We cannot engage in an intellectual discussion if we do not agree on definitions. So far, your definitions of understanding seem to be whatever vibe you are going for in the statement and I would urge you to think about what a sensible mathematical definition of understanding is so that it can sensibly be assessed on neural networks. Otherwise, this isn't science, it's a debate about personal experience.

> Understanding is a state of mind

This is meaningless, it is a circular definition at best.

> It exists entirely within the individual and nowhere else

Then why are we talking about it? What is the point if it is something that can only be defined per individual?

Regarding your language example; this is a case of missing vocabulary (excluding grammar of course, but I feel like that is second-order), which is not the same as conceptual understanding. We are often able to translate because we have shared concepts. Those concepts are what we really care to assess with LLMs.

> requires interpretation by a person to "know" an LLM "understands."

We are still not getting anywhere because you have not prescribed criteria to determine whether it understands. If it is a "know it when I see it" situation, that clearly isn't working. For example, if you say that you need to dig into its internals and figure out whether it is breaking things down appropriately, that doesn't work because you probably don't have the expertise to do that. The experts that do are telling you that it very likely understands because it pulls apart most concepts in the way we would expect.

I do object to the use of the word "simple". "Statistical" is so broad to be almost meaningless; it merely means that a prediction is being made in the presence of data which possibly contains some degree of uncertainty. "Simple" encompasses that which can be understood readily by a non-expert.

Quantum mechanics is statistical (this is literally the Born rule), but evolutions are not operating as stochastic processes in the sense of Kolmogorov. That is very different, and not relevant to our discussion.