Where does machine learning algorithme store the result?

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I think this is kind of "blasphemy" for someone who comes from the AI world, but since I come from the world where we program and get a result, and there is the concept of storing something un memory, here is my question :

Machine learning works by iterations, the more there are iterations, the best our algorithm becomes, but after those iterations, there is a result stored somewhere ? because if I think as a programmer, if I re-run the program, I must store previous results somewhere, or they will be overwritten ? or I need to use an array for example to store my results.

For example, if I train my image recognition algorithme with a bunch of cats pictures data sets, what are the variables I need to add to my algorithme, so if I use it with an image library, it will always success everytime I find a cat, but I will use what? since there is nothing saved for my next step ?

All videos and tutorials I have seen, they only draw a graph as decision making visualy, and not applying something to use it in future program ?

For example, this example, kNN is used to teach how to detect a written digit, but where is the explicit value to use ?

https://github.com/aymericdamien/TensorFlow-Examples/blob/master/examples/2_BasicModels/nearest_neighbor.py

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