Since LLMs can't do arithmetic, one has to think there's more going on, at least in the arithmetic part of the brain, than is going on in LLMs.
In fact it is damage to the prefrontal cortex (which has nothing to do with speech) which is mostly correlated with a detriment in intelligent behavior (suspiciously also social behavior; a food for though in what we consider “intelligence”). Victims of lobotomy had their prefrontal cortex destroyed, and their injuries resulted in them loosing their personalities and loosing basic function as human beings, even though they were still able (but perhaps not always willing) to speak and comprehend speech.
What you have that LLMs lack is a visual part of your brain - one which can instantly count quantities of objects up to about 7. That gives you tools that can be trained to do basic arithmetic operations. Although you have to be taught how to use that natural capability in your brain to solve arithmetic problems.
And of course for more complex things than simple arithmetic, you fall back on verbalized reasoning and association of facts (like multiplication tables) - which an LLM is capable of doing too.
Poor GPT though has only a one dimensional perceptual space - tokens and their embedding from start to end of its attention window - although who’s to say it doesn’t have some sense for ‘quantity’ of repeated patterns in that space too?
You could say the same for a character recognition system.
how am i supposed to have a conversation about someone who is gassing up "not perfect [arithmetic]" (something a wrist watch from the 80's can do) and won't even believe what the creators of said machine say about how it works
Prompt ChatGPT Actual Match
397,356 * 930,547 369,685,207,932 369,758,433,732 FALSE
36,330 * 26,951 979,458,630 979,129,830 FALSE
8,681 * 9,330 80,911,430 80,993,730 FALSE
278 * 903 250,734 251,034 FALSE
82 * 77 6,314 6,314 TRUE
I have a theory that it does arithmetic badly because the logic goes right-to-left, when LLMs write left-to-right. If the digits were to be reversed, it might not make as many mistakes. I ran out of attempts before I could test this properly.
Sometimes LLMs get math wrong because people got math wrong on the training data and so they match the error frequency (https://learnprompting.org/docs/basics/roles).
> Human: what is 36,330 26,951 * (input is expressed in reverse post fix notation)
> chatGPT: To evaluate this expression using reverse Polish notation, we need to use a stack to keep track of the intermediate results. Here's how we can evaluate the expression:
1. Read the first number "36,330" and push it onto the stack. 2. Read the second number "26,951" and push it onto the stack. 3. Read the operator "", pop the top two numbers (26,951 and 36,330) from the stack, multiply them, and push the result (971,914,830) onto the stack. 4. The stack now contains only one number, which is the final result.
Therefore, 36,330 26,951 = 971,914,830 in reverse Polish notation.
I dont think this is about notation.
A tangential point: Note that multiplication of decimal numbers _has_ to start with the rightmost digit to be done accurately. Consider x = 2/3 + 1/3 = 0.6(6) + 0.3(3), all digits repeating infinitely many times, so there's no rightmost digit: Notice that whichever digit you choose for x before the decimal point (either 0 or 1) could be wrong if you change any digit of 1/3. This is called the Table Maker's Dilemma.
The second paragraph is a tangent. My point was made in the first paragraph.
You said: "I dont think this is about notation" - Why did you ever think it was?
I also tried the show your work methods. I will not paste my conversations here as they are so long but even with showing it's work it doesn't give the right answer. Two funny things I noticed
1. It either uses a completely wrong method to calculate it, or it shows the right "kind" of work and then gets the wrong answer
2. If I tell it it was wrong and it will just agree with me. I multiply two huge numbers and tell it no the answer is actually 42, it will just apologize. Then when I ask the reason why it thinks it's right it will give the most bullshit things lol. Once it even said "I read the number wrong, the second number should be x I read y". The thing is if I had actually given x in the input it would have gotten the answer right.
It's all very confusing.
GPT’s attention window is not equivalent to it being able to ‘write stuff down’ - it’s its equivalent of being able to remember the foregoing few minutes of conversation.
What's also interesting, though not necessarily surprising, is how relatively close the incorrect answers are in your examples. It's not like the model will randomly spit out an answer like 42 if you ask it to multiply something like 36,330 by 26,951.
You did not. You have to explicitly select it from the dropdown which is only available on paid Plus accounts.
That has been my best analogy so far.
They'll never say I don't know and bullshit you into oblivion while never backtracking.