548828125,0.03448486328125,-0.01157379150390625,0.0237274169921875,-0.05712890625,0.099365234375,-0.0019664764404296875,0.056243896484375,-0.00019276142120361328,-0.027069091796875,0.1966552734375,-0.01096343994140625,0.00528717041015625,-0.0244140625,-0.0211944580078125,0.0116424560546875,-0.053863525390625,-0.042266845703125,-0.0241546630859375,0.016571044921875,0.01535797119140625,0.0203704833984375,-0.036376953125,0.029815673828125,-0.048858642578125,-0.027984619140625,0.0044097900390625,0.049072265625,-0.06146240234375,0.002292633056640625,-0.01023101806640625,-0.0404052734375,0.03216552734375,-0.0093536376953125,-0.01009368896484375,0.03692626953125,-0.0257568359375,0.0193939208984375,0.004894256591796875,0.005229949951171875,-0.007106781005859375,0.06427001953125,0.007354736328125,0.050048828125,0.05267333984375,0.044952392578125,-0.0908203125,-0.02679443359375,0.01000213623046875,0.0247955322265625,0.0106658935546875,-0.0261688232421875,0.0207672119140625,0.045806884765625,0.035491943359375,-0.014556884765625,0.0421142578125,-0.045654296875,-0.048065185546875,0.0234832763671875,-0.14111328125,-0.004230499267578125,0.024566650390625,-0.0244293212890625,0.00693511962890625,0.01145172119140625,0.040283203125,-0.06060791015625,0.00921630859375,0.029083251953125,-0.09417724609375,0.028656005859375,-0.00201416015625,0.09478759765625,-0.01023101806640625,0.0249786376953125,0.018310546875,-0.02783203125,-0.022979736328125,-0.032073974609375,-0.0009412765502929688,0.00971221923828125,0.0071563720703125,-0.06329345703125,-0.01146697998046875,0.0149078369140625,0.0007505416870117188,0.01476287841796875,-0.0672607421875,-0.05224609375,-0.004695892333984375,0.006256103515625,0.00579833984375,0.0203704833984375,-0.01812744140625,-0.003818511962890625,0.007167816162109375,0.041107177734375,-0.01318359375,0.01480865478515625,-0.05267333984375,-0.0017557144165039062,0.011199951171875,-0.0153656005859375,0.0550537109375,0.03387451171875,-0.0196990966796875,0.033782958984375,-0.0158233642578125,0.0,0.037567138671875,0.0020351409912109375,-0.0206451416015625,-0.0242767333984375,0.037933349609375,0.03271484375,-0.035003662109375,-0.0303802490234375,-0.0282440185546875,0.0411376953125,0.023040771484375,0.183349609375,0.034759521484375,-0.01788330078125,0.07275390625,-0.025360107421875,0.0416259765625,0.037567138671875,-0.04315185546875,-0.06610107421875,0.001766204833984375,0.06866455078125,0.0164642333984375,-0.014373779296875,-0.033905029296875,-0.01079559326171875,-0.03521728515625,0.07550048828125,-0.01229095458984375,0.0278778076171875,0.039764404296875,-0.046722412109375,-0.0186309814453125,0.033660888671875,0.00748443603515625,0.0007295608520507812,-0.0947265625,0.04132080078125,-0.0140380859375,0.01447296142578125,-0.051544189453125,-0.055419921875,0.02691650390625,0.0095062255859375,-0.01568603515625,0.004299163818359375,-0.041656494140625,-0.0280303955078125,0.07684326171875,0.00970458984375,0.04351806640625,-0.078125,-0.0384521484375,0.0222930908203125,-0.003314971923828125,-0.055999755859375,0.01373291015625,0.01485443115234375,-0.04168701171875,0.04571533203125,-0.04693603515625,-0.0166473388671875,-0.072998046875,-0.0240478515625,0.002040863037109375,0.0220794677734375,-0.0009369850158691406,-0.027069091796875,0.04248046875,-0.0750732421875,-0.0960693359375,-0.03765869140625,-0.0173187255859375,-0.0325927734375,0.050750732421875,-0.052520751953125,-0.038818359375,-0.177001953125,-0.0188751220703125,0.0130462646484375,0.04058837890625,0.042236328125,-0.03338623046875,-0.031982421875,0.04229736328125,-0.05474853515625,0.0287017822265625,0.007640838623046875,-0.033447265625,0.0033664703369140625,-0.055694580078125,-0.0714111328125,-0.036346435546875,0.00142669677734375,-0.03070068359375,0.0299530029296875,-0.03369140625,-0.009666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            AS distance
    FROM
        segment
    INNER JOIN
        asset ON segment.asset_id = asset.id
)
SELECT distances.id, distances.distance, distances.category
FROM distances
-- WHERE distances.distance < 0.99
ORDER BY distances.distance
LIMIT 100
;

The returned results look like this:

                  id                  |      distance      |  category                                                    
--------------------------------------+--------------------+------------                                                  
 1682b0d2-dd79-4231-863d-d1d0d98dba12 |  0.960260279756738 | visual                                                       
 f28e91e5-026b-4c60-b6a3-3902403a500b | 0.9632842782690324 | transcript                                                   
 eda23a8a-1ef6-4379-a21f-21d824dc4792 | 0.9663135067451195 | transcript                                                   
 3720395b-7ade-4823-80a8-98646fca05ba | 0.9750762789746499 | transcript                                                   
 30d2ffcb-cf6d-4c8d-ba3f-5b49c5f1cceb | 0.9752353304890004 | visual                                                       
 c81fcc6f-3c79-4ef7-b2d6-b403666bdc17 |   0.97599163534196 | visual                                                       
 2b016527-8b7e-47f7-bcfa-714c232c8b4c | 0.9669419663667158 | visual                                                       
 1246aabd-8d90-4329-a0cc-6d38724fa289 |  0.977015053030417 | visual                                                       
 6a88d7cd-ce4a-409e-a686-490c7ab1ef47 | 0.9775397428487486 | visual                                                       
 948a9eed-d29a-412f-9437-972d3057e2c9 | 0.9718445999991769 | transcript                                                   
 0695cfd3-6938-4286-8104-3a14b8a76acd | 0.9794526171269831 | visual                                                       
 db440e48-ab74-4b83-8906-964888f57dc7 | 0.9806165329040244 | visual                                                       
 d34f14d9-fed6-4fd5-b7e1-58544d4bd85e | 0.9693925578540148 | visual                                                       
 2e5685c4-41af-49d8-aecc-878ff0433a38 | 0.9809748534078074 | transcript                                                   
 20106940-d508-4ff7-b56c-c0fe8cf81ebc | 0.9814686007264342 | transcript                                                   
 e35cc9c8-c2b2-40e8-9c98-7a811f572216 | 0.9846205690803932 | visual                                                       
 a091bee7-287c-4a2d-a3f3-e3e240f3cc92 | 0.9847589042998348 | visual                                                       
 a7ae733e-76f9-49e7-9e59-1571e92ffc41 | 0.9589370761957909 | visual                                                       
 2fd88a69-57a6-462b-8862-3ab5931d4e4e | 0.9860259460850797 | visual                                                       
 a0aac10b-b33d-4085-b3fb-d622c6ea4996 | 0.9705202445579526 | transcript         
...

As you can see, the distance is not in order.

[cevian]

@rsomani95 can you try materializing the CTE? such as

WITH distances AS MATERIALIZED (
    SELECT
        segment.id, segment.category,
        embedding <=> 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            AS distance
    FROM
        segment
    INNER JOIN
        asset ON segment.asset_id = asset.id
)
SELECT distances.id, distances.distance, distances.category
FROM distances
-- WHERE distances.distance < 0.99
ORDER BY distances.distance
LIMIT 100
;

[rsomani95]

@cevian thanks, that seems to do the trick. However, this query seems to not use the index and instead compute distances for all rows. Here's the query plan:

                                                          QUERY PLAN                                                           
-------------------------------------------------------------------------------------------------------------------------------
 Limit  (cost=27830.23..27830.48 rows=100 width=56) (actual time=3473.009..3473.366 rows=100 loops=1)
   CTE distances
     ->  Hash Join  (cost=48.75..11972.34 rows=450000 width=32) (actual time=4.406..2818.668 rows=450000 loops=1)
           Hash Cond: (segment.asset_id = asset.id)
           ->  Seq Scan on segment  (cost=0.00..9614.00 rows=450000 width=58) (actual time=0.006..529.056 rows=450000 loops=1)
           ->  Hash  (cost=30.00..30.00 rows=1500 width=16) (actual time=4.370..4.374 rows=1500 loops=1)
                 Buckets: 2048  Batches: 1  Memory Usage: 87kB
                 ->  Seq Scan on asset  (cost=0.00..30.00 rows=1500 width=16) (actual time=0.006..2.165 rows=1500 loops=1)
   ->  Sort  (cost=15857.89..16232.89 rows=150000 width=56) (actual time=3473.005..3473.124 rows=100 loops=1)
         Sort Key: distances.distance
         Sort Method: top-N heapsort  Memory: 37kB
         ->  CTE Scan on distances  (cost=0.00..10125.00 rows=150000 width=56) (actual time=4.868..3465.088 rows=6195 loops=1)
               Filter: (distance < '0.99'::double precision)
               Rows Removed by Filter: 443805
 Planning Time: 0.309 ms
 Execution Time: 3476.112 ms

I tried adding ORDER BY to the CTE query, and while that does use the index and execute faster, it doesn't return ordered results. I need to run ORDER BY distances.distance after the CTE to get correct results, which runs a lot slower.

Here's what I mean more concretely:

-- Runs fast (~30ms), and uses vector index, but incorrectly ordered results
WITH distances AS MATERIALIZED (
    SELECT
        segment.id, segment.category,
        embedding <=> 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            AS distance
    FROM
        segment
    INNER JOIN
        asset ON segment.asset_id = asset.id
    ORDER BY
        distance
    -- LIMIT 300
)
SELECT distances.id, distances.distance, distances.category
FROM distances
-- WHERE distances.distance < 0.99
-- ORDER BY distances.distance
LIMIT 100
;

-- Runs quite slow (~5800ms)
WITH distances AS MATERIALIZED (
    SELECT
        segment.id, segment.category,
        embedding <=> 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            AS distance
    FROM
        segment
    INNER JOIN
        asset ON segment.asset_id = asset.id
    ORDER BY
        distance
    -- LIMIT 300
)
SELECT distances.id, distances.distance, distances.category
FROM distances
-- WHERE distances.distance < 0.99
ORDER BY distances.distance
LIMIT 100
;

[rsomani95]

There's a similar issue in pgvecto.rs: https://github.com/tensorchord/pgvecto.rs/issues/502#issuecomment-2174956857

Could the same thing be happening here?

[cevian]

@rsomani95 can you try putting all the order by, where, and limits inside the CTE, with the outer query only doing an ORDER BY distance again? Something like:

WITH distances AS MATERIALIZED (
    SELECT
        segment.id, segment.category,
        embedding <=> 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            AS distance
    FROM
        segment
    INNER JOIN
        asset ON segment.asset_id = asset.id
    ORDER BY
        distance
    LIMIT 100
)
SELECT distances.id, distances.distance, distances.category
FROM distances
ORDER BY distances.distance
;

Thanks

[oliver-kriska]

Indexes don't work without limits, so what happen when you keep limit in cte?

-- Runs quite slow (~5800ms)
WITH distances AS MATERIALIZED (
    SELECT
        segment.id, segment.category,
        embedding <=> 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            AS distance
    FROM
        segment
    INNER JOIN
        asset ON segment.asset_id = asset.id
    ORDER BY
        distance
    LIMIT 300
)
SELECT distances.id, distances.distance, distances.category
FROM distances
-- WHERE distances.distance < 0.99
ORDER BY distances.distance
LIMIT 100
;

and also moving WHERE distances.distance < 0.99 to cte? It will create much more bigger query but these two changes did really great job in performance for us.

-- Runs quite slow (~5800ms)
WITH distances AS MATERIALIZED (
    SELECT
        segment.id, segment.category,
        embedding <=> 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            AS distance
    FROM
        segment
    INNER JOIN
        asset ON segment.asset_id = asset.id
    WHERE ( embedding <=> 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< 0.99
    ORDER BY
        distance
    LIMIT 300
)
SELECT distances.id, distances.distance, distances.category
FROM distances
ORDER BY distances.distance
LIMIT 100
;

and not sure if you need both ORDER BY

[rsomani95]

I had a chance to install pgvectorscale into my Django project, and was able to use the Django ORM to do the right query (as opposed to my attempts at hand writing them in an isolated test DB above). This query uses the index, gives me the correct results and runs pretty fast (~10-30ms, depending on search params):

SELECT "segment"."id",
       ("segment"."embedding" <=> 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        AS "distance"
  FROM "segment"
 INNER JOIN "asset"
    ON ("segment"."asset_id" = "asset"."id")
 WHERE ("asset"."user_id" = '...'::uuid AND "asset"."library_id" = '...'::uuid AND "segment"."category" IN ('category_a') AND ("segment"."embedding" <=> 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< 0.6)
 ORDER BY 2 ASC
 LIMIT 100

[cnmoro]

I have noticed the same issue. No matter what I do, the top 2 results (at least) are unordered. Example (ORDER BY distance LIMIT 3)

0.6016618250810005 0.5856051692005884 0.8335382242753239

[oliver-kriska]

I have noticed the same issue. No matter what I do, the top 2 results (at least) are unordered. Example (ORDER BY distance LIMIT 3)

0.6016618250810005 0.5856051692005884 0.8335382242753239

can you show use your query?

[cnmoro]

I have noticed the same issue. No matter what I do, the top 2 results (at least) are unordered. Example (ORDER BY distance LIMIT 3) 0.6016618250810005 0.5856051692005884 0.8335382242753239

can you show use your query?

select
    metadata,
    (embedding <=> '[0.09586733, 0.020719072, 0.008679507, 0.04053912, 0.029493852, 0.034695935, -0.038164925, -0.007715375, 0.00082406483, -0.07208916, -0.016678622, -0.067358784, -0.08771782, -0.014110702, -0.02377782, -0.052753482, -0.0037526954, -0.0113868285, 0.06701236, 0.082030304, 0.033324923, 0.093905635, -0.034374002, -0.008801046, -0.026642114, -0.002762966, 0.0609442, -0.0038941926, 0.03911835, 0.005833535, 0.0004561665, -0.030606207, 0.0064804074, -0.08012132, 0.017767383, -0.07288163, 0.001515649, -0.0066404603, 0.036174186, -0.020761, 0.017364096, 0.035605706, 0.06314377, 0.03168773, -0.07710992, -0.07111517, 0.0143547915, 0.0421142, 0.056305744, 0.048123606, 0.07525468, -0.03223762, 0.062167134, -0.004322558, 0.006259412, -0.095755, 0.0098649515, 0.018187528, 0.08179606, 0.016372044, 0.052032676, 0.009867887, -0.027815543, 0.036073975, 0.0032286383, -0.009313007, 0.005308925, 0.015983678, -0.009059775, -0.03467183, -0.0022054543, -0.06798947, -0.04824895, 0.0010600855, 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        as distance
FROM document_embedding
ORDER BY distance limit 3

[oliver-kriska]

you can see from original post that there is a problem with ordering with regular query. Have you tried it with cte? Something like this:

WITH documents AS MATERIALIZED (select metadata,
                                       (embedding <=> '[0.09586733, .....]')
                                           as distance
                                FROM document_embedding
                                limit 300)
SELECT metadata, distance
FROM documents
ORDER BY distance DESC
LIMIT 3

But still, it's not good solution because cte will give you 300 documents and later you will sort it and select first 3. Depends on your data, 301st entry can be entry which you are trying to find. So in case you will not find other solution you should change 300 to some reasonable value based on your data and probably not MATERIALIZED.

[cnmoro]

well, let's wait for a fix then