You can't prove LLMs can build theories like humans can, because we can effectively prove they can't. Most code bases do not fit in a context window. And any "theory" an LLM might build about a code base, analogously to the recent reasoning models, itself has to carve a chunk out of the context window, at what would have to be a fairly non-trivial percentage expansion of tokens versus the underlying code base, and there's already not enough tokens. There's no way that is big enough to build a theory of a code base.
"Building a theory" is something I expect the next generation of AIs to do, something that has some sort of memory that isn't just a bigger and bigger context window. As I often observe, LLMs != AI. The fact that an LLM by its nature can't build a model of a program doesn't mean that some future AI can't.
This is correct. The model context is a form of short term memory. It turns out LLMs have an incredible short term memory, but simultaneously that is all they have.
What I personally find perplexing is that we are still stuck at having a single context window. Everyone knows that turing machines with two tapes require significantly fewer operations than a single tape turning machine that needs to simulate multiple tapes.
The reasoning stuff should be thrown into a separate context window that is not subject to training loss (only the final answer).
"Building a theory" is something I expect the next generation of AIs to do, something that has some sort of memory that isn't just a bigger and bigger context window. As I often observe, LLMs != AI. The fact that an LLM by its nature can't build a model of a program doesn't mean that some future AI can't.