it's sort of a weakness inherent to LLM's... next word prediction isn't really supposed to be good at math.
I doubt it will be ever 'cracked' with better LLM's, only multimodal ones with access to program execution and calculators.
I doubt it will be ever 'cracked' with better LLM's, only multimodal ones with access to program execution and calculators.
FWIW I don't agree with this in a theoretical sense. The reason LLMs can do as much as they can is because next token prediction attempts to infer a world model for the processes that generated each next-token in the training set. I don't see a reason that this would preclude learning arithmetic in order to better predict next tokens that require arithmetic.
I'd guess that arithmetic will become suddenly reliable with one of the next significant (e.g. 2-5x) jumps in parameter count.
Any perceived arithmetic ability is just a textual coincidence.
I agree that a sufficiently intelligent LLM, like 300+ IQ would have an excellent model of how multiplication works. It may even assist in finding new theorems, but a calculator will always be better at 926*725.
There's nothing "textual" about the tokens. They are arbitrary identifiers. There's nothing "textual" about transformers! The fact that e.g. GPT-4 can accept images as input, and that its textual performance improved as a result, and that transformers are also being used for text-to-speech models should have already communicated this.
> 2. Next token prediction is a terrible way to perform arithmetic.
This is just attempting to resolve our disagreement with pure assertion. It's certainly less efficient to use an artificial intelligence to do arithmetic. But whether it's efficient is a different question than how likely it is to be possible.
> 3. Perhaps most importantly, the loss function does not incentivise being good at arithmetic at all.
This is blatantly untrue. The same argument would suggest that LLMs can't do anything that wasn't exactly in their training set already. But they can.
2. it's a strong assertion but it is true. it's kind of inherent in the name; next word prediction. Why would you want a calculator to be making predictions? I agree that it's worth understanding whether it's possible, but your original point was that 'arithmetic will become suddenly reliable' - this is what I am disagreeing with.
3. this links to the above point - you are right: LLM's can already perform arithmetic, this could be easily proved by loading up gpt-2. but again, your original point was that LLM's will 'figure out' arithmetic - I don't believe they will. The loss function does not incentivize being good at arithmetic, it incentivizes making good predictions that are close to the true value. The loss function will not penalize an LLM who predict 'good' is the next word when it should have been 'great'. while it might penalize '2+2=3; since this sequence would be strongly represented in the training set, it's not going to penalize the model getting '1234*5678' one digit off - which is the problem.
> Why would you want a calculator to be making predictions?
If the predictions are correct, why wouldn't I? You are objecting to the entire concept of LLMs at this point, there's nothing specific to arithmetic here.
I'm guessing we'll see llms that do input>program(s)>run>summarize>output
I'm not really disagreeing - I just think llms will do "more of the work" themselves by way of writing and running prolog programs, symbolic math (Julia etc) and running theorem provers.