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The common-or-garden matrix multiplication together with its inverse is sort of completely what’s happening in lots of easy ML fashions
That is the fourth chapter of the in-progress e book on linear algebra, “A birds eye view of linear algebra”. The desk of contents to this point:
Chapter-1: The basicsChapter-2: The measure of a map — determinantsChapter-3: Why is matrix multiplication the best way it’s?Chapter-4 (present): Methods of equations, linear regression and neural networks
All pictures on this weblog, except in any other case acknowledged, are by the writer.
Fashionable AI fashions leverage excessive dimensional vector areas to encode data. And the device we have now for reasoning about excessive dimensional areas and mappings between them is linear algebra.
And inside that discipline, matrix multiplication (together with its inverse) is actually all you might want to construct many easy machine studying fashions finish to finish. Which is why spending the time to grasp it rather well is a superb funding. And that is what we did in chapter 3.
These easy fashions, helpful in their very own proper, kind the constructing blocks of extra complicated ML and AI fashions with state-of-the-art efficiency.
We’ll cowl a couple of of those functions (from linear regression to elementary neural networks) on this chapter.
However first, we have to go to the best case within the easiest mannequin — when the variety of knowledge factors equals the variety of mannequin parameters. The case of fixing a system of linear equations.
We’ve lastly arrived (within the context of this e book) on the coronary heart of linear algebra. Fixing programs of linear equations is how we found linear algebra within the first place and the motivations for many ideas on this discipline have deep roots on this software.
Let’s begin easy and one dimensional. The idea of division is rooted in a single…
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