veered's Shortform
post by veered (lucas-hansen) · 2023-04-07T17:39:41.941Z · LW · GW · 2 comments2 comments
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comment by veered (lucas-hansen) · 2023-04-07T17:39:42.467Z · LW(p) · GW(p)
For GPT-style LLMs, is it possible to prove statements like the following?
Choose some tokens , and a fixed :
There does not exist a prefix of tokens such that
More generally, is it possible to prove interesting universal statements? Sure, you can brute force it for LLMs with a finite context window but that's both infeasible and boring. And you can specifically construct contrived LLMs where this is possible but that's also boring.
I suspect that it's not possible/practical in general because the LLM can do arbitrary computation to predict the next token, but maybe I'm wrong.
Replies from: JBlack↑ comment by JBlack · 2023-04-08T11:37:03.987Z · LW(p) · GW(p)
Yes, in general statements like this are theoretically possible to prove, but not remotely practical. There might be some specific (A,B,LLM) triples for which you can prove such a statement but I expect that none of these are generalizable to actually useful statements.
No GPT-style architecture is (in itself) capable of truly universal computation, but in practice functions they can implement are far beyond our ability to adequately analyze.