✔ PASS Vector & Embeddings task_048_Q48_vector_quantization_distortion Scaled: 1M+ Records Ordered: Yes

Vector Quantization Precision Distortion & Reconstruction Error

Candidate Latency (1M Rows)

60.20 ms

(1.2x slower than golden)

Golden Latency (1M Rows)

51.89 ms

DuckDB in-memory engine

Underlying Data Volume

1,000,000 rows

26.7 MiB across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 23.3s

✔ 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 compress embeddings from 32-bit floats to 8-bit integers, engineers evaluate the reconstruction error (distance between uncompressed and quantized vector) to measure fidelity loss.

⚡ The Frontier Trap (Why LLMs Fail)

Deploying quantized embeddings without evaluating distortion leads to silent degradation in search accuracy.

Prompt / User Request Given to Model

To compress embeddings from 32-bit floats to 8-bit integers, engineers evaluate the reconstruction error (distance between uncompressed and quantized vector) to measure fidelity loss.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: vector_id, l2_quantization_error, cosine_distortion.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (1,000,000 rows • 26.7 MiB)

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

📊 vector_compression_test 1,000,000 rows 26.7 MiB Data Volume

vector_id (INTEGER) fp32_vec (FLOAT[3]) quantized_vec (FLOAT[3])

Data Preview (showing sample rows from 1,000,000 total rows):

#	vector_id	fp32_vec	quantized_vec
1	1	[0.12345 0.67891 0.44332]	[0.12 0.68 0.44]
2	2	[0.99123 0.02111 0.11005]	[0.99 0.02 0.11]
3	2	[0.7553 0.0597 0.0299]	[0.7553 0.0597 0.0299]
4	3	[0.9254 0.0531 0.0495]	[0.9254 0.0531 0.0495]
5	4	[ 0.8503 0.0391 -0.0012]	[ 0.8503 0.0391 -0.0012]
6	5	[0.8341 0.065 0.1105]	[0.8341 0.065 0.1105]
7	6	[ 0.8646 -0.0248 -0.0306]	[ 0.8646 -0.0248 -0.0306]
8	7	[0.8941 0.0856 0.0119]	[0.8941 0.0856 0.0119]
9	8	[0.8255 0.0444 0.0235]	[0.8255 0.0444 0.0235]
10	9	[ 0.8169 -0.0374 0.1182]	[ 0.8169 -0.0374 0.1182]
11	10	[0.8098 0.0563 0.0613]	[0.8098 0.0563 0.0613]
12	11	[0.8978 0.0433 0.0307]	[0.8978 0.0433 0.0307]
13	12	[0.8621 0.0939 0.086 ]	[0.8621 0.0939 0.086 ]
14	13	[0.8453 0.0448 0.0774]	[0.8453 0.0448 0.0774]
15	14	[0.8726 0.0797 0.0881]	[0.8726 0.0797 0.0881]

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: 147.08 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

⏳ ORDER_BY 🔥 29.4% Cost

Latency: 43.23 ms

Rows In/Out: 1,000,000

Data Vol: 11.44 MB

📐 PROJECTION 🔥 67.3% Cost

Latency: 98.92 ms

Rows In/Out: 1,000,000

Data Vol: 11.44 MB

📁 Projections: ['vector_id', 'l2_q...

🔍 TABLE_SCAN 3.4%

Latency: 4.93 ms

Rows In/Out: 1,000,000

Data Vol: 26.70 MB

📁 memory.main.vector_compression_t...

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
PROJECTION	67.3%	98.92 ms	1,000,000	11.44 MB	Projections: ['vector_id', 'l2_quantization_erro	🔥 BOTTLENECK
ORDER_BY	29.4%	43.23 ms	1,000,000	11.44 MB	-	🔥 BOTTLENECK
TABLE_SCAN	3.4%	4.93 ms	1,000,000	26.70 MB	memory.main.vector_compression_test	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

SELECT vector_id,
       round(array_distance(fp32_vec, quantized_vec), 6) AS l2_quantization_error,
       round(1.0 - array_cosine_similarity(fp32_vec, quantized_vec), 6) AS cosine_distortion
FROM vector_compression_test
ORDER BY l2_quantization_error DESC;

-- Evaluate Euclidean distortion and cosine fidelity loss per vector

SELECT vector_id,
       round(array_distance(fp32_vec, quantized_vec), 6) AS l2_quantization_error,
       round(1.0 - array_cosine_similarity(fp32_vec, quantized_vec), 6) AS cosine_distortion
FROM vector_compression_test
ORDER BY l2_quantization_error DESC;

CREATE TABLE vector_compression_test (vector_id INT, fp32_vec FLOAT[3], quantized_vec FLOAT[3]);


INSERT INTO vector_compression_test
VALUES (1, [0.12345, 0.67891, 0.44332]::FLOAT[3], [0.12, 0.68, 0.44]::FLOAT[3]),
       (2, [0.99123, 0.02111, 0.11005]::FLOAT[3], [0.99, 0.02, 0.11]::FLOAT[3]);

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (1,000,000 rows × 3 cols)

#	vector_id	l2_quantization_error
1	1	0.0049
2	2	0.0017
3	2	0
4	3	0
5	4	0
6	5	0
7	6	0
8	7	0
9	8	0
10	9	0
11	10	0
12	11	0
13	12	0
14	13	0
15	14	0
16	15	0
17	16	0
18	17	0
19	18	0
20	19	0
21	20	0
22	21	0
23	22	0
24	23	0
25	24	0

Showing first 25 of 1,000,000 total rows.

Expected Golden Output (1,000,000 rows × 3 cols)

#	vector_id	l2_quantization_error
1	1	0.0049
2	2	0.0017
3	122,882	0
4	122,883	0
5	122,884	0
6	122,885	0
7	122,886	0
8	122,887	0
9	122,888	0
10	122,889	0
11	122,890	0
12	122,891	0
13	122,892	0
14	122,893	0
15	122,894	0
16	122,895	0
17	122,896	0
18	122,897	0
19	122,898	0
20	122,899	0
21	122,900	0
22	122,901	0
23	122,902	0
24	122,903	0
25	122,904	0

Showing first 25 of 1,000,000 total rows.

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