Researchers found that ChatGPT’s performance varied significantly over time, showing “wild fluctuations” in its ability to solve math problems, answer questions, generate code, and do visual reasoning between March and June 2022. In particular, ChatGPT’s accuracy in solving math problems dropped drastically from over 97% in March to just 2.4% in June for one test. ChatGPT also stopped explaining its reasoning for answers and responses over time, making it less transparent. While ChatGPT became “safer” by avoiding engaging with sensitive questions, researchers note that providing less rationale limits understanding of how the AI works. The study highlights the need to continuously monitor large language models to catch performance drifts over time.
Mathematical language is a language, ChatGPT has been shown to come up with relationship between very distant elements of language that were not present in the training data… so there is nothing stopping it from, given enough mathematical training data, coming up with whatever relationships we call “logical rules”.
Mathematical language is a language, but mathematics is not just a language. It is a structure with internal rules that are not determined by pure convention (as natural languages are). We could internationally agree from tomorrow to call “blue” whatever it’s now called “red” and vice versa, but we couldn’t agree to say that “2 + 2 = 5”, because that would lead to internal inconsistencies (we could agree to use the symbol “5” for 4, but that’s a different matter).
This is also related to a staple of science: that scientific and mathematical truth is not determined by a majority vote, but by internal consistency. Indeed modern science started with this very paradigm shift. Quoting Galilei:
If we want to train an algorithm to infer rules from language, we need to give samples of language where the rules are obeyed strictly (and yet this may not be enough). Otherwise the algorithm will wrongly generalize that the rules aren’t strict (in fact it’ll just see a bunch of mutually inconsistent examples). Which is what happens with ChatGPT.
Edit: On top of this, Gödel’s theorem and other related theorems have shown that mathematical reasoning cannot be reduced to pure symbol manipulation, Hilbert’s unfulfilled dream. So one can’t infer mathematical reasoning from language patterns. Children learn reasoning not only through language training, but also through behaviour training (this was pointed out by Turing). This is why large language models have intrinsic limitations in what they can achieve and be used for.