Abstract Perplexity remains the primary intrinsic metric for evaluating language models, yet direct comparison across models with different tokenization schemes presents methodological challenges. We introduce a tokenizer-normalized perplexity metric that enables consistent comparison of language models regardless of their tokenization approaches. Through empirical analysis of 19 language models across five...
In my Xenosystems review, I discussed the Orthogonality Thesis, concluding that it was a bad metaphor. It's a long post, though, and the comments on orthogonality build on other Xenosystems content. Therefore, I think it may be helpful to present a more concentrated discussion on Orthogonality, contrasting Orthogonality with my...
The halting problem is the problem of taking as input a Turing machine M, returning true if it halts, false if it doesn't halt. This is known to be uncomputable. The consistent guessing problem (named by Scott Aaronson) is the problem of taking as input a Turing machine M (which...
The Löwenheim–Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, has a countably infinite model. This means that, in attempting to refer to uncountably infinite structures (such as in set theory), one "may as well" be referring to an...
This is an attempt to distill a model of AGI alignment that I have gained primarily from thinkers such as Eliezer Yudkowsky (and to a lesser extent Paul Christiano), but explained in my own terms rather than attempting to hew close to these thinkers. I think I would be pretty...
The paperclip maximizer is a thought experiment about a hypothetical superintelligent AGI that is obsessed with maximizing paperclips. It can be modeled as a utility-theoretic agent whose utility function is proportional to the number of paperclips in the universe. The Orthogonality Thesis argues for the logical possibility of such an...
Löb’s Theorem states that, if PA⊢□PA(P)→P, then PA⊢P. To explain the symbols here: * PA is Peano arithmetic, a first-order logic system that can state things about the natural numbers. * PA⊢A means there is a proof of the statement A in Peano arithmetic. * □PA(P) is a Peano arithmetic...