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[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
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[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
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p
That’s only the memory used to store the vector.
[ "articles", "articles/scalar-quantization" ]
3,073
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(2)
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p
There is also an overhead of the
[ "articles", "articles/scalar-quantization" ]
3,074
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(2)
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p
HNSW graph, so as a rule of thumb we estimate the memory size with the following formula:
[ "articles", "articles/scalar-quantization" ]
3,075
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(3)
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p
While Qdrant offers various options to store some parts of the data on disk, starting
[ "articles", "articles/scalar-quantization" ]
3,076
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(3)
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p
from version 1.1.0, you can also optimize your memory by compressing the embeddings.
[ "articles", "articles/scalar-quantization" ]
3,077
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(3)
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p
We’ve implemented the mechanism of Scalar Quantization!
[ "articles", "articles/scalar-quantization" ]
3,078
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(3)
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p
It turns out to have not
[ "articles", "articles/scalar-quantization" ]
3,079
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Qdrant under the hood: Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(3)
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p
only a positive impact on memory but also on the performance.
[ "articles", "articles/scalar-quantization" ]
3,080
[ "Qdrant under the hood: Scalar Quantization - Qdrant" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > h2:nth-of-type(1)
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h2
Scalar Quantization
[ "articles", "articles/scalar-quantization" ]
3,081
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
Scalar quantization is a data compression technique that converts floating point values
[ "articles", "articles/scalar-quantization" ]
3,082
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
into integers.
[ "articles", "articles/scalar-quantization" ]
3,083
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
In case of Qdrant float32 gets converted into int8, so a single number
[ "articles", "articles/scalar-quantization" ]
3,084
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
needs 75% less memory.
[ "articles", "articles/scalar-quantization" ]
3,085
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
It’s not a simple rounding though!
[ "articles", "articles/scalar-quantization" ]
3,086
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
It’s a process that makes that
[ "articles", "articles/scalar-quantization" ]
3,087
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
transformation partially reversible, so we can also revert integers back to floats with
[ "articles", "articles/scalar-quantization" ]
3,088
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Scalar Quantization" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(4)
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p
a small loss of precision.
[ "articles", "articles/scalar-quantization" ]
3,089
[ "Qdrant under the hood: Scalar Quantization - Qdrant" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > h3:nth-of-type(1)
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h3
Theoretical background
[ "articles", "articles/scalar-quantization" ]
3,090
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5)
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p
Assume we have a collection of float32 vectors and denote a single value as f32.
[ "articles", "articles/scalar-quantization" ]
3,091
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5)
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p
In reality neural embeddings do not cover a whole range represented by the floating
[ "articles", "articles/scalar-quantization" ]
3,092
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5)
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p
point numbers, but rather a small subrange.
[ "articles", "articles/scalar-quantization" ]
3,093
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5)
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p
Since we know all the other vectors, we can
[ "articles", "articles/scalar-quantization" ]
3,094
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5)
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p
establish some statistics of all the numbers.
[ "articles", "articles/scalar-quantization" ]
3,095
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5)
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p
For example, the distribution of the values
[ "articles", "articles/scalar-quantization" ]
3,096
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5)
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p
will be typically normal:
[ "articles", "articles/scalar-quantization" ]
3,097
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
Our example shows that 99% of the values come from a [-2.0, 5.0] range.
[ "articles", "articles/scalar-quantization" ]
3,098
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
And the
[ "articles", "articles/scalar-quantization" ]
3,099
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
conversion to int8 will surely lose some precision, so we rather prefer keeping the
[ "articles", "articles/scalar-quantization" ]
3,100
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
representation accuracy within the range of 99% of the most probable values and ignoring
[ "articles", "articles/scalar-quantization" ]
3,101
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
the precision of the outliers.
[ "articles", "articles/scalar-quantization" ]
3,102
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
There might be a different choice of the range width,
[ "articles", "articles/scalar-quantization" ]
3,103
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
actually, any value from a range [0, 1], where 0 means empty range, and 1 would
[ "articles", "articles/scalar-quantization" ]
3,104
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
keep all the values.
[ "articles", "articles/scalar-quantization" ]
3,105
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
That’s a hyperparameter of the procedure called quantile.
[ "articles", "articles/scalar-quantization" ]
3,106
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
A value
[ "articles", "articles/scalar-quantization" ]
3,107
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Theoretical background" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(7)
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p
of 0.95 or 0.99 is typically a reasonable choice, but in general quantile ∈ [0, 1].
[ "articles", "articles/scalar-quantization" ]
3,108
[ "Qdrant under the hood: Scalar Quantization - Qdrant" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > h4:nth-of-type(1)
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h4
Conversion to integers
[ "articles", "articles/scalar-quantization" ]
3,109
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(8)
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p
Let’s talk about the conversion to int8.
[ "articles", "articles/scalar-quantization" ]
3,110
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(8)
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p
Integers also have a finite set of values that
[ "articles", "articles/scalar-quantization" ]
3,111
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(8)
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p
might be represented.
[ "articles", "articles/scalar-quantization" ]
3,112
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(8)
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p
Within a single byte they may represent up to 256 different values,
[ "articles", "articles/scalar-quantization" ]
3,113
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(8)
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p
either from [-128, 127] or [0, 255].
[ "articles", "articles/scalar-quantization" ]
3,114
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(10)
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p
Since we put some boundaries on the numbers that might be represented by the f32, and
[ "articles", "articles/scalar-quantization" ]
3,115
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(10)
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p
i8 has some natural boundaries, the process of converting the values between those
[ "articles", "articles/scalar-quantization" ]
3,116
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(10)
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p
two ranges is quite natural:
[ "articles", "articles/scalar-quantization" ]
3,117
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(11)
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p
$$ f32 = \alpha \times i8 + offset $$
[ "articles", "articles/scalar-quantization" ]
3,118
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(12)
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p
$$ i8 = \frac{f32 - offset}{\alpha} $$
[ "articles", "articles/scalar-quantization" ]
3,119
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(13)
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p
The parameters $ \alpha $ and $ offset $ has to be calculated for a given set of vectors,
[ "articles", "articles/scalar-quantization" ]
3,120
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(13)
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p
but that comes easily by putting the minimum and maximum of the represented range for
[ "articles", "articles/scalar-quantization" ]
3,121
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(13)
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p
both f32 and i8.
[ "articles", "articles/scalar-quantization" ]
3,122
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(15)
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p
For the unsigned int8 it will go as following:
[ "articles", "articles/scalar-quantization" ]
3,123
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(16)
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$$ \begin{equation}
[ "articles", "articles/scalar-quantization" ]
3,124
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(16)
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p
\begin{cases} -2 = \alpha \times 0 + offset \\ 5 = \alpha \times 255 + offset \end{cases}
[ "articles", "articles/scalar-quantization" ]
3,125
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(16)
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p
\end{equation} $$
[ "articles", "articles/scalar-quantization" ]
3,126
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(17)
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p
In case of signed int8, we’ll just change the represented range boundaries:
[ "articles", "articles/scalar-quantization" ]
3,127
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(18)
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p
$$ \begin{equation}
[ "articles", "articles/scalar-quantization" ]
3,128
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(18)
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p
\begin{cases} -2 = \alpha \times (-128) + offset \\ 5 = \alpha \times 127 + offset \end{cases}
[ "articles", "articles/scalar-quantization" ]
3,129
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(18)
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p
\end{equation} $$
[ "articles", "articles/scalar-quantization" ]
3,130
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(19)
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p
For any set of vector values we can simply calculate the $ \alpha $ and $ offset $ and
[ "articles", "articles/scalar-quantization" ]
3,131
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(19)
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p
those values have to be stored along with the collection to enable to conversion between
[ "articles", "articles/scalar-quantization" ]
3,132
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Conversion to integers" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(19)
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html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > h4:nth-of-type(2)
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h4
Distance calculation
[ "articles", "articles/scalar-quantization" ]
3,134
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/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
We do not store the vectors in the collections represented by int8 instead of float32
[ "articles", "articles/scalar-quantization" ]
3,135
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
just for the sake of compressing the memory.
[ "articles", "articles/scalar-quantization" ]
3,136
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
But the coordinates are being used while we
[ "articles", "articles/scalar-quantization" ]
3,137
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
calculate the distance between the vectors.
[ "articles", "articles/scalar-quantization" ]
3,138
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
Both dot product and cosine distance requires
[ "articles", "articles/scalar-quantization" ]
3,139
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
multiplying the corresponding coordinates of two vectors, so that’s the operation we
[ "articles", "articles/scalar-quantization" ]
3,140
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
perform quite often on float32.
[ "articles", "articles/scalar-quantization" ]
3,141
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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p
Here is how it would look like if we perform the
[ "articles", "articles/scalar-quantization" ]
3,142
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(20)
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conversion to int8:
[ "articles", "articles/scalar-quantization" ]
3,143
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(21)
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$$ f32 \times f32’ = $$
[ "articles", "articles/scalar-quantization" ]
3,144
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(21)
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p
$$ = (\alpha \times i8 + offset) \times (\alpha \times i8’ + offset) = $$
[ "articles", "articles/scalar-quantization" ]
3,145
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(21)
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p
$$ = \alpha^{2} \times i8 \times i8’ + \underbrace{offset \times \alpha \times i8’ + offset \times \alpha \times i8 + offset^{2}}_\text{pre-compute} $$
[ "articles", "articles/scalar-quantization" ]
3,146
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22)
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p
The first term, $ \alpha^{2} \times i8 \times i8’ $ has to be calculated when we measure the
[ "articles", "articles/scalar-quantization" ]
3,147
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22)
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p
distance as it depends on both vectors.
[ "articles", "articles/scalar-quantization" ]
3,148
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22)
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p
However, both the second and the third term
[ "articles", "articles/scalar-quantization" ]
3,149
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22)
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p
($ offset \times \alpha \times i8’ $ and $ offset \times \alpha \times i8 $ respectively),
[ "articles", "articles/scalar-quantization" ]
3,150
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22)
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p
depend only on a single vector and those might be precomputed and kept for each vector.
[ "articles", "articles/scalar-quantization" ]
3,151
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22)
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p
The last term, $ offset^{2} $ does not depend on any of the values, so it might be even
[ "articles", "articles/scalar-quantization" ]
3,152
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22)
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computed once and reused.
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3,153
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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p
If we had to calculate all the terms to measure the distance, the performance could have
[ "articles", "articles/scalar-quantization" ]
3,154
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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p
been even worse than without the conversion.
[ "articles", "articles/scalar-quantization" ]
3,155
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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p
But thanks for the fact we can precompute
[ "articles", "articles/scalar-quantization" ]
3,156
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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p
the majority of the terms, things are getting simpler.
[ "articles", "articles/scalar-quantization" ]
3,157
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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And in turns out the scalar
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3,158
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
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html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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quantization has a positive impact not only on the memory usage, but also on the
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3,159
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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p
performance.
[ "articles", "articles/scalar-quantization" ]
3,160
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Distance calculation" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(23)
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p
As usual, we performed some benchmarks to support this statement!
[ "articles", "articles/scalar-quantization" ]
3,161
[ "Qdrant under the hood: Scalar Quantization - Qdrant" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > h2:nth-of-type(2)
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h2
Benchmarks
[ "articles", "articles/scalar-quantization" ]
3,162
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Benchmarks" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(24)
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p
We simply used the same approach as we use in all the other benchmarks we publish.
[ "articles", "articles/scalar-quantization" ]
3,163
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Benchmarks" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(24)
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p
Both Arxiv-titles-384-angular-no-filters
[ "articles", "articles/scalar-quantization" ]
3,164
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Benchmarks" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(24)
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p
and Gist-960 datasets were chosen to make
[ "articles", "articles/scalar-quantization" ]
3,165
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Benchmarks" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(24)
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p
the comparison between non-quantized and quantized vectors.
[ "articles", "articles/scalar-quantization" ]
3,166
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Benchmarks" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(24)
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p
The results are summarized
[ "articles", "articles/scalar-quantization" ]
3,167
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Benchmarks" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(24)
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A slight decrease in search precision results in a considerable improvement in the
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3,170
[ "Qdrant under the hood: Scalar Quantization - Qdrant", "Arxiv-titles-384-angular-no-filters" ]
/articles/scalar-quantization/
html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(25)
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