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Jiro comments on The Brain as a Universal Learning Machine - LessWrong
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Look at it from the other end: You can take a picture of a baseball and overlay noise on top of it. There could, at least plausibly, be a point where overlaying the noise destroys the ability for humans to see the baseball, but the information is actually still present (and could, for instance, be recovered if you applied a noise reduction algorithm to that). Perhaps when you are twiddling the pixels of random noise, you're actually constructing such a noisy baseball image a pixel at a time.
Agree with all you said, but have to comment on
You could be constructing a noisy image of a baseball one pixel at a time. In fact if you actually are then your network would be amazingly robust. But in a non-robust network, it seems much more probable that you're just exploiting the system's weaknesses and milking them for all they're worth.