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Bright Science is a free YouTube channel of over 1300 study videos for high schoolers (or precocious middle schoolers). Most are about five minutes (some longer, some shorter) and cover topics like chemistry, physics, calculus, geometry, biology, Algebra, trigonometry, grammar, ACT prep, and SAT prep. Explore.org. Futures Channel.
It’s not obvious that it would be feasible to find the path of the steepest descent on the “weight landscape” But calculus comes to the rescue. It turns out that the chain rule of calculus in effect lets us “unravel” the operations done by successive layers in the neural net.
He’s writing a paper, he says, basically to clarify the Second Law, (or, as he calls it, “the second fundamental theorem”—rather confidently asserting that he will “prove this theorem”): Part of the issue he’s trying to address is how the calculus is done: The partial derivative symbol ∂ had been introduced in the late 1700s.
It seemed as if there was a vast new domain that had suddenly been made accessible to scientific exploration. And in it I could see so much great science that could be done, and so many wonderful opportunities for so many people. In some ways, ruliology is like naturalscience. I myself was still only 25 years old.
But beginning a little more than a century ago there emerged the idea that one could build mathematics purely from formal axioms, without necessarily any reference to what is accessible to sensory experience. But observers like us can only “access” a certain type. And in a way our Physics Project begins from a similar place.
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