It seems like you’re imagining some sort of side-channel in which the LLM can take “free actions,” which don’t count as next-tokens, before coming back and making a final prediction about the next-tokens. This does not resemble anything in LM likelihood training, or in the usual user interaction modalities for LLMs.
These are limitations of current LLMs, which are GPTs trained via SGD. But there’s no inherent reason you can’t have a language model which predicts next tokens via shelling out to some more capable and more agentic system (e.g. a human) instead. The result would be a (much slower) system that nevertheless achieves lower loss according to the original loss function.
Or, another way of putting it:
These are limitations of current LLMs, which are GPTs trained via SGD. But there’s no inherent reason you can’t have a language model which predicts next tokens via shelling out to some more capable and more agentic system (e.g. a human) instead. The result would be a (much slower) system that nevertheless achieves lower loss according to the original loss function.