> reasoning ability should enable them to handle numbers of arbitrary size, just as it enables humans to do so, given some pencil and paper.
Or given a calculator. Which it's running on. Which it in some sense is. There's something deeply ironic about the fact that we have an "AI" running on the most technologically advanced calculator in the history of mankind and...it can't do basic math.
This is like saying it's ironic that an alternator in a car cannot combust gasoline when the gasoline engine is right beside it, even though the alternator 'runs' on the gasoline engine.
Or similarly having a gasoline engine without an alternator and making the observation that there's an absurdity there in that you're generating large amounts of energy, yet aren't able to charge a relatively small 12V battery with any of it. It's a very practical and natural limitation, yet in some sense you have exactly what you want - energy - you just can't use it because of the form. If you step back there's an amusing irony buried in that. At least in my humble opinion :-)
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 ...
If they were selling LLMs as “LLMs” instead of magic code-writing, answer-giving PhD replacements, the lack of basic arithmetic capability would be a given… but they aren’t. Judging a paid service using their own implied claims is perfectly reasonable.
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.
Easy to answer that one ... predictions are based upon accuracy. So if you have a int4 vs a float16, the chance that the prediction goes off is higher with a int4. But even with a float16, your still going to run into issues where your prediction model goes off. Its going to be a lot less, your still going to get rounding issue, what may result in a 5 being a 8 (just a example).
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
That's confusing basic arithmetic as a user feature and as an implementation requirement.
I guarantee that computer vision and email clients both use basic arithmetic in implementation. And it would be trivially easy to bolt a calculator into an email app, because the languages used to write email apps include math features.
That's not true of LLMs. There's math at the bottom of the stack. But LLMs run as a separate closed and opaque application of a unique and self-contained type, which isn't easily extensible.
They don't include hooks into math features on the GPUs, and there's no easy way to add hooks.
If you want math, you need a separate tool call to conventional code.
IMO testing LLMs as if they "should" be able to do arithmetic is bizarre. They can't. They're not designed to. And even if they did, they'd be ridiculously inefficient at it.
> Pretty sure the only thing computer vision does is math.
That is only marginally less pedantic than saying that the only thing computer vision does is run discrete electrical signals through billions of transistors.
Yes, everything that a computer does, it does using math. This does not imply that things running on the computer can do basic arithmetic tasks for the user.
Or given a calculator. Which it's running on. Which it in some sense is. There's something deeply ironic about the fact that we have an "AI" running on the most technologically advanced calculator in the history of mankind and...it can't do basic math.