ChatGPT-4o vs. Math • Hacker News Board

Re: ChatGPT-4o vs. Math

#161

Post by ifwinterco » Fri, May 17, 2024, 6:41 AM UTC

phatfish wrote: post #117

giaour wrote: post #67

Earlier quoted context omitted.

This depends on the grader and the context. Outside of an academic setting, sometimes being close to the right answer is better than nothing, and sometimes it is much worse. You can expect a human to understand which contexts require absolute precision and which do not, but that seems like a stretch for an LLM.

LLMs being confidently incorrect until they are challenged is a bad trait. At least they have a system prompt to tell them to be polite about it. Most people learn to avoid that person that is wrong/has bad judgment and is arrogant about it.

I think current LLMs suffer from something similar to the Dunning-Kruger effect when it comes to reasoning - in order to judge correctly that you don't understand something, you first need to understand it at least a bit.

Not only do LLMs not know some things, they don't know that they don't know because of a lack of true reasoning ability, so they inevitably end up like Peter Zeihan, confidently spouting nonsense

Re: ChatGPT-4o vs. Math

#162

Post by crvdgc » Fri, May 17, 2024, 8:53 AM UTC

If you read the details in some of the "correct" answers[1], they are not actually correct. The model used an assumption that the width is equal to the thickness, which is not given in the problem. The width is cancelled out in the end, so the resulting number is correct, but a math teacher would label such answers wrong.

[1] Text prompt only, run 2; prompt and image, run 3.

Re: ChatGPT-4o vs. Math

#163

Post by BOOSTERHIDROGEN » Fri, May 17, 2024, 9:11 AM UTC

wahnfrieden wrote: post #141

yatz wrote: post #96

Earlier quoted context omitted.

Once you correct the LLM, it will continue to provide the corrected answer until some time later, when it will again make the same mistake. At least, this has been my experience. If you are using LLM to pull answers programmatically and rely on their accuracy, here is what worked for the structured or numeric answers, such as numbers, JSON, etc. 1) Send the same prompt twice, including "Can you double check?" in the…

via api (harder to do via chat as cleanly) you can also try showing it do a false attempt (but a short one so it's effectively part of the prompt) and then you say try again.

Are there any examples?

Re: ChatGPT-4o vs. Math

#164

Post by grob-gambit » Fri, May 17, 2024, 12:07 PM UTC

jiiam wrote: post #100

slushy-chivalry wrote: post #70

Earlier quoted context omitted.

if you sampled N random people on the street and asked them to solve this problem, what would the outcome be? would it be better than asking chatgpt N times? I wonder

I am deeply interested in this point of view of yours so I will be hijacking your reply to ask another question: is "better than asking a few random people on the street" the bar we should be setting? As far as mathematical thinking goes this doesn't seem an interesting metric at all. Do you believe that optimizing for this metric will indeed lead to reliable mathematical thinking? I am of the idea that LLMs are not…

I don't have a counter argument. Not to be ironic but ChatGPT4o gives a better response to the question at hand than anything I have read in this thread:

https://chatgpt.com/share/c10c540f-b9c2-4714-ae6b-77460b900b...

Re: ChatGPT-4o vs. Math

#165

Post by sharemywin » Fri, May 17, 2024, 1:49 PM UTC

groby_b wrote: post #134

yatz wrote: post #96

Earlier quoted context omitted.

Once you correct the LLM, it will continue to provide the corrected answer until some time later, when it will again make the same mistake. At least, this has been my experience. If you are using LLM to pull answers programmatically and rely on their accuracy, here is what worked for the structured or numeric answers, such as numbers, JSON, etc. 1) Send the same prompt twice, including "Can you double check?" in the…

> Once you correct the LLM, it will continue to provide the corrected answer until some time later, That is only true if you stay within the same chat. It is not true across chats. Context caching is something that a lot of folks would really really like to see. And jumping to a new chat is one of the core points of the OP: "I restarted with a slightly modified prompt:" The iterations before where mostly to figure ou…

so what would you use instead?

Re: ChatGPT-4o vs. Math

#166

Post by ericmcer » Fri, May 17, 2024, 1:51 PM UTC

CooCooCaCha wrote: post #33

jcims wrote: post #21

I posted the same 'Zero-Shot Chain-of-Thought and Image' to ChatGPT-4o and it made the same error. I then followed up with 'Your math is good but you derived incorrect data from the image. Can you take another look and see if you can tell where the error is?'. It figured it out and corrected it: Let's re-examine the image and the data provided: * The inner radius r1 is given as 5cm * The outer radius r2 is given as 1…

This speaks to a deeper issue that LLMs don’t just have statistically-based knowledge, they also have statistically-based reasoning. This means their reasoning process isn’t necessarily based on logic, but what is statistically most probable. As you’ve experienced, their reasoning breaks down in less-common scenarios even if it should be easy to use logic to get the answer.

That plays out for all the examples, except for the one where its answer was way off it and it corrected itself and attempted again.

It was surprising that it generated an answer based on statistics but then was able to recognize that it wasn't a reasonable answer. I wonder how they are achieving that.

Re: ChatGPT-4o vs. Math

#167

Post by wahnfrieden » Fri, May 17, 2024, 2:11 PM UTC

BOOSTERHIDROGEN wrote: post #163

wahnfrieden wrote: post #141

Earlier quoted context omitted.

via api (harder to do via chat as cleanly) you can also try showing it do a false attempt (but a short one so it's effectively part of the prompt) and then you say try again.

Are there any examples?

I don’t have one but you can experiment with it

People just forget that prompting an AI can mean either a system prompt or a prompt AND a chat history, and the chat history can be inorganic

Re: ChatGPT-4o vs. Math

#168

Post by Tainnor » Fri, May 17, 2024, 3:14 PM UTC

12907835202 wrote: post #35

CooCooCaCha wrote: post #33

Earlier quoted context omitted.

This speaks to a deeper issue that LLMs don’t just have statistically-based knowledge, they also have statistically-based reasoning. This means their reasoning process isn’t necessarily based on logic, but what is statistically most probable. As you’ve experienced, their reasoning breaks down in less-common scenarios even if it should be easy to use logic to get the answer.

Does anyone know how far off we are having logical AI? Math seems like low hanging fruit in that regard. But logic as it's used in philosophy feels like it might be a whole different and more difficult beast to tackle. I wonder if LLM's will just get better to the point of being indistinguishable from logic rather than actually achieving logical reasoning. Then again, I keep finding myself wondering if humans actuall…

> Math seems like low hanging fruit in that regard.

First-order logic is undecidable, so no dice.

Re: ChatGPT-4o vs. Math

#169

Post by groby_b » Fri, May 17, 2024, 4:18 PM UTC

sharemywin wrote: post #165

groby_b wrote: post #134

Earlier quoted context omitted.

> Once you correct the LLM, it will continue to provide the corrected answer until some time later, That is only true if you stay within the same chat. It is not true across chats. Context caching is something that a lot of folks would really really like to see. And jumping to a new chat is one of the core points of the OP: "I restarted with a slightly modified prompt:" The iterations before where mostly to figure ou…

so what would you use instead?

Depends - what's your allowable error rate? What are you solving for?

Re: ChatGPT-4o vs. Math

#170

Post by glial » Fri, May 17, 2024, 4:35 PM UTC

monadINtop wrote: post #122

ezrast wrote: post #86

Earlier quoted context omitted.

Think of all the algebra problems you got in school where the solution started with "get all the x's on the same side of the equation." You then applied a bunch of rules like "you can do anything to one side of the equals sign if you also do it to the other side" to reiterate the same abstract concept over and over, gradually altering the symbology until you wound up at something that looked like the quadratic formul…

People don't uncover new mathematics with formal rules and symbols pushing, at least not for the most part. They do so first with intuition and vague belief. Formalisation and rigour is the final stage of constructing a proof or argument.

Perhaps, but then what's the point of symbolic systems at all?