This enables you to solve seemingly-discrete problems with deep learning -- as long as they are so structured as to be interpolative, and as long as you can gather a dense sampling of the manifold. The manifold hypothesis must apply.
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However, when faced with a problem where the manifold hypothesis no longer applies, fitting a differentiable curve via gradient is no longer a good strategy. This is actually *most* of the space of all interesting/useful problems! E.g. most programs that software engineers write.
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Again, if this is your jam, then this is your book:https://www.manning.com/books/deep-learning-with-python-second-edition?a_aid=keras&a_bid=76564dff …
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François Chollet Retweeted David Picard
Ah, but this is incorrect! Virtually all perception problems *do* feature entirely-connected latent manifolds. Natural images are no exception. This is very easy to demonstrate, and something that cinematographers are intimately familiar with...https://twitter.com/david_picard/status/1450697372930088963 …
François Chollet added,
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Take a picture of your dog in your backyard, and a picture of your coffee mug on your kitchen table. Unconnected, right? You can't morph one into the other in a continuous fashion, right? Of course you can!
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There's an infinity of ways you could do it, but here's a few trivial ones.
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1. The handheld camera: just keep the camera rolling as you walk from your kitchen to your backward. Boom, a smooth transition where *every single frame* is extracted from the real world.
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(be back soon)
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2. Fade to black: this trick exploits the fact that changing the brightness of an image still gives you a "valid" image. Just fade one frame to black then fade in to the new frame. A bit trivial, I know
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3. The shared focus: zoom in on one object shared between the two scenes (or background color/texture, e.g. the wood of the table) then zoom out into the new frame.
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4. A variant of this would be to, say, turn the camera towards the sky you can see from the window, then move it down, and boom, it's your backyard
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So anyways, the visual world is in fact an entirely connected space (you can go from any valid image to any other valid image via a continuous path where every frame is a valid image). This means that there exists a natural, intrinsic manifold of the visual world.
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This is true for every perception problem, remarkably. The *physical world* lies on a manifold. And that's what makes deep learning so effective -- its assumptions are a good match to reality.
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