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If that last slide felt like a lot, let it go. You don't need to hold the mechanics of every nudge in your head.
Here's the only thing worth keeping: nobody taught AlexNet what a dog looks like. It taught itself, just by being wrong over and over and correcting a little each time.
That is the part to keep. Everything else is detail.
Which leaves one irresistible question. If the network worked all this out on its own, what did it actually figure out? What is hiding inside those 60 million numbers?