[solarmist]

My only point here is that any framework for generalization needs to be able to account for and incorporate these kinds of "exception-seeking" cases. Similar to the same way that mathematics uses counter-examples to strengthen and reinforce the definitions chosen.

[ericjang]

I agree with your comment "In many languages, if you choose any of those supposed rules you can probably construct an algorithm to generate odd, but understandable words that defy that rule." - it comes many forms, from Goodhart's Law to the "hot dog vs. sandwich" debate.

I do mention this in my blog post - although I think Generalization is Language, I don't think it's possible to create a formal framework of language, for precisely because of "adversarial examples" that can be supplied for any formal definition.

Natural language itself, ignorant of formality, is able to account for these exceptions insofar as language is sufficient for people to convey a bare minimum of meaning. I am proposing to define language and generalization via the implicit understanding of large language models, in the same way you might use an image classifier to define "cat images" or "hot dogs"

[solarmist]

Hmm, I can understand the motivation. However, I feel it either won't work or will be very fragile because it's already part of the model because they're trained using natural language.

DL is already far from formal models, that's why deep learning “works.” And even at the current level of DL models, those exceptions are represented to some extent.

So ultimately, your idea is to push the models toward further generality, which in my option, will bake these “exceptions” deeper into the model.

And my question is, what does that mean for your idea? In my mind trying to exclude them would break what works. On the other hand, ignoring them means you can't direct development towards your goal because there’s no map from language to generalizations, so that you would be relying on random chance for progress.

If this is off in left field, let me know, but that's what I can see from your description.