Deep Learning(CS7015): Lec 13.5 Some Gory Details

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lec13mod05
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Can someone summarize in simpler words what this lecture clip was about ?
I felt a bit lost, this was tough to follow :(

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It is funny how he easily says derivative of a vector is tensor....actually, unlike scalars, derivative of a vector is almost certainly never a tensor! That is why we have notion of "Covariant derivatives" for vectors. This is why defining "Tensors" using Matrices is a very bad idea, no one can really appreciate what tensors actually are! An actual mathematician studying differential geom or physicist studying GR etc will jump off from roof after seeing this abuse of "Tensors"
Again, this is not a limitation of the teacher, this is how "Data science and its paraphernalia is" ...mathematically naive at this stage at best!
Another thing which is very peculiar in all ANN lectures i see is the way they convey the simple concept of back propagation in a horrendous way (computation networks etc.), why not teach it with theory of composite functions and total derivatives, chain rule etc.? Dimensions are self correcting, no need to even memorize them! I will even go on to say that teach students with the analogy of continuous functions first! Everything else will be so simple!!!!

paulhowrang