Thread by @j_bertolotti

#TheLongRoadToLearnSomethingNew
I decided it is high time I learn something about machine learning. I couldn't care less about learning how to use Tensorflow or any other package that do machine learning for you. I "just" want a Physicist's intuition for how and why it works.
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A million years ago I asked here for advices on resources. Some were very good advices, some were not. But I am mow armed with a textbook, and will irregularly update here on my progresses.
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I am not very far on my path. I've read a few online resources and (so far) the first 30 pages of this book.
I am aware machine learning is a HUGE topic, so I will begin by concentrating on neural networks (and probably a sub-sub-class of neural networks).
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Let's start as simple as it gets: we want "something" that given an input give us a output. E.g. input a picture and output the same picture with all cats highlighted.
The simplest possible object that connects pictures to pictures is matrix, so we start there.
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(If you are used to having matrices eat vectors and spit vectors, and this confuses you, just take all the pixels in the pictures, put them in a row and call that a vector. It works.)
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I am going to worry later about the (many) limitations of this approach. For now I will worry about how to make this work. Highlighting cats is too difficult for me at this level, so I will start with a much simpler problem: input a noisy image and output a less noisy one.
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To be honest, even this is too hard, so I will do it for just two (small) images. Now the problem is how to find the matrix entries that are able to perform this "simple" task. For this particular case there are smarter approaches, but we want to build toward ML.
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So what we will do is to start with some bad guess (a matrix filled with 1s), multiply it by a noisy image, calculate how far away from the correct answer (which we know) it is, modify slightly one of the matrix entries, and if it reduces the error, keep the modification.
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This is a very rough way to perform "gradient descent", i.e. to numerically find the set of parameters that minimize a certain metric.
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https://twitter.com/j_bertolotti/status/1121054414066810881

Gradient descent is a very active field of research, with a lot of very smart techniques available, but we will worry about them in the future. Right now I really want to keep things small and stupid. There will be time to make everything more efficient and elegant.
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So does this work? More or less yes. It takes some time to train (longer than the video below), but you can find a matrix that is quite good at giving you something close to the desired image even when the input is very noisy.
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