Submitted by **RadioFreeAmerika** t3_122ilav
in **singularity**

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**ArcticWinterZzZ**
t1_jdqsh5c wrote

None of the other posters have given the ACTUAL correct answer, which is that an LLM set up like GPT-4 can never actually be good at maths for the simple fact that GPT-4 runs in O(1) time when asked to perform mental math and the minimum theoretical time complexity for multiplication is O(n*log(n)). It is **impossible** for GPT-4 to be good at mathematics because it would breach the laws of physics.

At minimum, GPT-4 needs space to actually calculate its answer.

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**Kolinnor**
t1_jdr0g2h wrote

I could be wrong on this take, but...

I don't believe this is correct. What about chain of thought prompting ? If you ask it to do multiplication step by step, it does it. The current problem is, I would say, *it doesn't know when to take more time to think*, but there's probably no intrisic limitation due to time complexity.

Also, none of you actually compute 5x3 = 15. You just know the answer. But you're no parrot because if needed, you can manually do multiplication right ?

But that's because... someone taught you the algorithm when you were a kid. Suddenly sounds less glorious, no ?

Also, can you name one specific simple task that GPT-4 cannot do, and let's see next month...

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**jloverich**
t1_jdrgd0p wrote

Tbh, I parrot the value and then add 5 3 times to double check. One of the other things these chatbots aren't doing is double checking what they just spoke otherwise one of their statements would be immediately followed by another, "oh, that was wrong". Instead you need to prompt them that it was wrong.

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**Kolinnor**
t1_jdrjbj5 wrote

Yeah, definitely ! Althought I don't think this is an unfixable fundamental flaw, I agree this is a big advantage we still have over them

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**[deleted]**
t1_jdsjpyf wrote

You’re not asking it to do multiplication “step by step”.

You’re simplifying the question to the point where text prediction can answer it.

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**GoldenRain**
t1_jdr2unm wrote

>Also, can you name one specific simple task that GPT-4 cannot do, and let's see next month...

It cannot read even simple stuff in reverse, like "?uoy era woH"

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**Kolinnor**
t1_jdr412t wrote

I just copy-pasted this on GPT-4 and here's the answer :

​

>I am doing well, thank you! As an AI language model, I don't have feelings or emotions like humans do, but I'm here to help you with any questions or information you need. Please let me know how I can assist you.

- What was my sentence saying ?

​

>Your sentence appears to be written backwards. When reversed, it says, "How are you?" You were asking about my well-being.

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**GoldenRain**
t1_jdr57k1 wrote

Weird, didnt work when I tried it. Try with a more unique longer sentence in a new prompt and see how it goes.

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**Kolinnor**
t1_jdr6m19 wrote

- This is a special puzzle for you. Can you read it ? ! enihcam ,uoy rof drah oot si siht teb I .oot hcnerf ni ,yakO .tset a si sihT .seog ti woh ees dna tpmorp wen a ni ecnetnes regnol euqinu erom a htiw yrT .ti deirt I nehw krow tndid ,drieW

>Of course! The text appears to be reversed. Here's the corrected version:

>

>Weird, didn't work when I tried it. Try with a more unique longer sentence in a new prompt and see how it goes. This is a test. Okay, in french too. I bet this is too hard for you, machine! Can you read it?

It kinda fucked up at the end because it repeated "can you read it", but it got the reversed text correct

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**skob17**
t1_jdrenvs wrote

It's puzzling. It recognized the last sentence as being normal, and did not reverse it

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**GoldenRain**
t1_jdr6z8w wrote

Ah great, that's impressive!

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**BigMemeKing**
t1_jds2hjp wrote

Yeah, I can read it. And if I can read it why couldn't they? I'm not particularly bright. Why couldn't I believe a machine could do my job better than me?what do you want your job to be says the machine? Live long and prosper, you reply. Ok says the machine. Sweet, im the star in the amazing new movie franchise Fast and the Furbinous, my life's lookin tits right now, I'm gonna go grab some "micheladas" ifykyk. And do what Christ died for me to do. Aint that right buddy?! Now imma drive my fast ass car right down this road and bam I'm wrapped around her finger.

Just snug right on in there. We'll everyone else said I was too young! Oh? Did they now? Everyone else according to who? Like everyone else according to the animals you have dominion over?what did they think when you stomped them out? Used them by the millions, to create new protein sources. Save one cow! Eat a whole bunch of ground up bugs instead!one plus one is relatively ♾️ you see

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**BigMemeKing**
t1_jds1225 wrote

So how long ago did you try it? How long fast is it going to be able to narrow down everything? To know exactly what happend? How many times do certain people have to go to confessions and appeal their case to God, or a higher power. Because they're going to take care of it. theyre going to find the time in their schedule to fix my needs you'll see. And God said "Look out for me!" Oh cool, what does that mean? It's something personal. But it's something different to different folks. How much time do you spend on you knees praying to the lord and begging for forgiveness. How much time have others spent on their knees for you? To help you succeed, to become the person you said you would be praying for you, begging their God for you. And how much time did you spend on your knees giving thanks, for all of life's blessings. Weigh it against weather or not, if the option for eternity was on the table who's version of heaven, and whose version of hell would you enter? And what are you weighing it against?

How much do you trust the information you're given? How much do you trust to be real? What could you defend in a court of higher thinking. And what would have to be defended against you. What do you really know? Who do you own? And who owns you? In the grand scheme of things? How much debt do you really owe? And how much do you own? And what truly belongs to you?

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**BigMemeKing**
t1_jdrzb61 wrote

Yet. How long until it gets there? At the rate we're going? How long until it hits all the little nooks and crannies that the dark was hiding in? The unknown variables become known variables so we create new variables to vary.

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**Dwanyelle**
t1_jdrym2j wrote

I ran into this issue (skipping steps and messing up the answer) when I was learning algebra *all the time*

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**ArcticWinterZzZ**
t1_jdt0dyi wrote

You are correct in that chain of thought prompting does work for this. That's because it gives it more time to run an algorithm to get the answer. I'm specifically talking about "instant" multiplication. Yes, GPT-4 can multiply, so long as it runs the algorithm for it manually. We then run into a small hitch because it will eventually hit its context window, but this can be circumvented. Reflexion and similar methods will also help to circumvent this.

As for SIMPLE specific tasks, I really don't think there's any GPT-4 can't do, not with an introspection step, at least.

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**Kolinnor**
t1_jdughns wrote

But I don't understand your point ? Humans don't do instant multiplication. At best, we have some mental tricks that are certainly algorithms too. Or we choose wisely to allocate more effort doing long multiplication if needed.

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**rhettandlick**
t1_jebmjp4 wrote

"Also, none of you actually compute 5x3 = 15. You just know the answer."

Yes, you are using a mental hash table, which have an expected access time complexity of O(1). GPT can also do this, it has already memorized a huge amount of data. However, ArcticWinter's statement remains correct: for non-O(1) questions that it has not yet memorized, it is IMPOSSIBLE for the current GPT versions to calculate the answer.

Of course, it can still guess and come pretty close, but it will never be certain of the answer.

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**zero_for_effort**
t1_jdqvirs wrote

Explain it like we're five?

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**0382815**
t1_jdr6r9p wrote

The ELI5 is that it doesn’t actually calculate anything when you ask it to solve an equation. It guesses what the answer looks like—probably some combination of numbers—based on what it saw in the training dataset.

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**Ok_Faithlessness4197**
t1_jdrt7xy wrote

That's not quite correct. While all it does is guess what the next token will be, it can intelligently infer that an equation (even one outside its training set) needs to be calculated, and then calculate it. The problem is it's inability to utilize it's understanding of mathematics to answer prompts in an efficient and accurate manner. Once a calculator is implemented (Probably in GPT 4.1 given the recent paper by Microsoft demonstrating its capability to use one), this problem will hopefully be resolved.

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**0382815**
t1_jds9yxv wrote

It is quite correct, actually. When you prompt it to multiply, it does not run a multiplication algorithm.

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**Ok_Faithlessness4197**
t1_jdsl2be wrote

Input: Solve 343 x 875 with long multiplication.

Output (ChatGPT): Sure! Here's how to solve 343 x 875 with long multiplication: 3 x 5 = 15 Write down 5, carry-over 1 3 x 7 = 21, plus the carried-over 1 = 22 Write down 2, carry-over 2 3 x 8 = 24, plus the carried-over 2 = 26 Write down 6, carry-over 2 3 x 5 = 15, plus the carried-over 2 = 17 Write down 7, carry-over 1 Add the carried-over 1 to the result of 3 x 4 = 12, which gives 13 Write down 3, carry-over 1 4 x 5 = 20 Write down 0, carry-over 2 4 x 7 = 28, plus the carried-over 2 = 30 Write down 0, carry-over 3 4 x 8 = 32, plus the carried-over 3 = 35 Write down 5, carry-over 3 4 x 5 = 20, plus the carried-over 3 = 23 Write down 3, carry-over 2 Add the carried-over 2 to the result of 3 x 8 = 24, which gives 26 Write down 6, carry-over 2 Add the carried-over 2 to the result of 3 x 3 = 9, which gives 11 Write down 1, carry-over 1 Add the carried-over 1 to the result of 3 x 8 = 24, which gives 25 Write down 5 So, the final result is 300125.

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**0382815**
t1_jdsn7o1 wrote

Once again, if you prompt it to multiply it does not run a multiplication algorithm.

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**[deleted]**
t1_jdss5i8 wrote

[deleted]

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**robobub**
t1_jdst84e wrote

Why? Each of those tokens is O(1) and it is predicting each one incrementally, taking into account the ones it has just generated. So the full answer has taken O(m) where m is the number of tokens.

If it is possible for GPT to do 1+1, it can do a large number of them incrementally. It's not smart enough to do it all the time (you'll have more success if you encourage GPT to have a train of thought reasoning) but it's possible.

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**Ok_Faithlessness4197**
t1_jdsqqgg wrote

Alright, go ahead and ignore the multiplication algorithm it **just demonstrated**.

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**0382815**
t1_jdsrl52 wrote

What you did was prompt it to multiply. For the third time this thread, I will tell you that what it is doing is not running a multiplication algorithm. It is guessing the next token based on the preceding tokens. The model is large enough to predict correctly in this case. It is still not running a multiplication algorithm the same way the calculator app on Windows does.

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**Ok_Faithlessness4197**
t1_jdsskog wrote

I absolutely agree, it's multiplication algorithm is very slow, very inefficient, and very different from the way a calculator would handle it. I think it does differ too from how you're considering it, though. It's more than just a really good text predictor. It can use logic and solve novel problems in many unprecedented ways. Here, I would argue, it has a greater-than-superficial understanding of the math algorithm it used to multiply numbers. Can I ask how you'd define an algorithm, and what you'd consider "running a multiplication algorithm"?

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**Ok_Tip5082**
t1_jdtzd17 wrote

Chat GPT is not running the multiplication algorithm. You're being the human in the loop here by having it iterate through every step in the algorithm. You're manually executing a bunch of constant time operations and feeding the input back into itself.

You're basically writing and running code. If this qualified as being able to derive a multiplication algorithm then all CPUs are already sentient.

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**Ok_Faithlessness4197**
t1_jdu12qm wrote

I make no claims about sentience. I will say however that this is far ahead of what was previously achievable by AI standards. In its current form, it has to be allowed enough time to satisfy the mathematical time requirement. In the future, once it's linked with WolframAlpha (A math AI) it will not make the simple mistakes it makes now.

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**Ok_Tip5082**
t1_jdu2er4 wrote

Yeah, pragmatically I don't see any issues with arithmetic or using any math already proved. Imo it's still to be seen if LLMs can do novel thought, but even if not that's still ... what's a word signifying a greater change than revolutionary? Game changing?

I did see some AI coming up with independent models of physics that have no analog yet were able to properly model real physical systems and make valid predictions with a formula whose variables could not all be determined by the researchers, but idk if that was an LLM

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**MassiveIndependence8**
t1_jdr6u2t wrote

It takes GPT the same amount time to do anything, and since it’s impossible to multiple say “18837678995747 x 29747778847678877” in the same amount of time as “2 x 2” due to the fact that it’s more complicated, we can confidently say that GPT will never be able to do math since it means that every hard problems out there is as easy as the easy ones.

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**ArcticWinterZzZ**
t1_jdt0plo wrote

GPT-4 always takes the same amount of time to output a token. However, multiplication has been proven to take more time than GPT-4 has available. Therefore, an LLM like GPT-4 cannot possibly "grow" the requisite structures required to actually calculate multiplication "instantly". There are probably quite a few more problems like this, which is why chain-of-thought prompting can be so powerful.

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**zero_for_effort**
t1_jdt4nz1 wrote

This is the explanation I found easiest to understand, cheers.

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**Cryptizard**
t1_jdqtgon wrote

Thank you! I have commented this exact thing about a billion times on all these posts and nobody seems to get it.

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**CommunismDoesntWork**
t1_jdqzp8i wrote

How do you know GPT runs in O(1)? Different prompts seen to take more or less time to compute.

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**liqui_date_me**
t1_jdr7fob wrote

All GPT does is next token prediction, where tokens = words. The lag you see is probably network/bandwidth/queuing issues on the server side rather than the model itself.

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**skob17**
t1_jdrex9t wrote

One prompt takes only one path through the network to generate the answer. Still a few 100 layers deep, but only one pass. It cannot iterate over a complicated math problem to solve it step by step.

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**Ok_Faithlessness4197**
t1_jdrrdia wrote

Yes it can, just need to prompt for a chain of thought. As another user mentioned, it can work through complicated math problems easily. The issue lies in its inability to determine when such an increase in resources is necessary, without human input.

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**ArcticWinterZzZ**
t1_jdt0urg wrote

I don't think that's impossible to add. You are right: chain of thought prompting circumvents this issue. I am specifically referring to "mental math" multiplication, which GPT-4 will often attempt.

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**liqui_date_me**
t1_jdt531o wrote

You would think that GPT would have discovered a general purpose way to multiply numbers, but it really hasn’t, and it isn’t accurate even with chain-of-thought prompting.

I just asked GPT4 to solve this: 87176363 times 198364

The right answer should be 17292652070132 according to wolfram alpha.

According to GPT4 the answer is 17,309,868,626,012.

This is the prompt I used:

**What is 87176363 times 198364? Think of the problem step by step and give me an exact answer.**

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**ArcticWinterZzZ**
t1_jdtlkru wrote

Even if it were to perform the addition manually, *addition* takes place in the opposite order that GPT-4 thinks. It's unlikely to be very good at it.

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**elehman839**
t1_jdt94ba wrote

Here's a neat illustration of this. Ask ChatGPT to multiply any two four-digit numbers. For example:

*Input: 3742 * 7573*

*Output: The product of 3742 and 7573 is 28350686*

The correct answer is **283**3816**6**. The **bolded** digits are right, and the plain digits are wrong. So it gets the first bit right, the last bit right, and the middle bit wrong. This seems to be very consistent.

Why is this? In general, computing the first digits and the last digits requires less computation than the middle digits. For example:

- Determining that that last digit should be a 6 is easy: notice that the last digits of the multiplied numbers are 2 and 3 and 2 * 3 = 6.
- Similarly, it is easy to see that 3000-something times 7000-something should start with a 2, because 3 * 7 = 20-something.
- But figuring out that the middle digits of the answer are 38 is far harder, because every digit of the input has to be combined with every other digit.

So I think what we're seeing here is ChatGPT hitting a "compute per emitted token" limit. It has enough compute to get the leading digits and the trailing digits, but not the middle digits. Again, this seems to be quite reliable.

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**RadioFreeAmerika**
OP
t1_jdr3b6j wrote

Thank you very much for your clarification! Do you know if it is possible to make a LLM with more space and greater complexity than O(1) or how it possibly could be added to GPT-4 with or without plug-ins?

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**ArcticWinterZzZ**
t1_jdt10ie wrote

Yes, it can probably be done. How? I don't know. Maybe some kind of neural loopback structure that runs layers until it's "done". No idea how this would really work.

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**liqui_date_me**
t1_jdr7pnr wrote

Tough to say, probably in 10-20 years at the very least. Modern LLMs are transformers which are architected to predict the next token in a sequence in O(1) time, regardless of the input. Unless we get a radically different neural network architecture it’s not possible we’ll ever get GPT to perform math calculations exactly

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**sdmat**
t1_jdut7jg wrote

Or just go with a workable hack for calculation like the Wolfram plugin.

Does it matter if the model isn't doing it natively if it understands how and when to use the tool? How often do *we* multiply large numbers unaided?

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**submarine-observer**
t1_jdro777 wrote

Great answer! Very insightful. Thank you.

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**robobub**
t1_jdsrlbi wrote

While GPT-4 is autoregressive, it takes into account the tokens it has chosen to generate incrementally. So it is only limited to O(1) if it attempts to answer with the correct answer immediately. It can in theory take O(m) steps, where m is the number of intermediate tokens it predicts.

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**masonw32**
t1_jdsyi4v wrote

This is only an issue for insanely large numbers though. GPT-4 already performs a ton of multiplications and additions in every layer of every forward pass. You can overfit a much smaller network for multiplication trained on full numbers as tokens, and a GPT-4 like architecture can learn to multiply full numbers for all practical purposes.

It's true that GPT-4 only does a constant number of operations per input though, and asymptotically, the number of operations required to generate the output will scale by O(n log (n)), where n is proportional to the input length. But this is not why it's failing.

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**ArcticWinterZzZ**
t1_jdt1h3m wrote

Yes, but we are interested in its general purpose multiplication abilities. If it remembers the results, that's nice, but we can't expect it to do that for every single pair of numbers. And then, what about multiplication with 3 factors? We should start thinking of ways around this limitation.

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**liqui_date_me**
t1_jdt48m5 wrote

You would think that GPT would have discovered a general purpose way to multiply numbers, but it really hasn’t, and it isn’t accurate even with chain-of-thought prompting.

I just asked GPT4 to solve this: 87176363 times 198364

The right answer should be 17292652070132 according to wolfram alpha.

According to GPT4 the answer is 17,309,868,626,012.

This is the prompt I used:

**What is 87176363 times 198364? Think of the problem step by step and give me an exact answer.**

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