Temperature 0 is also sometimes a convenient mathematical environment for proving properties of Solomonoff induction, as in Li and Vitanyi (pdf of textbook).
I was not able on a quick skim of the pdf to identify which passage you were referring to. If possible can you point me to an example Temperature 0 in the textbook?
Sorry, on my phone for a few days, but iirc in ch. 3 they consider the loss you get if you just predict according to the simplest hypothesis that matches the data (and show it’s bounded).
thank you, will look into that. I intuitively expect that in the setting where compute is precisely 0 cost, you can always just convert multiplicity to negative-length by building an iterate/sort/index loop around the bit segment where the multiplicity lies, and this just costs you the length of the iterate/sort/index loop (a constant which depends on your language). I also intuitively expect this to break in the infinite bitstring setting because you can have multiplicity that isn’t contained in a finite substring?
Temperature 0 is also sometimes a convenient mathematical environment for proving properties of Solomonoff induction, as in Li and Vitanyi (pdf of textbook).
I was not able on a quick skim of the pdf to identify which passage you were referring to. If possible can you point me to an example Temperature 0 in the textbook?
Sorry, on my phone for a few days, but iirc in ch. 3 they consider the loss you get if you just predict according to the simplest hypothesis that matches the data (and show it’s bounded).
thank you, will look into that. I intuitively expect that in the setting where compute is precisely 0 cost, you can always just convert multiplicity to negative-length by building an iterate/sort/index loop around the bit segment where the multiplicity lies, and this just costs you the length of the iterate/sort/index loop (a constant which depends on your language). I also intuitively expect this to break in the infinite bitstring setting because you can have multiplicity that isn’t contained in a finite substring?