Back in October 2024, I tried to test various LLM Chatbots with the question:
"Is there a way to convert a correlation to a probability while preserving the relationship 0 = 1/n?"
Years ago, I came up with an unpublished formula that does just that:
p(r) = (n^r * (r + 1)) / (2^r * n)
So I was curious if they could figure it out. Alas, back in October 2024, they all made up formulas that didn't work.
Yesterday, I tried the same question on ChatGPT and, while it didn't get it quite right, it came, very, very close. So, I modified the question to be more specific:
"Is there a way to convert a correlation to a probability while preserving the relationships 1 = 1, 0 = 1/n, and -1 = 0?"
This time, it came up with a formula that was different and simpler than my own, and... it actually works!
I tried this same prompt with a bunch of different LLM Chatbots and got the following:
Correct on the first prompt:
GPT4o, Claude 3.7
Correct after explaining that I wanted a non-linear, monotonic function:
Gemini 2.5 Pro, Grok 3
Failed:
DeepSeek-V3, Mistral Le Chat, QwenMax2.5, Llama 4
Took too long thinking and I stopped it:
DeepSeek-R1, QwQ
All the correct models got some variation of:
p(r) = ((r + 1) / 2)^log2(n)
This is notably simpler and arguably more elegant than my earlier formula. It also, unlike my old formula, has an easy to derive inverse function.
So yeah. AI is now better than me at coming up with original math.