cross-posted from: https://slrpnk.net/post/5501378

For folks who aren't sure how to interpret this, what we're looking at here is early work establishing an upper bound on the complexity of a problem that a model can handle based on its size. Research like this is absolutely essential for determining whether these absurdly large models are actually going to achieve the results people have already ascribed to them on any sort of consistent basis. Previous work on monosemanticity and superposition are relevant here, particularly with regards to unpacking where and when these errors will occur.

I've been thinking about this a lot with regards to how poorly defined the output space they're trying to achieve is. Currently we're trying to encode one or more human languages, logical/spatial reasoning (particularly for multimodal models), a variety of writing styles, and some set of arbitrary facts (to say nothing of the nuance associated with these facts). Just by making an informal order of magnitude argument I think we can quickly determine that a lot of the supposed capabilities of these massive models have strict theoretical limitations on their correctness.

This should, however, give one hope for more specialized models. Nearly every one of the above mentioned "skills" is small enough to fit into our largest models with absolute correctness. Where things get tough is when you fail to clearly define your output space and focus training so as to maximize the encoding efficiency for a given number of parameters.