It also sounds like from the paper transformers are formally proven to capable of it, but the training can't get the weights to make it capable of it, even though there should exist such weights, if I am reading them right.
on the ohter hand, thinking with the parenthesis takes language up to the level of functional-thinking. computable stuff is all about substitution of all things inside a parenthesis for a single thing. and this is the essence of all classic computation
In the paper I don't think they are looking for perfect, but they show which models can't seem to learn significantly beyond the size of examples they explicitly saw.
I missed it because it was spaced over a few lines and I was tired.
Pattern recognition can fail. Mine does, GPT's does.
I count further than I subitize, but from experience my mind may wander and I may lose track after 700 of a thing even if there's literally nothing else to focus on.
But I still didn't notice an error at depth 3.
You get the general rule (in linguistics known as competency) but can't flawlessly do it (performance). Transformers can't seem to get competence here.
In standard automata theory, all inputs to automatons are finite.
Formally transformers should be capable of modeling it with the right weights, but they show good evidence those weights can't be learned with gradient descent. Whereas a neural turing machine or stack machine can learn them with gradient descent.
I'm thinkin if your understanding were sound I would have to listen to it, but I rather read about these kinds of things, so whis is why I say unsound is best
on the other hand, putting things down into writing is difficult. So while you diminish this paper's accomplishments, you couldn't have done it yourself in spite of easily understanding it.
Not to crit the paper: formally stating things is good. But it feels like the outcome was highly predictable. Inferences being drawn from the language model where the language is a real world language and not a restricted subset were always going to hit up against the complexities of real languages.
And I'd be mindful that conforming to Chomsky Hierarchies says nothing about the nature of universal language models, or {{GPT or turing machines} and emergent intelligence}. Which again, isn't to lay things on the authors. People have a habit (here, in general) of taking things out of context.
I kind of feel thats about it: If the analysis of the classifier architecture shows constructs which map to a machine capable of being the higher Chomsky class, then its likely that reflects the complexity of the languages being analysed.