There’s a pattern in machine learning that blows my mind every time, even though I’ve seen it more than I can count.

Look at this expression:

Yes, I know. You are more than familiar with linear regression; we are not here to discuss that. I want to share a wonderful mathematical principle with you, learning through the example of linear regression.

Depending on what we understand by *a*, *x*, *b*, +, and ·, the expression “*ax* + *b*” can either be the very first machine learning model a student encounters or the main component of a powerful neural network.

Its evolution from basic to state-of-the-art was shaped by the two great forces of mathematics:

generalizing the meaning of simple symbols such as + and · to make them do more,

and then abstracting the complex symbols into

*a*-s,*b*-s, and*x*-es to keep them simple.

This dance of generalization and abstraction is the essence of mathematics; it’s why we can treat functions as vectors, use matrices as exponents, build the foundations of mathematics by dr…

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