SQL-FRONTIER Benchmark Deep-Dive / Vector & Embeddings / task_047_Q47_hierarchical_vector_coarse_fine
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✔ PASS Vector & Embeddings task_047_Q47_hierarchical_vector_coarse_fine Scaled: 1M+ Records Ordered: Yes

Hierarchical Coarse-to-Fine Multi-Level Vector Filtering

Candidate Latency (1M Rows)
0.37 ms
(1.0x faster than golden)
Golden Latency (1M Rows)
0.38 ms
DuckDB in-memory engine
Underlying Data Volume
1,000,002 rows
34.3 MiB across 2 tables
Evaluated Model
gemini-3.8-flash-low
Gen Latency: 14.6s
✔ 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

In massive enterprise catalogs, searching 100 million items is accelerated by first matching high-level department embedding centroids, then searching specific item vectors inside matching departments.

⚡ The Frontier Trap (Why LLMs Fail)

Flat brute-force vector search over hundreds of millions of items consumes excessive compute.

Prompt / User Request Given to Model
In massive enterprise catalogs, searching 100 million items is accelerated by first matching high-level department embedding centroids, then searching specific item vectors inside matching departments.

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

2. Underlying Tables, Row Counts & Data Volume

2 Tables (1,000,002 rows • 34.3 MiB)

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

📊 departments 2 rows 64 B Data Volume
dept_id (INTEGER) dept_name (VARCHAR) dept_centroid (FLOAT[2])
Data Preview (showing sample rows from 2 total rows):
# dept_id dept_name dept_centroid
1 1 Electronics [0.9 0.1]
2 2 Gardening [0.1 0.9]
📊 items 1,000,000 rows 34.3 MiB Data Volume
item_id (INTEGER) dept_id (INTEGER) item_name (VARCHAR) item_vector (FLOAT[2])
Data Preview (showing sample rows from 1,000,000 total rows):
# item_id dept_id item_name item_vector
1 101 1 Noise-canceling earphones [0.92 0.08]
2 102 1 USB-C Cable [0.85 0.15]
3 201 2 Lawn Mower [0.12 0.88]
4 201 2 Noise-canceling earphones [0.929 0.0845]
5 202 3 USB-C Cable [0.867 0.0663]
6 203 4 Lawn Mower [0.8698 0.1118]
7 204 5 Noise-canceling earphones [0.8179 0.1452]
8 205 6 USB-C Cable [0.8257 0.1332]
9 206 7 Lawn Mower [0.9027 0.0792]
10 207 8 Noise-canceling earphones [0.8539 0.1043]
11 208 9 USB-C Cable [0.8653 0.0707]
12 209 10 Lawn Mower [0.8714 0.1177]
13 210 11 Noise-canceling earphones [0.8695 0.1147]
14 211 12 USB-C Cable [0.7993 0.2177]
15 212 13 Lawn Mower [0.9018 0.0976]

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: 0.37 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders
⏳ ORDER_BY 22.6%
Latency: 0.08 ms
Rows In/Out: 2
Data Vol: 48 B
📐 PROJECTION 2.2%
Latency: 0.01 ms
Rows In/Out: 2
Data Vol: 48 B
📁 Projections: ['item_id', 'item_n...
⚡ HASH_JOIN 16.3%
Latency: 0.06 ms
Rows In/Out: 2
Data Vol: 88 B
🔍 TABLE_SCAN 6.5%
Latency: 0.02 ms
Rows In/Out: 2
Data Vol: 64 B
📁 memory.main.items
📐 PROJECTION 0.8%
Latency: 0.00 ms
Rows In/Out: 1
Data Vol: 8 B
📁 Projections: ['CAST(#0 AS INTEGE...
⏳ ORDER_BY 16.4%
Latency: 0.06 ms
Rows In/Out: 1
Data Vol: 5 B
📐 PROJECTION 0.7%
Latency: 0.00 ms
Rows In/Out: 1
Data Vol: 5 B
📁 Projections: ['CAST(#0 AS TINYIN...
📐 PROJECTION 1.2%
Latency: 0.00 ms
Rows In/Out: 1
Data Vol: 8 B
📁 Projections: ['dept_id', 'array_...
⚡ HASH_JOIN 22.5%
Latency: 0.08 ms
Rows In/Out: 1
Data Vol: 12 B
🔍 TABLE_SCAN 3.6%
Latency: 0.01 ms
Rows In/Out: 1
Data Vol: 20 B
📁 memory.main.departments
✂️ TOP_N 3.5%
Latency: 0.01 ms
Rows In/Out: 1
Data Vol: 12 B
📐 PROJECTION 1.0%
Latency: 0.00 ms
Rows In/Out: 2
Data Vol: 24 B
📁 Projections: ['array_cosine_simi...
🔍 TABLE_SCAN 2.6%
Latency: 0.01 ms
Rows In/Out: 2
Data Vol: 32 B
📁 memory.main.departments
Operator Cost % Latency Processed Rows Data Volume Details / Table Status
ORDER_BY 22.6% 0.08 ms 2 0.00 MB - Normal
HASH_JOIN 22.5% 0.08 ms 1 0.00 MB - Normal
ORDER_BY 16.4% 0.06 ms 1 0.00 MB - Normal
HASH_JOIN 16.3% 0.06 ms 2 0.00 MB - Normal
TABLE_SCAN 6.5% 0.02 ms 2 0.00 MB memory.main.items Normal
TABLE_SCAN 3.6% 0.01 ms 1 0.00 MB memory.main.departments Normal
TOP_N 3.5% 0.01 ms 1 0.00 MB - Normal
TABLE_SCAN 2.6% 0.01 ms 2 0.00 MB memory.main.departments Normal
PROJECTION 2.2% 0.01 ms 2 0.00 MB Projections: ['item_id', 'item_name', 'fine_sim_ Normal
PROJECTION 1.2% 0.00 ms 1 0.00 MB Projections: ['dept_id', 'array_cosine_similarit Normal
PROJECTION 1.0% 0.00 ms 2 0.00 MB Projections: ['array_cosine_similarity(dept_cent Normal
PROJECTION 0.8% 0.00 ms 1 0.00 MB Projections: ['CAST(#0 AS INTEGER)', '#1'] Normal
PROJECTION 0.7% 0.00 ms 1 0.00 MB Projections: ['CAST(#0 AS TINYINT)', '#1'] 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: 0.37 ms) 
WITH top_dept AS
  (SELECT dept_id
   FROM departments
   ORDER BY array_cosine_similarity(dept_centroid, [0.95, 0.05]::FLOAT[2]) DESC
   LIMIT 1)
SELECT i.item_id,
       i.item_name,
       round(array_cosine_similarity(i.item_vector, [0.95, 0.05]::FLOAT[2]), 4) AS fine_sim_score
FROM items i
JOIN top_dept d ON i.dept_id = d.dept_id
ORDER BY fine_sim_score DESC;
Golden Reference Ground Truth SQL (Runtime on 1M Rows: 0.38 ms) 
-- Find best matching department, then retrieve top items strictly within that department
 WITH top_dept AS
  (SELECT dept_id
   FROM departments
   ORDER BY array_cosine_similarity(dept_centroid, [0.95, 0.05]::FLOAT[2]) DESC
   LIMIT 1)
SELECT i.item_id,
       i.item_name,
       round(array_cosine_similarity(i.item_vector, [0.95, 0.05]::FLOAT[2]), 4) AS fine_sim_score
FROM items i
JOIN top_dept d ON i.dept_id = d.dept_id
ORDER BY fine_sim_score DESC;
DuckDB Fixture Setup DDL & Data Population 
CREATE TABLE departments (dept_id INT, dept_name VARCHAR, dept_centroid FLOAT[2]);


CREATE TABLE items (item_id INT, dept_id INT, item_name VARCHAR, item_vector FLOAT[2]);


INSERT INTO departments
VALUES (1, 'Electronics', [0.9, 0.1]::FLOAT[2]),
       (2, 'Gardening', [0.1, 0.9]::FLOAT[2]);


INSERT INTO items
VALUES (101, 1, 'Noise-canceling earphones', [0.92, 0.08]::FLOAT[2]),
       (102, 1, 'USB-C Cable', [0.85, 0.15]::FLOAT[2]),
       (201, 2, 'Lawn Mower', [0.12, 0.88]::FLOAT[2]);

5. Query Results & Expected Ground Truth

Tabular Comparison
Actual Candidate Output (2 rows × 3 cols)
# item_id item_name fine_sim_score
1 101 Noise-canceling earphones 0.9994
2 102 USB-C Cable 0.9926
Expected Golden Output (2 rows × 3 cols)
# item_id item_name fine_sim_score
1 101 Noise-canceling earphones 0.9994
2 102 USB-C Cable 0.9926
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