Computers make continuous math unnecessary. More than that, it becomes a hindrance.
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Gradients were invented long before computers started approximating them for us.
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Gradients/derivatives are a limit, and limits are definitely continuous math. More importantly, how do computers actually compute gradients? Do they evaluate the function at a bunch of points and take differences? No, backprop is based on continuous math.pic.twitter.com/SRlmyWqGh2
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Thomas, this guy is clearly a troll (though my phone tried to autocorrect this as "a tool"). You're wasting your time here arguing against takes a bot fed on first-year "Intro to CS" and the worst of Reddit would come up with.
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That’s my point. Derivatives, limits and continuous math are approximations that computers need not make.
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So why do we compute gradients via continuous math (product rule, chain rule, etc.) instead of by evaluating the function at several points and taking differences?https://twitter.com/shortstein/status/1473836163609739264 …
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