Quantization Types since v1.1.0

Quantization can be applied not only to indexes but also directly to vectors. To this end, VectorChord provides data types for quantized vectors.

rabitq8 is the data type of a quantized vector. For the same dimension, its cost is about that of a full-precision vector (vector) and that of a half-precision vector (halfvec). This type is named after its quantization algorithm.^[1]

CREATE TABLE items (id bigserial PRIMARY KEY, embedding rabitq8(3));
INSERT INTO items (embedding) VALUES (quantize_to_rabitq8('[0,0,0]'::vector));
INSERT INTO items (embedding) VALUES (quantize_to_rabitq8('[1,1,1]'::vector));
INSERT INTO items (embedding) VALUES (quantize_to_rabitq8('[2,2,2]'::vector));
--- ...
SELECT id FROM items ORDER BY embedding <-> quantize_to_rabitq8('[0.9,0.9,1.1]'::vector) LIMIT 100;

Like them, an index can be created on columns of type rabitq8, too.

CREATE INDEX ON items USING vchordrq (embedding rabitq8_l2_ops);

By using rabitq8, both the table size and index size become of what they would be when the type of the column is vector. The cost is that both performance and precision are compromised by quantization noticeably. Therefore, it is applicable in scenarios that retrieve a large number of results.

In addition, there is also the rabitq4 type. rabitq8 quantized vectors use bits per dimension, whereas rabitq4 quantized vectors use only bits per dimension. It is designed for constrained situations that favor low storage over high precision.

Reference

Operator Classes

Refer to

• Operator Classes (vchordrq).
• Operator Classes (vchordg).

Types

rabitq8 since v1.1.0

• Description: The data type of a quantized vector that uses uint8 for internal storage. It's based on extended RaBitQ.^[1:1]
• Textual representation: Unlike vector/halfvec, the textual representation of rabitq8 is more complex. Suppose the dimension is ; it consists of a concatenation of an array of floating-point numbers enclosed in parentheses and an array of uint8 integers enclosed in brackets. For example, (2.999999, 160.63234, 647, 2.8498733)[255, 205, 187]. Its interpretation is internal, but you can get the vector it represents by using dequantize_to_vector(rabitq8)/dequantize_to_halfvec(rabitq8).

rabitq4 since v1.1.0

• Description: The data type of a quantized vector that uses uint4 for internal storage. It's based on extended RaBitQ.^[1:2]
• Textual representation: Unlike vector/halfvec, the textual representation of rabitq4 is more complex. Suppose the dimension is ; it consists of a concatenation of an array of floating-point numbers enclosed in parentheses and an array of uint4 integers enclosed in brackets. For example, (2.999999, 9.420722, 38, 2.8498733)[15, 12, 11]. Its interpretation is internal, but you can get the vector it represents by using dequantize_to_vector(rabitq4)/dequantize_to_halfvec(rabitq4).

Functions

quantize_to_rabitq8(vector) since v1.1.0

• Description: Quantize a vector to rabitq8. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines.
• Result: rabitq8, the quantized vector
• Arguments:
  • vector, the vector to be quantized
• Example:
  • SELECT quantize_to_rabitq8('[1,1,1]'::vector)
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (vector AS rabitq8) WITH FUNCTION quantize_to_rabitq8(vector) AS ASSIGNMENT.

quantize_to_rabitq8(halfvec) since v1.1.0

• Description: Quantize a vector to rabitq8. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines.
• Result: rabitq8, the quantized vector
• Arguments:
  • halfvec, the vector to be quantized
• Example:
  • SELECT quantize_to_rabitq8('[1,1,1]'::halfvec)
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (halfvec AS rabitq8) WITH FUNCTION quantize_to_rabitq8(halfvec) AS ASSIGNMENT.

dequantize_to_vector(rabitq8) since v1.1.1

• Description: Dequantize a quantized vector to vector. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines. The original vector cannot be precisely reconstructed using this function.
• Result: vector, the dequantized vector
• Arguments:
  • rabitq8, the quantized vector to be dequantized
• Example:
  • SELECT dequantize_to_vector(quantize_to_rabitq8('[1,1,1]'::vector))
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (rabitq8 AS vector) WITH FUNCTION dequantize_to_vector(rabitq8) AS ASSIGNMENT.

dequantize_to_halfvec(rabitq8) since v1.1.1

• Description: Dequantize a quantized vector to halfvec. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines. The original vector cannot be precisely reconstructed using this function.
• Result: halfvec, the dequantized vector
• Arguments:
  • rabitq8, the quantized vector to be dequantized
• Example:
  • SELECT dequantize_to_halfvec(quantize_to_rabitq8('[1,1,1]'::halfvec))
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (rabitq8 AS halfvec) WITH FUNCTION dequantize_to_halfvec(rabitq8) AS ASSIGNMENT.

quantize_to_rabitq4(vector) since v1.1.0

• Description: Quantize a vector to rabitq4. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines.
• Result: rabitq4, the quantized vector
• Arguments:
  • vector, the vector to be quantized
• Example:
  • SELECT quantize_to_rabitq4('[1,1,1]'::vector)
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (vector AS rabitq4) WITH FUNCTION quantize_to_rabitq4(vector) AS ASSIGNMENT.

quantize_to_rabitq4(halfvec) since v1.1.0

• Description: Quantize a vector to rabitq4. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines.
• Result: rabitq4, the quantized vector
• Arguments:
  • halfvec, the vector to be quantized
• Example:
  • SELECT quantize_to_rabitq4('[1,1,1]'::halfvec)
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (halfvec AS rabitq4) WITH FUNCTION quantize_to_rabitq4(halfvec) AS ASSIGNMENT.

dequantize_to_vector(rabitq4) since v1.1.1

• Description: Dequantize a quantized vector to vector. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines. The original vector cannot be precisely reconstructed using this function.
• Result: vector, the dequantized vector
• Arguments:
  • rabitq4, the quantized vector to be dequantized
• Example:
  • SELECT dequantize_to_vector(quantize_to_rabitq4('[1,1,1]'::vector))
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (rabitq4 AS vector) WITH FUNCTION dequantize_to_vector(rabitq4) AS ASSIGNMENT.

dequantize_to_halfvec(rabitq4) since v1.1.1

• Description: Dequantize a quantized vector to halfvec. Note that this function may produce sightly different results for identical inputs with different versions of VectorChord or with different machines. The original vector cannot be precisely reconstructed using this function.
• Result: halfvec, the dequantized vector
• Arguments:
  • rabitq4, the quantized vector to be dequantized
• Example:
  • SELECT dequantize_to_halfvec(quantize_to_rabitq4('[1,1,1]'::halfvec))
• Note: This function does not have a corresponding CAST. If needed, you can create one manually using CREATE CAST (rabitq4 AS halfvec) WITH FUNCTION dequantize_to_halfvec(rabitq4) AS ASSIGNMENT.

Operators

<->(rabitq8, rabitq8) since v1.1.0

• Description: Calculates L2 distance of two quantized vectors.
• Result: real, L2 distance of two quantized vectors
• Arguments:
  • rabitq8
  • rabitq8

<#>(rabitq8, rabitq8) since v1.1.0

• Description: Calculates negative dot product distance of two quantized vectors.
• Result: real, negative dot product distance of two quantized vectors
• Arguments:
  • rabitq8
  • rabitq8

<=>(rabitq8, rabitq8) since v1.1.0

• Description: Calculates cosine distance of two quantized vectors.
• Result: real, cosine distance of two quantized vectors
• Arguments:
  • rabitq8
  • rabitq8

<->(rabitq4, rabitq4) since v1.1.0

• Description: Calculates L2 distance of two quantized vectors.
• Result: real, L2 distance of two quantized vectors
• Arguments:
  • rabitq4
  • rabitq4

<#>(rabitq4, rabitq4) since v1.1.0

• Description: Calculates negative dot product distance of two quantized vectors.
• Result: real, negative dot product distance of two quantized vectors
• Arguments:
  • rabitq4
  • rabitq4

<=>(rabitq4, rabitq4) since v1.1.0

• Description: Calculates cosine distance of two quantized vectors.
• Result: real, cosine distance of two quantized vectors
• Arguments:
  • rabitq4
  • rabitq4

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1. Jianyang Gao, Yutong Gou, Yuexuan Xu, Yongyi Yang, Cheng Long, Raymond Chi-Wing Wong, "Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search", SIGMOD 2025, available at https://arxiv.org/abs/2409.09913. ↩︎ ↩︎ ↩︎