SQL-FRONTIER Benchmark Deep-Dive / Vector & Embeddings / task_034_Q34_user_profile_embedding_centroid
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✔ PASS Vector & Embeddings task_034_Q34_user_profile_embedding_centroid Scaled: 1M+ Records Ordered: Yes

User Profile Preference Vector Centroid Aggregation

Candidate Latency (1M Rows)
936.97 ms
(1.0x faster than golden)
Golden Latency (1M Rows)
955.89 ms
DuckDB in-memory engine
Underlying Data Volume
1,000,000 rows
19.1 MiB across 1 table
Evaluated Model
gemini-3.8-flash-low
Gen Latency: 30.4s
✔ Correctness Verified on 1M+ Records
Candidate SQL output matches ground truth golden query across all multiset rows and numeric tolerances (tol=1e-3). Zero data skew or anti-patterns detected on full dataset scale.

1. Analytical Significance & What It Means

Scenario & Frontier Trap
Business Scenario & Problem

To personalize feeds, recommendation engines compute a dynamic user preference vector by calculating the average centroid of the embeddings of products the user clicked in the last 7 days.

⚡ The Frontier Trap (Why LLMs Fail)

SQL standard lacks native array averaging; unnesting arrays without proper positional indexes scrambles vector dimensions.

Prompt / User Request Given to Model
To personalize feeds, recommendation engines compute a dynamic user preference vector by calculating the average centroid of the embeddings of products the user clicked in the last 7 days.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: user_id, user_preference_centroid.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (1,000,000 rows • 19.1 MiB)

Production-scale fixtures loaded into the isolated DuckDB sandbox with at least 1,000,000 records per table:

📊 user_clicks_vectors 1,000,000 rows 19.1 MiB Data Volume
user_id (INTEGER) item_id (INTEGER) item_vector (FLOAT[3])
Data Preview (showing sample rows from 1,000,000 total rows):
# user_id item_id item_vector
1 42 1 [0.8 0.2 0.1]
2 42 2 [0.6 0.4 0.2]
3 42 3 [0.7 0.3 0.3]
4 42 3 [0.8619 0.061 0.1141]
5 43 4 [0.9237 0.0698 0.0604]
6 44 5 [0.864 0.0736 0.0779]
7 45 6 [0.7997 0.0715 0.0555]
8 46 7 [ 0.8986 0.0281 -0.0062]
9 47 8 [0.881 0.0378 0.0101]
10 48 9 [0.9201 0.0299 0.1033]
11 49 10 [ 0.9281 0.1134 -0.026 ]
12 50 11 [0.8155 0.0768 0.127 ]
13 51 12 [0.8685 0.1808 0.0363]
14 52 13 [0.812 0.048 0.0435]
15 53 14 [ 0.8737 -0.0019 0.0637]

3. Graphical Query Execution Plan & Cost Bottlenecks

Physical Operator Tree (DuckDB 2.0 Profiler)

Visual flowchart of the physical execution pipeline. Operators with high relative costs (≥ 20% of query runtime or heavy latency) are visually highlighted:

Pipeline Latency Distribution (Total Plan Time: 1433.24 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders
📐 PROJECTION 1.2%
Latency: 16.86 ms
Rows In/Out: 999,997
Data Vol: 15.26 MB
📁 Projections: ['user_id', 'user_p...
📊 HASH_GROUP_BY 🔥 31.0% Cost
Latency: 444.61 ms
Rows In/Out: 999,997
Data Vol: 41.96 MB
⚠️ Heavy Execution Bottleneck (31.0% of query runtime)
📐 PROJECTION 0.0%
Latency: 0.37 ms
Rows In/Out: 2,999,991
Data Vol: 34.33 MB
📁 Projections: ['user_id', 'avg_di...
⏳ ORDER_BY 🔥 19.4% Cost
Latency: 277.89 ms
Rows In/Out: 2,999,991
Data Vol: 34.33 MB
⚠️ Heavy Execution Bottleneck (19.4% of query runtime)
📐 PROJECTION 🔥 6.1% Cost
Latency: 87.27 ms
Rows In/Out: 2,999,991
Data Vol: 57.22 MB
📁 Projections: ['user_id', 'dim_id...
⚠️ Heavy Execution Bottleneck (6.1% of query runtime)
📊 HASH_GROUP_BY 🔥 33.9% Cost
Latency: 485.72 ms
Rows In/Out: 2,999,991
Data Vol: 57.22 MB
⚠️ Heavy Execution Bottleneck (33.9% of query runtime)
📐 PROJECTION 0.2%
Latency: 2.89 ms
Rows In/Out: 3,000,000
Data Vol: 57.22 MB
📁 Projections: ['user_id', 'dim_id...
📐 PROJECTION 0.0%
Latency: 0.48 ms
Rows In/Out: 3,000,000
Data Vol: 45.78 MB
📁 Projections: ['user_id', 'val', ...
⚙️ UNNEST 🔥 7.9% Cost
Latency: 112.90 ms
Rows In/Out: 3,000,000
Data Vol: 80.11 MB
⚠️ Heavy Execution Bottleneck (7.9% of query runtime)
🔍 TABLE_SCAN 0.3%
Latency: 4.26 ms
Rows In/Out: 1,000,000
Data Vol: 15.26 MB
📁 memory.main.user_clicks_vectors
Operator Cost % Latency Processed Rows Data Volume Details / Table Status
HASH_GROUP_BY 33.9% 485.72 ms 2,999,991 57.22 MB - 🔥 BOTTLENECK
HASH_GROUP_BY 31.0% 444.61 ms 999,997 41.96 MB - 🔥 BOTTLENECK
ORDER_BY 19.4% 277.89 ms 2,999,991 34.33 MB - 🔥 BOTTLENECK
UNNEST 7.9% 112.90 ms 3,000,000 80.11 MB - 🔥 BOTTLENECK
PROJECTION 6.1% 87.27 ms 2,999,991 57.22 MB Projections: ['user_id', 'dim_idx', 'avg_dim_val 🔥 BOTTLENECK
PROJECTION 1.2% 16.86 ms 999,997 15.26 MB Projections: ['user_id', 'user_preference_centro Normal
TABLE_SCAN 0.3% 4.26 ms 1,000,000 15.26 MB memory.main.user_clicks_vectors Normal
PROJECTION 0.2% 2.89 ms 3,000,000 57.22 MB Projections: ['user_id', 'dim_idx', 'CAST(val AS Normal
PROJECTION 0.0% 0.48 ms 3,000,000 45.78 MB Projections: ['user_id', 'val', 'dim_idx'] Normal
PROJECTION 0.0% 0.37 ms 2,999,991 34.33 MB Projections: ['user_id', 'avg_dim_val'] Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted
Candidate SQL Executed by gemini-3.8-flash-low (Runtime on 1M Rows: 936.97 ms) 
WITH unnested_dims AS
  (SELECT user_id,
          item_id,
          unnest(item_vector) AS val,
          generate_subscripts(item_vector, 1) AS dim_idx
   FROM user_clicks_vectors),
     avg_dims AS
  (SELECT user_id,
          dim_idx,
          round(avg(val), 4) AS avg_dim_val
   FROM unnested_dims
   GROUP BY user_id,
            dim_idx
   ORDER BY user_id,
            dim_idx)
SELECT user_id,
       list(avg_dim_val)::FLOAT[3] AS user_preference_centroid
FROM avg_dims
GROUP BY user_id;
Golden Reference Ground Truth SQL (Runtime on 1M Rows: 955.89 ms) 
-- Calculate element-wise centroid vector for user 42
 WITH unnested_dims AS
  (SELECT user_id,
          item_id,
          unnest(item_vector) AS val,
          generate_subscripts(item_vector, 1) AS dim_idx
   FROM user_clicks_vectors),
      avg_dims AS
  (SELECT user_id,
          dim_idx,
          round(avg(val), 4) AS avg_dim_val
   FROM unnested_dims
   GROUP BY user_id,
            dim_idx
   ORDER BY user_id,
            dim_idx)
SELECT user_id,
       list(avg_dim_val)::FLOAT[3] AS user_preference_centroid
FROM avg_dims
GROUP BY user_id;
DuckDB Fixture Setup DDL & Data Population 
CREATE TABLE user_clicks_vectors (user_id INT, item_id INT, item_vector FLOAT[3]);


INSERT INTO user_clicks_vectors
VALUES (42, 1, [0.8, 0.2, 0.1]::FLOAT[3]),
       (42, 2, [0.6, 0.4, 0.2]::FLOAT[3]),
       (42, 3, [0.7, 0.3, 0.3]::FLOAT[3]);

5. Query Results & Expected Ground Truth

Tabular Comparison
Actual Candidate Output (999,997 rows × 2 cols)
# user_id user_preference_centroid
1 122,931 [0.8655 0.0875 0.0423]
2 122,953 [0.816 0.1015 0.0534]
3 122,994 [0.9023 0.0663 0.106 ]
4 123,011 [0.8523 0.0908 0.0349]
5 123,063 [0.8406 0.0121 0.067 ]
6 123,128 [0.84 0.0523 0.048 ]
7 123,133 [0.8357 0.0686 0.0371]
8 123,145 [0.8705 0.0387 0.108 ]
9 123,171 [0.8836 0.0691 0.043 ]
10 123,193 [ 8.858e-01 -6.000e-04 8.780e-02]
11 123,202 [0.8755 0.1499 0.0262]
12 123,226 [0.848 0.0713 0.0347]
13 123,273 [ 0.8268 -0.017 0.032 ]
14 123,296 [0.7384 0.095 0.0598]
15 123,300 [ 0.8679 -0.0261 0.0951]
16 123,335 [0.7767 0.0255 0.0081]
17 123,362 [0.833 0.129 0.0868]
18 123,364 [0.9065 0.045 0.0366]
19 123,417 [0.8785 0.0356 0.0632]
20 123,435 [0.8399 0.0932 0.098 ]
21 123,448 [0.8838 0.0351 0.003 ]
22 123,561 [0.881 0.0617 0.0554]
23 123,588 [0.8224 0.0061 0.0279]
24 123,603 [ 0.8578 0.051 -0.0084]
25 123,624 [0.8661 0.0458 0.0311]
Showing first 25 of 999,997 total rows.
Expected Golden Output (999,997 rows × 2 cols)
# user_id user_preference_centroid
1 41,112 [0.8723 0.0454 0.1048]
2 41,184 [0.9091 0.0832 0.0179]
3 41,264 [0.8683 0.0859 0.1011]
4 41,267 [ 0.8071 -0.0497 0.0563]
5 41,270 [0.9379 0.0648 0.0504]
6 41,273 [0.8786 0.0557 0.0634]
7 41,294 [0.8597 0.0757 0.0177]
8 41,327 [ 0.9344 -0.0357 0.1159]
9 41,345 [0.9081 0.0705 0.0488]
10 41,390 [0.9292 0.0237 0.0424]
11 41,397 [ 0.8642 -0.0125 0.0641]
12 41,429 [ 0.804 -0.01 0.0559]
13 41,441 [0.913 0.0972 0.0399]
14 41,483 [0.7996 0.0916 0.0619]
15 41,514 [0.8481 0.0892 0.1075]
16 41,571 [0.8035 0.1089 0.0782]
17 41,700 [0.8303 0.01 0.0816]
18 41,834 [0.8153 0.033 0.0189]
19 41,852 [0.8677 0.0977 0.0595]
20 41,856 [0.9301 0.0755 0.0918]
21 41,919 [0.8274 0.0323 0.0128]
22 41,935 [0.8808 0.0563 0.0759]
23 41,989 [0.7926 0.0013 0.0686]
24 42,029 [0.823 0.0679 0.0149]
25 42,069 [0.8013 0.0467 0.0897]
Showing first 25 of 999,997 total rows.
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