21–30 of 74 posts
Can anyone explain the significance of this finding? Any technologies that can benefit from the application of this?
Most importantly, though, Huang’s result lays to rest nagging worries about whether sensitivity might be some strange outlier in the world of complexity measures, Servedio said. “I think a lot of people slept easier that night, after hearing about this.”
Earlier quoted context omitted.
This is pure intuition, but from reading this I get the sense that this conjecture is some generalization of a fixed point theorem?
Can you explain your intuition for how this relates to fixed points?
The article discusses non-fixed equivalents, though, both a contextual variable length and a quantum super position length bit array.
Surprisingly good for a Quanta Magazine article.
Earlier quoted context omitted.
Can you explain your intuition for how this relates to fixed points?
A Boolean array is isomorphic to a fixed point number. The article discusses non-fixed equivalents, though, both a contextual variable length and a quantum super position length bit array.
A fine article. A great science writer like Dr. Erica Kalrreich can make anything interesting, even theoretical CS. Other articles by this author: https://www.quantamagazine.org/authors/erica-klarreich/
Can anyone explain the significance of this finding? Any technologies that can benefit from the application of this?
I'll have to reread the paper a couple more times, but I think Boolean sensitivity could be related to the security one has around any given need. There may be further implications around how to assess one's strategies for meeting needs, as those would be the individual inputs to the Boolean function of "Is the need for _____ security met?" This could help provide a theoretical framework for designing systems oriented around well-being.
Can anyone explain the significance of this finding? Any technologies that can benefit from the application of this?
Usually with things like this, the result is already fairly well established, or close enough at least, within the scale any real-world application would require. You can think of it like the four color theorem. A beautiful theoretical result (though a far less beautiful proof), but the only practical significance is now cartographers know they'll never need that extra crayon....
Earlier quoted context omitted.
Usually with things like this, the result is already fairly well established, or close enough at least, within the scale any real-world application would require. You can think of it like the four color theorem. A beautiful theoretical result (though a far less beautiful proof), but the only practical significance is now cartographers know they'll never need that extra crayon....
I think the most interesting point of the paper isn't simply the proof the conjecture but also the sqrt(n) bound. I doubt many downstream results were predicated on that particular bound.
If I interpret this correctly it's a tighter bound than the original conjecture, so it should allow better optimizations.
On boolean sensitivies: https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/07/Boolea... The closing quote: > [Huang] was able to prove that in any collection of more than half the points in an n-dimensional cube, there will be some point that is connected to at least √n of the other points — and the sensitivity conjecture instantly followed from this result The actual paper: https://arxiv.org/abs/1907.00847 Another b…
This is pure intuition, but from reading this I get the sense that this conjecture is some generalization of a fixed point theorem?