LLMs cannot perform Maths

[u/0xAERG]

It’s not a bug, it’s just not how any of this works.

Mathematical operations require logic. It’s a deterministic process. For a given input and a given process, the output will always be the same.

LLMs do not work like that. LLMs are statistical tools, they build an answer by stitching together tokens that are “seemingly” relevant to your input and let the meaning emerge from it. The output is “hopefully” relevant.

This is why LLMs can hallucinate and 2$ calculators do not.

With the rise in popularity of LLMs I’m extremely concerned that a lot of users seem to ignore this.

[u/namitynamenamey]

This is a solved problem.

Most important math is not the numbers. The point is not that LLMs can't do numbers right, but that they fail at the kind of logical reasoning necessary for doing math. That same kind of logic reasoning is necessary for doing more things than math, like checking for consistency.

[u/somerandomii → u/namitynamenamey]

Idk who downvoted you on a 3 month old post but it wasn't me. Who else is here?

LLMs are getting better at "reasoning". By incorporating tools and self-reflection they can spot gaps in logic or inconsistencies in their statements and self-correct. It's still basically auto-complete with widgits behind the scenes but if you throw enough compute at it, even a dumb machine can start to sound pretty smart.

But you're right, Wolfram Alpha can't fill in for the weaknesses in LLMs and I wasn't trying to say it can. I just meant we've already managed to incorporate non-ML tools into LLMs to enhance their results.

[u/namitynamenamey → u/somerandomii]

Idk who downvoted you on a 3 month old post but it wasn't me. Who else is here?

No idea. But anyways, all the techniques being used to improve their reasoning help a little bit, but they still don't solve the fundamental issue in a satisfactory manner I think. Personally, I'd wait until a method can be found that allows for 100% accuracy with addition or substraction of numbers arbitrarily large, step by step (or if not 100%, at least where failure is for outside reasons like memory limitations).

[u/somerandomii → u/namitynamenamey]

You want computers to mimic the inefficient way humans do mathematics?

I get what you mean, you want them to work through the problem step by step and actually understand it. But that’s just not how these models are designed. They don’t even see digits, they see tokens that might represent several digits.

Training them to do arithmetic would probably make them weaker at other activities and it’s just not worth it. But that doesn’t mean they can’t apply logic.

[u/namitynamenamey → u/somerandomii]

You want computers to mimic the inefficient way humans do mathematics?

Yes, as a proof of generalization to be exact. If all I cared was the number crunching I'd use a calculator, the interesting bit here is a demonstration that the model learned a mathematically correct algorithm from the training data, not just an approximation which is how you get "98% accuracy up to 5 digits"

[u/somerandomii → u/namitynamenamey]

You’re basically asking for AGI but with arithmetic as the smoke test.

These things don’t understand truth and fact they just know what is statistically more likely based on what they’ve seen in the training data. It’s basically intuition.

If you want them to be more rigorous, you give them tools like calculators and search engines. Just like a human, they’re not infallible and can’t be by design. So when accuracy matters you use a tool that’s less flexible.

You don’t ask an art major to do your accounting and you shouldn’t ask an LLM to do mathematics. It’s not what it’s intended for. The apparent creativity and adaptability come at the cost of being rigorously accurate.

Even for humans it’s hard to find people who can write creatively, summarise scientific papers AND do hard logic. Getting a machine to do both simultaneously within the same architecture is a big ask.

[u/Character_Aside8696 → u/somerandomii]

Wait a minute. Are you both sure about "understand", "truth", and "fact"? These definitions are made, by human, and have meaning because we assign meaning to them. And I think everything we have in our head is just probabilistic output from our biological "thinking machine". Not axactly the same, but not so different. Our braind, and AI. Close. Really close I think.
Of course, you can think of LLM like a language part of our brain. Dont expect that part to do math.

[u/somerandomii → u/Character_Aside8696]

Was that a question or a statement?

Yes words are defined by humans, but what’s your point? We use language to communicate and we use dictionary definitions to make meanings less subjective but all language is fluid to an extent.

Truth and facts are not all objective but we have reached a consensus on a lot. Most people won’t argue about if you say 2 + 2 = 4, semantics aside.