OK, so it will predict one of multiple different ~ 1 terabyte programs as having different likelihoods. I’d still rather it predict random{0,1} for less than 10 bytes, as the most probable. Inability to recognize noise as noise seems like a fundamental problem.
There is an SI that works over programs (which I was referring to originally), and there is an SI that works over computable distributions (that will produce random{0,1} with high probability).
No, it will always make a prediction according to the the infinitely many programs which are consistent with the observed string. In the observed string is 1 terabyte of uniform random noise, the shortest of these programs will be most likely ~ 1 terabyte long, but Solomonoff induction also considers the longer ones.
OK, so it will predict one of multiple different ~ 1 terabyte programs as having different likelihoods. I’d still rather it predict random{0,1} for less than 10 bytes, as the most probable. Inability to recognize noise as noise seems like a fundamental problem.
random{0,1} is not an algorithm, so...
Explained here.
There is an SI that works over programs (which I was referring to originally), and there is an SI that works over computable distributions (that will produce random{0,1} with high probability).
No, it will always make a prediction according to the the infinitely many programs which are consistent with the observed string. In the observed string is 1 terabyte of uniform random noise, the shortest of these programs will be most likely ~ 1 terabyte long, but Solomonoff induction also considers the longer ones.