Earlier quoted context omitted.
Thing is, a LLM is nothing but a prediction algorithm based upon what it trained. So it missing basic calculator functionality is a given. This is why tool usage is more and more a thing for LLMs. So that the LLM can from itself use a calculator for the actual math parts it needs. Thus increasing accuracy ...
Why is it a given? The universal approximation theorem should apply since addition is a continuous function. Now whether the network is sufficiently trained for that is another question but I don’t think it's a given that a trillion parameter model can’t approximate the most basic math operations. I think the tokenization is a bigger problem than the model itself.
So while it can look like a LLM calculates correctly, its still restricted by this accuracy issue. What happens when you get a single number wrong in a calculation, everything is wrong.
While a calculator does not deal with predictions but basic adding/multiplying/subtracting etc .. Things that are 100% accurate (if we not not count issues like cosmic rays hitting, failures in silica etc).
A trillion parameter model is just that, a trillion parameters, but what matter is not the tokens but the accuracy as in, the do they use int, float16, float32, float64 ... The issue is, the higher we go, the memory usage explodes.
There is no point in spending terabytes of memory, to just get a somewhat accurate predictive calculator, when we can just have the LLM call a actual calculator, to ensure its results are accurate.
Think of a LLM more like somebody with Dyslexia / Dyscalculia... It does not matter how good you are, all it takes is to switch one number in a algebraic calculation to get a 0/10 ... The reason why i mention this, is because i often think of a LLM like a person with Dyslexia / Dyscalculia. It can have insane knowledge, be smart, but be considered dumb by society because of that less then accurate prediction (or number swiping issue).
Take it from somebody that wasted a few years in school thanks to that issue, it really does not matter if your a good programmer later in life, when you flunk a few years thanks to undiagnosed issues. And yet, just like a LLM, i simply rely on tool usage to fix my inaccuracy issues. No point in wasting good shoulder space trying to graft a dozen more heads/brains onto me, when i can simply delegate the issue away. ;)
The fact that we can get computer models, that can almost program, write texts, ... and do so much more like a slightly malfunctioning human, amazes me. And at the same time, i curse at it like my teachers did, and also call it dumb at times hehehe ... I now understand how my teachers felt loool