Vector Operations

PostgresML adds optimized vector operations that can be used inside SQL queries. Vector operations are particularly useful for dealing with embeddings that have been generated from other machine learning algorithms, and can provide functions like nearest neighbor calculations using various distance functions.

Embeddings can be a relatively efficient mechanism to leverage the power of deep learning, without the runtime inference costs. These functions are fast with the most expensive distance functions computing upwards of ~100k per second for a memory resident dataset on modern hardware.

The PostgreSQL planner will also automatically parallelize evaluation on larger datasets, if configured to take advantage of multiple CPU cores when available.

Vector operations are implemented in Rust using ndarray and BLAS, for maximum performance.

Element-wise Arithmetic with Constants

Addition

pgml.add(a REAL[], b REAL) -> REAL[]

• SQL
• Output

SELECT pgml.add(ARRAY[1.0, 2.0, 3.0], 3);

pgml=# SELECT pgml.add(ARRAY[1.0, 2.0, 3.0], 3);
   add
---------
 {4,5,6}
(1 row)

Subtraction

pgml.subtract(minuend REAL[], subtrahend REAL) -> REAL[]

Multiplication

pgml.multiply(multiplicand REAL[], multiplier REAL) -> REAL[]

Division

pgml.divide(dividend REAL[], divisor REAL) -> REAL[]

Pairwise arithmetic with Vectors

Addition

pgml.add(a REAL[], b REAL[]) -> REAL[]

Subtraction

pgml.subtract(minuend REAL[], subtrahend REAL[]) -> REAL[]

Multiplication

pgml.multiply(multiplicand REAL[], multiplier REAL[]) -> REAL[]

Division

pgml.divide(dividend REAL[], divisor REAL[]) -> REAL[]

Norms

Dimensions not at origin

pgml.norm_l0(vector REAL[]) -> REAL

Manhattan distance from origin

pgml.norm_l1(vector REAL[]) -> REAL

Euclidean distance from origin

pgml.norm_l2(vector REAL[]) -> REAL

Absolute value of largest element

pgml.norm_max(vector REAL[]) -> REAL

Normalization

Unit Vector

pgml.normalize_l1(vector REAL[]) -> REAL[]

Squared Unit Vector

pgml.normalize_l2(vector REAL[]) -> REAL[]

-1:1 values

pgml.normalize_max(vector REAL[]) -> REAL[]

Distances

Manhattan

pgml.distance_l1(a REAL[], b REAL[]) -> REAL

Euclidean

pgml.distance_l2(a REAL[], b REAL[]) -> REAL

Projection

pgml.dot_product(a REAL[], b REAL[]) -> REAL

Direction

pgml.cosine_similarity(a REAL[], b REAL[]) -> REAL

Nearest Neighbor Example

If we had precalculated the embeddings for a set of user and product data, we could find the 100 best products for a user with a similarity search.

SELECT
    products.id,
    pgml.cosine_similarity(
        users.embedding,
        products.embedding
    ) AS distance
FROM users
JOIN products
WHERE users.id = 123
ORDER BY distance ASC
LIMIT 100;