Humans are good at performing reliable calculations with pen and paper. That is the same kind of tools that LLMs works with. I'm not sure why humans can do that but not LLMs, the task should be way easier for an LLM.
> Humans are good at performing reliable calculations with pen and paper.
Speak for yourself. Even though I've always been strong at my conceptual understanding and problem solving in math, I always found it difficult to avoid arithmetic mistakes on pen and paper and could never understand why I was assessed on that. I could have done so much better in high-school math if I was allowed to use a programmable computer for the calculations.
And I think it's the same for LLMs, we should assess them on doing the arithmetic in a single pass, but rather on writing the code to perform the calculation, and responding based on that.
Maybe a lot of people suffer from a degree of dyscalculia, but in my experience if you do it a lot you just stop making mistakes. Not just me, many others I've seen reliably do calculations pretty quick without making errors, you just do everything twice as you go and then arithmetic errors go to basically 0.
But I do acknowledge that there are probably some or many humans that maybe can't reach that level of reliability with arithmetics.
LLMs (internally) don't have a pen and paper equivalent. Their output is the output of their neurons. Like if I was a head on a table with a screen on my forehead that printed out my thoughts as they appeared in my head. Ask (promt) me my favorite color and "green" would show up on the screen.
This is why prompting LLM's to show their steps works so well, it makes them work through the problem "in their head" more efficiently, rather than just spit out an answer.
However, you can give LLM's external access to tools. Ask GPT4 a particularly challenging math problem, and it will write a python script and run it to get a solution. That is an LLM's "pen and paper".
No, that is an LLM's calculator or programming, it doesn't actually do the steps when it does that. When I use pen and paper to solve a problem I do all steps on my own, when I use a calculator or a programming language the tool does a lot of the work.
That difference is massive, since when I use a calculator that doesn't help me learn numbers and how they interact and how algorithms works, while if I do the steps myself I do. So getting an LLM that can reliably execute algorithms like us humans can is probably a critical step towards making them as reliable and smart as humans.
I do agree though that if LLMs could keep a hidden voice they used to reason before writing they could do better, but that voice being shown to the end user shouldn't make the model dumber, you would just see more spam.
You are spitting hairs on technicalities here. You need to do a lot of "steps" to write a program that solves your question. Debatably even more steps and more complexity than using pen and paper.
Maybe we should be giving the LLM's MS paint instead of python to work out problems? There is nothing unique or "human" about running through a long division problem, it is ultimately just an algorithm that is followed to arrive at a solution.
> There is nothing unique or "human" about running through a long division problem, it is ultimately just an algorithm that is followed to arrive at a solution.
Yes, which is why we should try to make LLMs do them and that way open them up to learn much more complex understanding of algorithms and instructions that humans has yet to build a tool for.
> You need to do a lot of "steps" to write a program that solves your question. Debatably even more steps and more complexity than using pen and paper.
What does this have to do with anything? I am highlighting a core deficiency in how LLMs are able to reason, you saying that what they currently do is harder doesn't change the fact that they are bad at this sort of reasoning.
And no, making such a program doesn't require more steps or understanding. You Google for a solution and then paste in your values, that is much easier to teach a kid than to teach them math. I am sure I can teach almost any 7 year old kid to add two numbers by changing values in a python program in about an hour, much faster than they could learn math the normal way. Working with such templates is the easiest task for an LLM, what we want is to try to get the LLM to do things that is harder for it.
"I have a problem for you to solve. Muffins sell for $3/each. rick bakes 30 muffins a day. Tom bakes 2 muffins monday, 4 tuesday, 6 wednsdays, up to 14 on sunday. On days which tom and jerry combined bake more than 41 muffins, the price of the muffins drops to $2.50. How much total revenue do rick and tom take in during a full week, combined."
Please tell me how ChaptGPT4 writing a script to solve that is not logical reasoning, while a human pulling out pen and paper to do it is...
> Please tell me how ChaptGPT4 writing a script to solve that is not logical reasoning, while a human pulling out pen and paper to do it is...
I changed the prompt a bit (made all the numbers 3-4 digits) and gpt-4 answered with this, it just made up numbers for the days that you didn't add numbers for so it failed before it even came to arithmetics. Here is what it said, after I said this about tom "Tom bakes 2911 muffins monday, 491 tuesday, 699 wednsdays, up to 149 on sunday.", it just assumed sundays number was for all other weekdays not given a human wouldn't do that, and it missed the "up to" statement. Maye the large numbers I gave threw it off, but if that is enough to throw it of just shows that it can't really reason.
So thanks for that, more evidence these models are bad at reasoning.
Here is the first part of what it responded with, it is wrong already here:
First, let's calculate the number of muffins baked by Tom during the week:
Monday: 2911
Tuesday: 491
Wednesday: 699
Thursday: 149
Friday: 149
Saturday: 149
Sunday: 149
Edit: Here it made an arithmetics error just below, the error is that 4062 is not greater than 4199, so two critical errors, I taught math at college for years and you wouldn't find many students making mistakes like this:
Let's determine the days when Tom and Rick combined bake more than 4199 muffins:
Monday: 2911 (Tom) + 3571 (Rick) = 6482
Tuesday: 491 (Tom) + 3571 (Rick) = 4062
Wednesday: 699 (Tom) + 3571 (Rick) = 4270
On Monday, Tuesday, and Wednesday, they bake more than 4199 muffins combined, so the price of the muffins drops to $2851.50 on those days.
I know they can do that, but not as reliably as I can for example or typical engineers from 80 years ago. I did engineer exams without a calculator just did all the calculations with pen and paper, didn't make mistakes, just takes a bit longer since calculating trigonometric functions takes a bit but still not a lot of time compared to how much you have.
That was how everyone did it back then, it really isn't that hard to do. Most people today never tried to do it so they think it is much harder than it actually is.
Speak for yourself. Even though I've always been strong at my conceptual understanding and problem solving in math, I always found it difficult to avoid arithmetic mistakes on pen and paper and could never understand why I was assessed on that. I could have done so much better in high-school math if I was allowed to use a programmable computer for the calculations.
And I think it's the same for LLMs, we should assess them on doing the arithmetic in a single pass, but rather on writing the code to perform the calculation, and responding based on that.