I didn't think you were a grifter but you only presented heuristics so if you have formal references then you can share them & people can decide on their own what to believe based on the evidence presented.
Fine, that's fair. I believe the statement that you made is countered by my claim, which is:
Theorem. For any tolerance epsilon > 0, there exists a transformer neural network of sufficient size that follows, up to the factor epsilon, the policy that most optimally achieves arbitrary goals in arbitrary stochastic environments.
Proof (sketch). For any stochastic environment with a given goal, there exists a model that maximizes expected return under this goal (not necessarily unique, but it exists). From Solomonoff's convergence theorem (Theorem 3.19 in [1]), Bayes-optimal predictors under the universal Kolmogorov prior converge with increasing context to this model. Consequently, there exists an agent (called the AIXI agent) that is Pareto-optimal for arbitrary goals (Theorem 5.23 in [1]). This agent is a sequence-to-sequence map with some mild regularity, and satisfies the conditions of Theorem 3 in [2]. From this universal approximation theorem (itself proven in Appendices B and C in [2]), there exists a transformer neural network of a sufficient size that replicates the AIXI agent up to the factor epsilon.
This is effectively the argument made in [3], although I'm not fond of their presentation. Now, practitioners still cry foul because existence doesn't guarantee a procedure to find this particular architecture (this is the constructive bit). This is where the neural scaling law comes in. The trick is to work with a linearization of the network, called the neural tangent kernel; it's existence is guaranteed from Theorem 7.2 of [4]. The NTK predictors are also universal and are a subset of the random feature models treated in [5], which derives the neural scaling laws for these models. Extrapolating these laws out as per [6] for specific tasks shows that the "floor" is always below human error rates, but this is still empirical because it works with the ill-defined definition of superintelligence that is "better than humans in all contexts".
[1] Hutter, M. (2005). Universal artificial intelligence: Sequential decisions based on algorithmic probability. Springer Science & Business Media.
Good question. It's because we don't need to be completely optimal in practice, only epsilon close to it. Optimality is undecidable, but epsilon close is not, and that's what the claim says that NNs can provide.
That doesn't address what I asked. The paper I linked proves undecidability for a much larger class of problems* which includes the case you're talking about of asymptotic optimality. In any case, I am certain you are unfamiliar w/ what I linked b/c I was also unaware of it until recently & was convinced by the standard arguments people use to convince themselves they can solve any & all problems w/ the proper policy optimization algorithm. Moreover, there is also the problem of catastrophic state avoidance even for asymptotically optimal agents: https://arxiv.org/abs/2006.03357v2.
* - Corollary 3.4. For any fixed ε, 0 < ε < 1, the following problem is undecidable: Given is a PFA M for which one of the two cases hold:
(1) the PFA accepts some string with probability greater than 1 − ε, or
(2) the PFA accepts no string with probability greater than ε.
Oh yes, that's one of the more recent papers from Hutter's group!
I don't believe there is a contradiction. AIXI is not computable and optimality is undecidable, this is true. "Asymptotic optimality" refers to behaviour for infinite time horizons. It does not refer to closeness to an optimal agent on a fixed time horizon. Naturally the claim that I made will break down in the infinite regime because the approximation rates do not scale with time well enough to guarantee closeness for all time under any suitable metric. Personally, I'm not interested in infinite time horizons and do not think it is an important criterion for "superintelligence" (we don't live in an infinite time horizon world after all) but that's a matter of philosophy, so feel free to disagree. I was admittedly sloppy with not explicitly stating that time horizons are considered finite, but that just comes from the choice of metric in the universal approximation which I have continued to be vague about. That also covers the Corollary 3.4, which is technically infinite time horizon (if I'm not mistaken) since the length of the string can be arbitrary.
