Does anyone know if the probabilities output by Solomonoff Induction have been proven to converge? There could be as many as O(2^n) hypotheses of length n, each of which get a probability proportional to 2^-n. Once you sum that over all n, it doesn't converge, therefore the probability can't be normalized unless there's some other constraint on the number of hypotheses of length n consistent with the data. Does anyone know of such a constraint?