Similarity Is Not Truth: Comparing vector distance, is_true(), and extract() in Azure AI for PostgreSQL

Vector search queries often use top-k similarity, assuming the highest-scoring results are true and can serve as factual validation. These scores represent distances between vectors (e.g., <=> for cosine distance in PostgreSQL with pgvector), so they should be used to retrieve relevant results—not as a final ranking of truth. Azure AI on HorizonDB can call an AI model to generate embeddings for comparison and provides more specific functions, such as is_true() or extract(), for structured responses.

Objective

In this blog post, I'll use the three of them on a small dataset, a table of countries, with the same goal: tell me if the country is an island or not.

<=> should return a very high score for countries that are islands and a very low score for those that are not, so I can try to determine a threshold that tells me the truth
is_true() should return true for countries that are islands and false for those that are not
extract() should extract the "is an island?" information as a boolean.

Create the table

I import a list of countries from a public resource

 DROP TABLE IF EXISTS countries; CREATE TABLE countries ( country text primary key, region text ); \copy countries(country,region) FROM PROGRAM 'curl -L "https://raw.githubusercontent.com/cs109/2014_data/master/countries.csv"' WITH (FORMAT csv, HEADER true); SELECT * FROM countries WHERE region = 'OCEANIA' LIMIT 10;

Here is a sample:

 country | region ------------------+--------- Australia | OCEANIA Fiji | OCEANIA Kiribati | OCEANIA Marshall Islands | OCEANIA Micronesia | OCEANIA Nauru | OCEANIA New Zealand | OCEANIA Palau | OCEANIA Papua New Guinea | OCEANIA Samoa | OCEANIA (10 rows)

I generate embeddings from the country name, assuming that the model has enough knowledge about countries:

 CREATE EXTENSION vector; CREATE EXTENSION azure_ai; ALTER TABLE countries ADD COLUMN embedding vector(1536); UPDATE countries SET embedding = azure_openai.create_embeddings( input => country, dimensions => 1536 )::vector(1536);

For a real application, you may provide more information, such as a geographical description of the country, rather than using the AI model as a source of knowledge, but I keep this simple for the demo.

Naive query

Here is a query that uses Azure AI functions to generate embeddings for 'is an island' to compare the vector distance with the country, return a true or false for the question 'is an island' with the country name, and extract an 'is an island' boolean:

SELECT country -- cosine distance to 'is an island' , azure_openai.create_embeddings( input => 'is an island', dimensions => 1536 )::vector(1536) <=> embedding AS distance -- boolean answer to 'is an island' , azure_ai.is_true( statement => country ||' is an island' ) AS is_true_result -- extract 'is an island?' as a boolean, in addition to other questions , azure_ai.extract( country, ARRAY[ 'land: boolean - is an area of land', 'water: boolean - is surrounded by water', 'continent: boolean - is a continent', 'island: boolean - is an island?', 'neighbours: string - list the countries with common border' ] ) AS extracted FROM countries ORDER BY distance ;

I get this result:

 country | distance | is_true_result | extracted ----------------------------------+--------------------+----------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Iceland | 0.5288325821583937 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Dominica | 0.583984959074203 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Marshall Islands | 0.5923968276529713 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Seychelles | 0.5933297352264011 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Solomon Islands | 0.5992036897764201 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Barbados | 0.6026798894629409 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Bahamas | 0.6037901963467236 | f | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Mauritius | 0.6124306023780004 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Jamaica | 0.6180866747206792 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Ireland | 0.6208333769699201 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": "United Kingdom (Northern Ireland)"} Grenada | 0.6314871259473416 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Palau | 0.6331963890581136 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Kiribati | 0.6340927146328686 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Cyprus | 0.6354914993816243 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Maldives | 0.6368475975326672 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Malta | 0.6370369487669678 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} New Zealand | 0.6520422783711599 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Antigua and Barbuda | 0.6560949198973425 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Fiji | 0.6563765953128096 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Saint Lucia | 0.6565374364556272 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Saint Kitts and Nevis | 0.6569025217334334 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Madagascar | 0.6579842393491677 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Nauru | 0.6588623575239401 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Belize | 0.6617206536439253 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Mexico, Guatemala"} Cape Verde | 0.6656987305382893 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Guyana | 0.6690943980832992 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Brazil, Suriname, Venezuela"} Micronesia | 0.6694775662174064 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Sri Lanka | 0.6755248175409809 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Andorra | 0.6756446018762446 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "France, Spain"} Israel | 0.6763307658990072 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Lebanon, Syria, Jordan, Egypt, Palestine"} Cuba | 0.6780035821480603 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Tonga | 0.6854439801282708 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Vanuatu | 0.6898198008050471 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Dominican Republic | 0.6930591990187845 | f | {"land": true, "water": true, "island": true, "continent": false, "neighbours": "Haiti"} Saint Vincent and the Grenadines | 0.6936146574365081 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Singapore | 0.6939824470932374 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Samoa | 0.6942054226212125 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Haiti | 0.6970099016123408 | f | {"land": true, "water": false, "island": true, "continent": false, "neighbours": "Dominican Republic"} Indonesia | 0.6982757826983539 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Malaysia, Papua New Guinea, Timor-Leste"} Bahrain | 0.7010005561641666 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Comoros | 0.7067622419634335 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Estonia | 0.7085149756741925 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Latvia, Russia"} Liechtenstein | 0.7098232671398083 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Austria, Switzerland"} Tuvalu | 0.7100676352558253 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Brunei | 0.710790435672632 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Malaysia"} San Marino | 0.7188084142495059 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Italy"} Vatican City | 0.7195959897300721 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Italy"} Suriname | 0.7227729682040444 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Brazil, Guyana, French Guiana"} Sao Tome and Principe | 0.7228708359839435 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Guinea-Bissau | 0.7250435443354935 | f | {"land": true, "water": true, "island": false, "continent": false, "neighbours": "Senegal, Guinea"} Trinidad and Tobago | 0.7255906511994212 | t | {"land": true, "water": true, "island": true, "continent": false, "neighbours": ""} Greece | 0.7294355944328467 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Albania, North Macedonia, Bulgaria, Turkey"} Qatar | 0.7311974837740045 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": "Saudi Arabia"} Bhutan | 0.7334687504057431 | f | {"land": true, "water": false, "island": false, "continent": false, "neighbours": Source：https://dev.to/franckpachot/similarity-is-not-truth-comparing-vector-distance-istrue-and-extract-in-azure-ai-for-2andMy favorites

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