> But that's exactly the > question I'm asking you. *Do* you believe that Novamente and AIXI rest on > the same foundations?
Hmmm.... The "foundations" metaphor is troublesome. The perspective underlying AIXI is certainly a perspective one can take as regards Novamente. For instance, I think one could prove a theorem about Novamente similar to the theorem Hutter proved about AIXItl. That is, one could prove something like (roughly speaking -- not rigorously stated): ** Given any computable reward function R, and any AI system X using computational resources W, there is a probability p(X,W,c,d) that Novamente will outperform X at fulfilling R using computational resources c*W+d. The formula for p(X,W,c,d) would be complex, but we'd want to show that for some fixed (large) c and d, p converges to 1 as W goes to infinity. ** The math would be more complex than for AIXItl because Novamente is a stochastic system. (Considered mathematically, it's not a deterministic system, though as implemented it uses pseudorandom number generators instead of true randomness.) The basic proof would be: Given enough resources, Novamente's procedure learning component could learn a schema imitating the AI system X, and it could then act like X if it decided this was the best thing to do. My conceptual problem is: This theorem, even if one went through the large amount of work required to prove it using the current overcomplicated mathematical machinery, wouldn't really tell you much of value about Novamente. So although the conceptual perspective underlying AIXItl does seem to apply to Novamente, it doesn't seem to be a very useful perspective on Novamente. This perspective is not the "foundation" of Novamente in any strong sense. However, the universal computational capability of Novamente schemata/predicates is part of the conceptual and mathematical foundation of Novamente. And this universal computational capability is what the above speculative "theorem/proof" relies on. So I guess my answer is that the foundations of Novamente include ideas closely related to AIXI's foundations, but also include a number of other things. As for whether AIXI is of any use for Novamente -- it's of use if one wants to prove theorems like the above about Novamente. But, such a theorem seems not to be of any practical use. We already know schemata/predicates can compute anything under the sun if you give them enough resources. We don't really need to construct rigorous proofs relating to this fact, do we? And we already know that this is not the only foundational concept underlying Novamente AI. -- Ben G ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
