Comment by danbruc
6 days ago
I think the main thing I want from an AI in order to call it intelligent is the ability to reason. I provide an explanation of how long multiplication works and then the AI is capable of multiplying arbitrary large numbers. And - correct me if I am wrong - large language models can not do this. And this despite probably being exposed to a lot of mathematics during training whereas in a strong version of this test I would want nothing related to long multiplication in the training data.
I'm not sure if popular models cheat at this, but if I ask for it (o3-mini) I get correct results/intermediate values (for 794206 * 43124, chosen randomly).
I do suspect this is only achieveable because the model was specifically trained for this.
But the same is true for humans; children can't really "reason themselves" into basic arithmetic-- that's a skill that requires considerable training.
I do concede that this (learning/skill aquisition) is something that humans can do "online" (within days/weeks/months) while LLMs need a separate process for it.
> in a strong version of this test I would want nothing related to long multiplication in the training data.
Is this not a bit of a double standard? I think at least 99/100 humans with minimal previous math exposure would utterly fail this test.
I just tested it with Copilot with two random 45 digit numbers and it gets it correct by translating it into Python and running it in the background. When I asked to not use any external tools, it got the first five, the last two, and a hand full more digits in the middle correct, out of 90. It also fails to calculate the 45 intermediate products - one number times one digit from the other - including multiplying by zero and one.
The models can do surprisingly large numbers correctly, but they essentially memorized them. As you make the numbers longer and longer, the result becomes garbage. If they would actually reason about it, this would not happen, multiplying those long numbers is not really harder than multiplying two digit numbers, just more time consuming and annoying.
And I do not want the model to figure multiplication out on its own, I want to provide it with what teachers tell children until they get to long multiplication. The only thing where I want to push the AI is to do it for much longer numbers, not only two, three, four digits or whatever you do in primary school.
And the difference is not only in online vs offline, large language models have almost certainly been trained on heaps of basic mathematics, but did not learn to multiply. They can explain to you how to do it because they have seen countless explanation and examples, but they can not actually do it themselves.
When kids learn multiplication, they learn it on paper, not just in their heads. LLMs don’t have access to paper.
“Do long arithmetic entirely in your mind” is not a test most humans can pass. Maybe a few savants. This makes me suspect it is not a reliable test of reasoning.
Humans also get a training run every night. As we sleep, our brains are integrating our experiences from the day into our existing minds, so we can learn things from day to day. Kids definitely do not learn long multiplication in just one day. LLMs don’t work like this; they get only one training run and that is when they have to learn everything all at once.
LLMs for sure cannot learn and reason the same way humans do. Does that mean they cannot reason at all? Harder question IMO. You’re right that Python did the math, but the LLM wrote the Python. Maybe that is like their version of “doing it on paper.”
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