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"math genius" not sure about it. I gave it a problem from IMO 2022. In my opinion not a very hard one. It failed even if you give it some hints. Let R+ denote
by MichaelRazum 4y ago
"math genius" not sure about it. I gave it a problem from IMO 2022. In my opinion not a very hard one. It failed even if you give it some hints.
Let R+ denote the set of positive real numbers. Find all functions f : R+ → R+ such that for each x ∈ R+, there is exactly one y ∈ R+ satisfying
xf(y) + yf(x) <= 2.
It just struggeld to reason. So I would be very surprised if the plugin somehow helps here.
- Donald 4y agoIt's a language completion model, so it's not surprising at all that it struggles with logical inference. That's probably one of the reasons that instruction fine-tuning has such a dramatic effect in the performance of these models: they're finally given some of the underlying causal priors of the task domain.
- knrdev 4y agoVery strange. I gave this problem to GPT-3.5 and it answered `f(x)=1/x`. https://www.youtube.com/watch?v=13YrZLBmu7A https://www.youtube.com/watch?v=13YrZLBmu7A gives the same solution. GPT-4 failed but was close. Maybe GPT-3.5 is smarter ;) Query i used was: ``` Can you think step by step about this math problem and solve it? Let R+ denote the set of positive real numbers. Find all functions f : R+ → R+ such that for each x ∈ R+, there is exactly one y ∈ R+ satisfying xf(y) + yf(x) <= 2. ``` Response: https://pastebin.com/sTXM9kLt https://pastebin.com/sTXM9kLt Edit: Maybe i should say Bing not GPT-4 because i asked it there.
- MichaelRazum 4y agoI asked gpt4 to think through it step by step and then to recheck the answer. At least it got 1/x right. So now kind of impressed.
- rcpt 4y agoPutnam asked "can a parabola of arc length 4 fit inside the unit circle?" Should be simple for a computer to just try every parabola but all the LLMs try to solve it like a human would (and get it wrong)