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How trustable the answer is depends on knowing where the answers come from, which is unknowable. If the probability of the answers being generated from the original problem are high because it occurred in many different places in the training data, then maybe it's correct. Or maybe everyone who came up with the answer is wrong in the same way and that's why there is so much correlation. Or perhaps the probability match is simply because lots of math problems tend towards similar answers.
The core issue is that the LLM is not thinking or reasoning about the problem itself, so trusting it with anything is more assuming the likelihood of it being right more than wrong is high. In some areas this is safe to do, in others it's a terrible assumption to make.
I'm a little confused after listening to a podcast with.... Damn I can't remember his name. He's English. They call him the godfather of AI. A pioneer.
Well, he believes that gpt 2-4 were major breakthroughs in artificial infection. He specifically said chat gpt is intelligent. That some type of reasoning is taking place. The end of humanity could come in a year to 50 years away. If the fella who imagined a Neural net that is mapped using the human brain. And this man says it is doing much more. Who should I listen too?. He didn't say hidden AI. HE SAID CHAT GPT. HONESTLY ON OFFENSE. I JUST DON'T UNDERSTAND THIS EPIC SCENARIO ON ONE SIDE AND TOTALLY NOTHING ON THE OTHER
One step might be to try and understand the basic principles behind what makes a LLM function. The Youtube channel 3blue1brown has at least one good video on transformers and how they work, and perhaps that will help you understand that "reasoning" is a very broad term that doesn't necessarily mean thinking. What is going on inside a LLM is fascinating and amazing in what does manage to come out that's useful, but like any tool it can't be used for everything well, if at all.
I'll ask AI what's really going on lolool.
Funny, but also not a bad idea, as you can ask it to clarify on things as you go. I just reference that YT channel because he has a great ability to visually show things to help them make sense.