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Comment by xrd | Hacker News Reader

  In particular, Mixtral vastly outperforms Llama 2 70B on mathematics, code generation, and multilingual benchmarks

I'm interested in seeing how it does with mathematics. That has always seemed like a particular weakness that no one yet has effectively cracked.

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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.

Agreed. But they do call it out here and I'm interested in understanding why.

There's been attempts to use different embeddings for numbers, which helps a lot. E.g., https://news.ycombinator.com/item?id=37936005

> it's sort of a weakness inherent to LLM's... next word prediction isn't really supposed to be good at math.

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.

I disagree; 1. the parameters are there to make the model better at learning textual patterns, not arithmetic patterns. 2. Next token prediction is a terrible way to perform arithmetic. 3. Perhaps most importantly, the loss function does not incentivise being good at arithmetic at all.

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.

> 1. the parameters are there to make the model better at learning textual patterns, not arithmetic patterns.

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.

1. this is interesting. tokens are arbitrary identifiers... of text. It's called a 'text encoder' for a reason

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.

About 3., isn't that done specifically in order to not overfit?

LLMs are compression functions. An LLM that internalizes the rules of arithmetic will compress better than one that doesn't. That improvement will be measurable in the loss function, as it correctly predicts more of its training data that depends on arithmetic answers to predict the next word.

> 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.

Annoyingly, Bard with Gemini will apparently use coding to answer every logical thinking question and get them all wrong. If you end with "Do not use code", it will get them all right.

ChatGPT-4 is starting to do this now all of the sudden, and it is also annoyingly returning erroneous information.

You don't need multimodals to access tools such as calculator. Check out PandasAI or Langchain Agent workflow. Rather than workout 451 * 995 for example the llm constructs the pandas query, runs it, returns result to user. Works pretty well.

Sure, llms don't do discreet math or logic directly. On the other hand, they write surprisingly good code.

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.

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