If you go to the Museu
Picasso in Barcelona
, you’ll
see many of the artist’s early works. They’re really interesting because they don’t look
like what we think of as
Picasso’s style. These paintings, completed during his early years, are
displays of his technical genius – as a classical painter.

Some particularly amazing examples are “Science
and Charity
” and “First
“. One of my favorites is “Portrait of the
Artist’s Mother.” These were all painted when he was fifteen.

You can see
both the artist’s
innate ability to make art, and his immense potential future. But to get to the point
where Picasso could reject traditional styles, he had
to master them first.

This is also true for machine learning.
There’s a
whole universe
of exciting developments at the forefront of large language models. But in the noise of
the bleeding edge, a lot of
foundational concepts get lost. If we don’t

understand the fundamentals
of how we get from a single word to a BERT
representation, and more importantly, why we do so,
the models will remain black boxes to us. We won’t be able to build on them and
master them in the ways
that we want.

Peter Norvig urges us to teach ourselves programming in ten
. In this spirit, after several years of working with embeddings,
foundational data structures in deep learning models, I realized it’s not trivial to
have a good conceptual model of them. Moreover, when I did
want to learn more, there was no
good, general text I could refer to as a starting point. Everything was either too deep
and academic or too shallow and content from vendors in the space selling their

So I started a project to understand the
fundamental building blocks of machine learning and natural language processing,
particularly as they relate to recommendation systems today. The results of this
project are the PDF on this site, which is aimed at a generalist audience and not trying
to sell you anything except the idea that vectors are cool. I’ve also been working on Viberary to implement these ideas in practice.

In addition to his art, Picasso also left us with the quote,

When art
get together they talk about Form and Structure and Meaning. When artists get
they talk about where you can buy cheap turpentine.

I wrote this text for my own learning process. But it’s my
hope that this
document puts embeddings in a business and engineering context so that others including
engineers, PMs, students, and
looking to
learn more about
fundamentals finds it useful.

Machine learning, like all good engineering and like good art, is
ultimately, a way for us to express ourselves, a craft made up of fundamental building
blocks and patterns that empower us and
allow us to build something
beautiful on strong foundations of those that came before us. and I hope you find as
much joy in exploring embeddings and using them
as I did.



Anyone who needs to understand embeddings, from machine learning engineers, to SWE,
or project manager, student, or simply curious. That said, there are different levels of
understanding in
document. Here are my recommendations on how to read:

# You want Sections Prereqs
1 a high-level intro 1,2 how apps work
2 to understand engineering concerns 1,2,5 Python, engineering, Big O Notation
3 an ML internal deep dive 3,4 Linear Algebra, ML, Python, engineering


“What are embeddings” is licensed under a Creative Commons
3.0. This means that you are welcome to use, download and share the text, provided
attribution is given to the author (Vicki Boykis) and that it is released under the


Feedback on the clarity of concepts or just typos is welcome. Feel
free to submit a PR

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