Solomonoff induction is essentially pattern matching and humans seem to be quite good at pattern matching. It is arguable that this ability is an important part of the human problem solving ability.
AIXIt is only “smarter than the human brain” in the ridiculous sense that it performs as well as the brain up to a gargantuan slow-down factor of 2^{length of program emulating human brain}. To seriously show it is smarter than the brain for general problem solving one would have to use an intelligence metric that takes resource bounds into account like a resource-bounded version of Legg-Hutter or my updateless metric.
I’m somewhat disappointed in this answer. Sure, it’s pattern matching, but there are many, many kinds of pattern matching, of which Solomonoff induction is just one kind.
it performs as well as the brain up to a gargantuan slow-down factor of 2^{length of program emulating human brain}.
That is not true. There is a large multiplicative factor but it’s not what you’re describing.
I’m not sure what kings of pattern matching you have in mind. Possibly you mean the sort of “pattern matching” typical to narrow AI e.g. a neural network firing with response to a certain “pattern”. Usually it is just clustering by dividing spaces with hypersurfaces constructed from some (very restricted) set of mathematical primitives. This sort of “pattern matching” is probably very important to the low-level working of the brain and the operation of unconscious systems such as visual processing, however it is not what I mean by “pattern matching” in the current context. I am referring to patterns expressible by language or logic. For example, if you see all numbers in a sequence are prime, it is a pattern. If you see all shapes in a collection are convex, it is a pattern. This sort of patterns are of fundamental importance in conscious thought and IMO can only be modeled mathematical by constructions akin to Solomonoff induction and Kolmogorov complexity.
There is a large multiplicative factor but it’s not what you’re describing.
On each step, AIXIt loops over all programs of given length and selects the one with the best performance in the current scenario. This is exponential in the length of the programs.
About the first point on pattern matching, I suggest you look at statistical inference techniques like GMM, DPGMM, LDA, LSA, or BM/RBMs. None of these have to do with Solomonoff induction, and they are more than capable of learning ‘patterns expressible by language or logic,’ yet they seem to more closely correspond to what the brain does than Solomonoff induction.
On each step, AIXIt loops over all programs of given length and selects the one with the best performance in the current scenario
Not precisely, but anyway that doesn’t lead to 2^{length of program emulating human brain} for human-level intelligence.
Solomonoff induction is essentially pattern matching and humans seem to be quite good at pattern matching. It is arguable that this ability is an important part of the human problem solving ability.
AIXIt is only “smarter than the human brain” in the ridiculous sense that it performs as well as the brain up to a gargantuan slow-down factor of 2^{length of program emulating human brain}. To seriously show it is smarter than the brain for general problem solving one would have to use an intelligence metric that takes resource bounds into account like a resource-bounded version of Legg-Hutter or my updateless metric.
I’m somewhat disappointed in this answer. Sure, it’s pattern matching, but there are many, many kinds of pattern matching, of which Solomonoff induction is just one kind.
That is not true. There is a large multiplicative factor but it’s not what you’re describing.
I’m not sure what kings of pattern matching you have in mind. Possibly you mean the sort of “pattern matching” typical to narrow AI e.g. a neural network firing with response to a certain “pattern”. Usually it is just clustering by dividing spaces with hypersurfaces constructed from some (very restricted) set of mathematical primitives. This sort of “pattern matching” is probably very important to the low-level working of the brain and the operation of unconscious systems such as visual processing, however it is not what I mean by “pattern matching” in the current context. I am referring to patterns expressible by language or logic. For example, if you see all numbers in a sequence are prime, it is a pattern. If you see all shapes in a collection are convex, it is a pattern. This sort of patterns are of fundamental importance in conscious thought and IMO can only be modeled mathematical by constructions akin to Solomonoff induction and Kolmogorov complexity.
On each step, AIXIt loops over all programs of given length and selects the one with the best performance in the current scenario. This is exponential in the length of the programs.
About the first point on pattern matching, I suggest you look at statistical inference techniques like GMM, DPGMM, LDA, LSA, or BM/RBMs. None of these have to do with Solomonoff induction, and they are more than capable of learning ‘patterns expressible by language or logic,’ yet they seem to more closely correspond to what the brain does than Solomonoff induction.
Not precisely, but anyway that doesn’t lead to 2^{length of program emulating human brain} for human-level intelligence.