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I asked the following question to both ChatGPT 4 and Bard to see if they can get a simple matrix calculation right (after all Bill Gates said he was impressed by ChatGPT's math ability).

So I asked,

explain to me the result of d in the following numpy code

a = np.array([[[1, 2, 3], [2, 1, 3]]])
b = np.array([[[2, 1, 1], [2, 4, 0]]])
b1 = b.reshape(1, 3, 2)
d= a @ b1

Both ChatGPT and Bard got it totally wrong no matter how many times I tried. Because every time they will give me a slightly different result, so I just paste one of them.

This one is from GPT4 and as you can see, 2 out of 4 calculations are wrong, (1*2)+(2*1)+(3*1) = 7 NOT 5, (2*2)+(1*1)+(3*1) = 8 NOT 7

But Why is that?

ChatGPT 4

Bard is no different. The second mistake they both made is they both got reshape wrong but I am only concerned with matrix calculation here.

Bard

I let Bard do it many times and the closest I can get is 3 out 4 calculations right. d_10 = [[2, 1, 3]] @ [[2, 1, 1]] = 2 * 2 + 1 * 1 + 3 * 1 = 7 is wrong:

Bard again

---- update for chatgpt 4 turbo ----

I tried chatgpt 4 turbo, this time although it still got reshape wrong (and a silly mistake I really don't understand) but it finally got the 4 arithmetic calculations right.

reshape wrong for 4 turbo

The last row should [4,0]!

Finally, 4 arithmetic calculations right (but to the wrong reshape matrix)

4 arithmetic calculations right

---- update for Claude v2 & Llama v2 ----

I decided to let Claude v2 & Llama v2 try it. They did not even come closer. I am really surprised to see that. I just pasted llama's answer here.

llama

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  • $\begingroup$ LLM do not have mathematical rules set in their core, they just generate text. If you ask him to add two random numbers he will probably get it wrong if those numbers were never seen before. LLM see numbers as text as well. Even if LLM have emergent properties since there is no a priori mathematical knowledge it will fail easily. $\endgroup$
    – Lelouch
    Nov 8, 2023 at 9:19
  • $\begingroup$ But you may refer to the math ability test mentioned in the answer. According to that result, ChatGPT 4 should do the all calculations right in my example. After all, they are simple arithmetic operations compared to the test mentioned. $\endgroup$
    – Qiulang
    Nov 8, 2023 at 9:36
  • $\begingroup$ I do not believe human and AI have the same difficulty scale. Something very hard for a human can be trivial for an AI, in mathematics or any domain. And it's not necessarily something "monotonic". ChatGPT can be successfull at university level exams and still fails on basic logical reasoning that an elementary children could do... It also highly depends on the prompt (different prompt can lead to a fail or success in the problem solving). There is a reason why AI interpretability is still an active research topic. $\endgroup$
    – Lelouch
    Nov 8, 2023 at 10:53
  • $\begingroup$ Did you add that reshape on purpose? How many people would do this right with 3d tensors without knowing how reshape works in numpy? $\endgroup$
    – Valentas
    Nov 10, 2023 at 15:05
  • $\begingroup$ A bit and both of them do it wrong. But what surprised me most was they failed to do simple arithmetic operations in the end. They both failed to get the correct reshaped result but even using their reshaped matrix, they still failed to get the correct result. $\endgroup$
    – Qiulang
    Nov 10, 2023 at 15:42

1 Answer 1

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In my understanding, LLMs are, very simplified speaking, probabilistic solvers. Math problems such as matrix multiplications are, on the other hand, deterministic in nature. Thus, using a an LLM for solving a math problem mostly comes down to using the wrong tool for the task.

Of course, when it comes to text problems, LLMs should be beneficial because they can "understand" language and thus should be able to do precisely the task in question, translate a problem from language to mathematics. However, this does not work on more complex tasks (generally, many of them apparently do not pass the 6th grade in China https://arxiv.org/pdf/2306.16636.pdf).

An entire discussion about the use of LLMs and their obstacles with math problems can be found here https://arxiv.org/abs/2301.09723

However, some the shortcomings of LLMs can be circumventent. Instead of asking an LLM "How much is 3+2" it should be asked "Please write a program which adds two numbers and use the program to add 3 and 3 and show me the result" - just for much more sophisticated problems, as can be seen here https://www.pnas.org/doi/abs/10.1073/pnas.2123433119

As a simple thought experiment, you can try to set up a feedforward network which adds two numbers, preferably they should add to less than ten. Even when setting up a perfect network (and there is no gurantee that it would actually turn out like that once learned) there are a number of obstacles to face. The idea comes from the book (which I haven't read in a while and have no access to any more) "Deep Learning with Python, Second Edition" by Francois Chollet.

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  • $\begingroup$ Thanks for letting me know the test about the Chinese Elementary School Math Test. My son is in the 6th grade (I am Chinese, obviously) so I am familiar with those tests. But for my particular matric calculation, (1*2)+(2*1)+(3*1) = 7 NOT 5, (2*2)+(1*1)+(3*1) = 8 NOT 7, I would say they are like 3rd grade test at most. $\endgroup$
    – Qiulang
    Nov 8, 2023 at 2:00
  • $\begingroup$ BTW, you may refer to my other question datascience.stackexchange.com/questions/118371/… to see how ridiculours ChatGPT can be even for text problems. $\endgroup$
    – Qiulang
    Nov 8, 2023 at 2:06
  • $\begingroup$ From the discussion paper, this one shows how LLMs fail at adding large numbers arxiv.org/pdf/2208.05051.pdf $\endgroup$ Nov 8, 2023 at 12:38
  • $\begingroup$ "Surprisingly, we find that these models have limitations on certain basic symbolic manipulation tasks such as copy, reverse, and addition. When the total number of symbols or repeating symbols increases, the model performance drops quickly." lol $\endgroup$
    – Qiulang
    Nov 8, 2023 at 14:10
  • $\begingroup$ Thanks for the answer and comments I have accepted it. That math ability test is really interesting. $\endgroup$
    – Qiulang
    Nov 8, 2023 at 14:11

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