Differential forms, reverse derivatives and machine learning

I was recently trying to convince Bruno that covectors (in the form of differentials of functions) are the real deal in gradient descent, despite the misleading name and countless pictures showing little arrows pointing downhill.

This is a companion discussion topic for the original entry at https://matteocapucci.wordpress.com/2021/02/14/differential-forms-reverse-derivatives-and-machine-learning/