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A comment on Computer Scientists Discover Limits of Gradient Descent. Parent comment

Re:Computer Scientists Discover Limits of Gradient Descent by mbeex on Sunday July 30, 2023 @08:16AM (#36930396)
Show me a mathematical continuum in the real-world. And this is just the domain, nothing said about the mapping yet (the continuous function). Every analogy has its limits.
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Re:Computer Scientists Discover Limits of Gradient Descent by tomrod on Sunday July 30, 2023 @09:01AM (#36930749)
The space represented in a flat piece of paper.

The space is continuous even if we can only measure down to the Planck length.

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Re:Computer Scientists Discover Limits of Gradient Descent by mbeex on Sunday July 30, 2023 @09:06AM (#36930801)
Key here: "represented"

I'm only a mathematician, no physicist. But I think to remember, that the concept of a continuous physical space becomes quite muddled at this scale.

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Re:Computer Scientists Discover Limits of Gradient Descent by nerdponx on Sunday July 30, 2023 @11:38AM (#36932345)
* * *
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Re:Computer Scientists Discover Limits of Gradient Descent by hgsgm on Sunday July 30, 2023 @11:36AM (#36932311)
If you get to assume continuous paper, then I get assumed continuous paper.

If you don't want to assume continuity, then you get it back by rephrasing your theorems as "within a margin of error equal to the distance between discrete objects".

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