practically, a poly-time reduction can increase teh size of hte problem instance. So maybe you transform a 3-color instance (graph on n vertices) into a n^2 sized SAT instance. You can then solve this in time 2^{n^2 /…
complex searches are quite valuable in mathematics. For example, Maryna Viazovska's fields medal was for finding the right gadget (roughly, a complex search) to prove optimality results in sphere packings.
yes, but even the dramatic underestimate shows how useless it is. I also imagine that current estimates could be significantly optimized if there was some usecase for them. the 1k-10k multiplication regime has actual…
it doesn't. it might if you're multiplying numbers in the thousands of digits (but even that is almost assuredly too low). for essentially everyone this is purely a theoretical result.
not at all. even the previous O(n \log n) multiplier is almost never used in practice. In general fourier-based multipliers only start being useful at a minimum when you are multiplying 1000-digit numbers, but even that…
you (mostly) can't. In computing, "random" is a property of a process to generate a number, not a property of a number itself. You cannot directly analyze a number to determine it has been randomly generated. There are…
unless your guess is that the hypothetical ECC weakness is somehow correlated with the LCG structure, the draws from the LCG are as good as random. It is possible such a correlation could occur. but it would be much…
why though? in particular if the NSA wanted to hide their nefarious intent here, why wouldn't they use something stronger than an LCG so the question for how they're generated remained open forever?
it's worth clarifying that Fourier-based integer multiplication as a general class of algorithms are not galactic. For example, there are techniques that are competitive on some computing platforms for as few as 2048…
I've heard that certain inference providers may have different quality of caching implementations, so even if the listed numbers are as you say, the practical cache hit % you get might be significantly different/incur…
communicating results clearly is just as important for specialists/experts. A reaction by many mathematicians to the OpenAI dump (and many LLM breakthroughs) is simultaneously 1. if this is true, it is interesting, and…
there have been explicit attempts at this in the past. Nicholas Bourbaki was the pseudonym of a group of French mathematicians who had this goal mid 20th century. You can see e.g.…
for say FFT/integer multiplication or 3SUM, we have natural algorithms that have existed a long time with a given complexity (O(n \log n) and O(n^2), respectively). Given how long these natural algorithms have been the…
to depress you even more, it is consistent with everything that we know that P != NP and that cryptography does not exist. So there is a worst of both worlds, and we cannot rule it out.
worth mentioning that "NP" is not "non-polynomial" but "non-deterministic polynomial (time)". If NP was non-polynomial time then NP != P would be trivial (and in fact, P != EXP is known by the time hierarchy theorem).…
that's misunderstanding what lean does. It proves many statements of the form A implies C (I'll write this as A => C). If you chain many of these together, say A => B1 => B2 => ... => B500_000 => C, what you do is 1.…
while yarvin does not explicitly adopt the label of facist (and I might personally argue that it doesn't match him), he explicitly espouses for the fall of American democracy, and a return to a monarchist system. I…
the apple lawsiut about hw theft at openai is ongoing lol
see the Grothendiek prime https://en.wikipedia.org/wiki/57_(number)
those numbers are "adjusted" though. so they are not profitable by the standard definition.
helicoptors are a much more dangerous way to travel though? this is already true in the best of times/when you aren't anticipating a possible attack on the passengers.
there's a funny paper on this theme, titles "Could a Neuroscientist Understand a Microprocessor" https://pmc.ncbi.nlm.nih.gov/articles/PMC5230747/ roughly, it reviews common techniques in neuroscience, and comes to the…
tanks have very much run over people to kill them. a wheel can very much be used as a weapon.
isn't blitzscaling essentially the same thing, except for when American companies do it (not always within their own country, e.g. spotify, netflix, or amazon)
the way LLMs write math is not beautiful. it is exactly analogous to the software that LLMs develop is not beautiful. it may achieve impressive end products, but if you like understanding the methods/architecture,…
practically, a poly-time reduction can increase teh size of hte problem instance. So maybe you transform a 3-color instance (graph on n vertices) into a n^2 sized SAT instance. You can then solve this in time 2^{n^2 /…
complex searches are quite valuable in mathematics. For example, Maryna Viazovska's fields medal was for finding the right gadget (roughly, a complex search) to prove optimality results in sphere packings.
yes, but even the dramatic underestimate shows how useless it is. I also imagine that current estimates could be significantly optimized if there was some usecase for them. the 1k-10k multiplication regime has actual…
it doesn't. it might if you're multiplying numbers in the thousands of digits (but even that is almost assuredly too low). for essentially everyone this is purely a theoretical result.
not at all. even the previous O(n \log n) multiplier is almost never used in practice. In general fourier-based multipliers only start being useful at a minimum when you are multiplying 1000-digit numbers, but even that…
you (mostly) can't. In computing, "random" is a property of a process to generate a number, not a property of a number itself. You cannot directly analyze a number to determine it has been randomly generated. There are…
unless your guess is that the hypothetical ECC weakness is somehow correlated with the LCG structure, the draws from the LCG are as good as random. It is possible such a correlation could occur. but it would be much…
why though? in particular if the NSA wanted to hide their nefarious intent here, why wouldn't they use something stronger than an LCG so the question for how they're generated remained open forever?
it's worth clarifying that Fourier-based integer multiplication as a general class of algorithms are not galactic. For example, there are techniques that are competitive on some computing platforms for as few as 2048…
I've heard that certain inference providers may have different quality of caching implementations, so even if the listed numbers are as you say, the practical cache hit % you get might be significantly different/incur…
communicating results clearly is just as important for specialists/experts. A reaction by many mathematicians to the OpenAI dump (and many LLM breakthroughs) is simultaneously 1. if this is true, it is interesting, and…
there have been explicit attempts at this in the past. Nicholas Bourbaki was the pseudonym of a group of French mathematicians who had this goal mid 20th century. You can see e.g.…
for say FFT/integer multiplication or 3SUM, we have natural algorithms that have existed a long time with a given complexity (O(n \log n) and O(n^2), respectively). Given how long these natural algorithms have been the…
to depress you even more, it is consistent with everything that we know that P != NP and that cryptography does not exist. So there is a worst of both worlds, and we cannot rule it out.
worth mentioning that "NP" is not "non-polynomial" but "non-deterministic polynomial (time)". If NP was non-polynomial time then NP != P would be trivial (and in fact, P != EXP is known by the time hierarchy theorem).…
that's misunderstanding what lean does. It proves many statements of the form A implies C (I'll write this as A => C). If you chain many of these together, say A => B1 => B2 => ... => B500_000 => C, what you do is 1.…
while yarvin does not explicitly adopt the label of facist (and I might personally argue that it doesn't match him), he explicitly espouses for the fall of American democracy, and a return to a monarchist system. I…
the apple lawsiut about hw theft at openai is ongoing lol
see the Grothendiek prime https://en.wikipedia.org/wiki/57_(number)
those numbers are "adjusted" though. so they are not profitable by the standard definition.
helicoptors are a much more dangerous way to travel though? this is already true in the best of times/when you aren't anticipating a possible attack on the passengers.
there's a funny paper on this theme, titles "Could a Neuroscientist Understand a Microprocessor" https://pmc.ncbi.nlm.nih.gov/articles/PMC5230747/ roughly, it reviews common techniques in neuroscience, and comes to the…
tanks have very much run over people to kill them. a wheel can very much be used as a weapon.
isn't blitzscaling essentially the same thing, except for when American companies do it (not always within their own country, e.g. spotify, netflix, or amazon)
the way LLMs write math is not beautiful. it is exactly analogous to the software that LLMs develop is not beautiful. it may achieve impressive end products, but if you like understanding the methods/architecture,…