Quantum info, Magic the Gathering jokes, Lean, whatever else. | Assistant Professor, Applied Math @ UWaterloo IQC, Perimeter Institute.
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I can't think of a single interesting game where the matches are, realistically, independent.
(But assuming they are: 2-0.)
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Simplest sincere answer: we frequently need to solve polynomials over finite fields, or fields that aren't C (e.g. field of meromorphic functions). Radicals "work" there, numerical search like you describe doesn't.
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There's a story about how Kitaev found his algorithm for Abelian HSP. He heard someone had found a quantum algorithm for factoring (Shor), but couldn't access the article living in Russia. He reconstructed and generalized the proof just knowing someone had it.
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It's nrf52840. 1MB memory, 64MHz clock. I wanted to leave other keyboard functionality in tact so I'm capped somewhere at like 50-100kB range on parameters. Sensible latency means something like 1ms/char, or something like ~20k muls.
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Probably comparable capacity at this size. I'm still twiddling with seeing what the best model I can fit in at this size (~50kB) is.
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I was considering something like this! Like Shift+Tab to auto-send the next most probable key. It generates the exact same signal over USB as if you'd hit the key yourself, so your computer would "never know".
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Okay most common questions:
1) This isn't supposed to be useful. It's just for fun/looking cool
2) I can touch type quite quickly, slow video is so you can see what's happening
3) It doesn't learn/memorize your habits, so won't memorize passwords!
4) It's a ROG AZOTH
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You mean because I could use a Markov chain instead? Markov chains are a language model too! (And you train them, too!) I'm currently experimenting to see what kind of model works best. The very tight memory constraints mean that even just storing an English dictionary is too big
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I overwrote my keyboard's firmware so that it runs a tiny character-level language model to predict the next key you'll hit. It has per-key backlight LEDs and just lights up the ones you're likely to hit. All inference local on the microprocessor - works without the computer too!
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Got me Googling "can flies hear" like nobody's business. (Yes, they can, through their feet. Please someone add the music to the environment.)
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... please try this first! It's not just an easier version, it will almost certainly guide you towards any putative P vs NP solution in the process. It's a better place to throw away your token credits!!
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... there's not many other "similar looking" results.
A very very weak version of P != NP is: does NC1 = CH? Probably not. It's hard to explain how much more "obviously" these two are not equal. But it hasn't been proved either!
If you want to get an AI to prove P!=NP, then..
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Another issue is that there's essentially no interesting easier version of the problem that has been solved. This isn't true for other Millennium problems: there are toy versions with interesting mathematical meat. For P vs. NP, the oracle separation is entirely trivial, and ...
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Maybe an AI is about to solve / has solved a Millenium problem, but I think there's good reason to believe that it definitely isn't P vs. NP. One thing that people don't realize is that the vast majority "progress" on the problem has been *ruling out possible proof strategies*.
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Of course, many hard problems have naturally "harder" variants. Even if they prove P != NP, we can ask whether BPP/poly ⊇ NP ∩ coNP, which is probably far harder.
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...solved by 2028, then yes, we'll have new open problems, but very little sense of how hard those are. And with no sense of how hard they are, it's very hard to gauge how impressed we should be!
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If someone tells you that a model found a squibblemorphic decaform that /isn't/ perfectly ramous, and there is exactly one human in the world who understands why that's surprising... is that very impressive? Is that publishable?
If all of the "big open problems" of 2020 are...
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