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Re:Likelihood of discontinuous progress around the developme... by whereismypwd on Sunday February 25, 2018 @02:36PM (#16460714)
I think the better argument is that most "breakthroughs" are exponentially hard, or we wouldn't consider them breakthroughs!
Re:Likelihood of discontinuous progress around the developme... by mannykannot on Sunday February 25, 2018 @08:59PM (#16462459)
'Exponential' means something more specific than 'big' or 'largest in class'.
Re:Likelihood of discontinuous progress around the developme... by whereismypwd on Tuesday February 27, 2018 @11:41PM (#16480725)
Exponential is probably the easiest way to say "a search without usable gradients in a high-dimensional problem space."
Re:Likelihood of discontinuous progress around the developme... by mannykannot on Wednesday February 28, 2018 @02:06PM (#16485726)
'Breakthrough' means something less specific than 'a solution to a problem having a search without usable gradients in a high-dimensional problem space.' This is rather beside the point, however, as the the claim that kicked off this thread (most problems are exponentially hard) is about the difficulty of problem-solving in general, not the subset of problems that are pretty much hard by definition, in that their solution was/would be a breakthrough.