I think the problem here is that 'understanding' is not the same as curve fitting.
If all one is doing is giving a model lots of data and fitting curves it's not really 'understanding' but brute forcing it's way (with gradient descent) and then storing the weights and finally approximate the solution when a query is passed in.
This is not the same as understanding. Human intelligence can operate deterministically as well as non-deterministically. We can listen to language, which is by it's nature non-deterministic and convert that into deterministic operations and vice a versa. IE we can operate on some logic and explain it in multiple ways to other people.
Understanding requires much less data than brute forcing your way into pattern recognition.
When you see a simple number like this 2 * 4 you are able to understand that it's equivalent to 2 + 2 + 2 + 2 and that in turn means 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 <- Count that and you've got your answer.
Because you 'understand' this basic concept and all the operations in between you are able to compute more examples. But you only need to understand it once. Once you understand multiplications and additions and all the tricks in between you are able to compute 23 * 10 without being fed 23 * 10 as prior data. Understanding is very different from fitting a curve. You can reach conclusions and understanding through pattern recognition, but it's important to differentiate 'approximation' from 'calculation'. If you understand something in it's entirety you should be able to calculate an outcome deterministically.
Right now LLMs lack 'understanding', and seems to only 'approximate' which may seem like 'understanding' but is actually not.
I think you are mixing layers of abstraction. To make a crude but I think not unhelpful analogy: 'Understanding' is a natural language concept that is our way to describe whats happening in our heads, and like most other such concepts is resistant to any clear definition and will exhibit sorites type paradoxes when one is attempted. It belongs to the presentation layer of the stack. While the process of curve fitting, however it is implemented, with whatever NN structure (like transformers) or maybe something else entirely belongs to the physical layer of the stack -- akin to frequency modulation.
While I am unsure whether LLMs are really understanding, whatever that means, I think it is not difficult to believe that any form of understanding we implement will involve 'curve fitting' as a central part.
This seems like its confusing how we conceptualize the training/learning process with what the system is actually doing. We conceptualize tuning parameters as curve fitting, and we conceptualize predicting the next token as maximizing probability. But that doesn't mean there is anything like curve fitting or probability maxxing happening as the system's parameters converge.
The core feature of curve fitting is learning explicit examples and then interpolating (in an uninformative manner) between unlearned examples. But there's no reason to think this completely describes what the system is doing, in the sense that there are no more informative descriptions of its behavior. Take an example that LLMs are surprisingly good at, creating poetry given arbitrary constraints. Imagine the ratio of the poems it has seen during its training over the number of unique poems it could create in principle. This number would be vanishingly small. Interpolating between two strings representing well-formed poems in an uninformative manner (i.e. some finite polynomial) will not generate well-formed poems. The only way you could move between two examples of well-formed poems while staying on the manifold of well-formed poems is if you captured all relevant features of the manifold. But I fail to see a difference between capturing all relevant features of the poetry-manifold and understanding poetry.
What LLMs do can be described as curve fitting in only the most uninformative description possible. What they do is discover features of the structures referred to by the training text and competently deploy these features in predicting the next token. A human that could do this would be consider to understand said structure.
If all one is doing is giving a model lots of data and fitting curves it's not really 'understanding' but brute forcing it's way (with gradient descent) and then storing the weights and finally approximate the solution when a query is passed in.
This is not the same as understanding. Human intelligence can operate deterministically as well as non-deterministically. We can listen to language, which is by it's nature non-deterministic and convert that into deterministic operations and vice a versa. IE we can operate on some logic and explain it in multiple ways to other people.
Understanding requires much less data than brute forcing your way into pattern recognition.
When you see a simple number like this 2 * 4 you are able to understand that it's equivalent to 2 + 2 + 2 + 2 and that in turn means 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 <- Count that and you've got your answer.
Because you 'understand' this basic concept and all the operations in between you are able to compute more examples. But you only need to understand it once. Once you understand multiplications and additions and all the tricks in between you are able to compute 23 * 10 without being fed 23 * 10 as prior data. Understanding is very different from fitting a curve. You can reach conclusions and understanding through pattern recognition, but it's important to differentiate 'approximation' from 'calculation'. If you understand something in it's entirety you should be able to calculate an outcome deterministically.
Right now LLMs lack 'understanding', and seems to only 'approximate' which may seem like 'understanding' but is actually not.