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.
My point was that a coffee machine is designed to make coffee, not to keep track of time. Maybe it always takes roughly the same amount of time to make a coffee, and so someone uses it as a proxy stopwatch. But it can very well suddenly take more or less time, without anything being wrong about it – maybe different coffee brands, cleaned pipes, or whatnot.
ChatGPT is an algorithm designed to parrot language, not to perform mathematical reasoning based on logic rules.
ChatGPT is an algorithm designed to parrot language, not to perform mathematical reasoning based on logic rules.
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:
But in the natural sciences, whose conclusions are true and necessary and have nothing to do with human will, one must take care not to place oneself in the defense of error; for here a thousand Demostheneses and a thousand Aristotles would be left in the lurch by every mediocre wit who happened to hit upon the truth for himself.
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.
You are not wrong, but I think public perception is different. It doesn’t help, that OpenAI is pushing their models as problem solvers:
GPT-4 can solve difficult problems with greater accuracy, thanks to its broader general knowledge and problem solving abilities.
(https://openai.com/gpt-4)
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My point was that a coffee machine is designed to make coffee, not to keep track of time. Maybe it always takes roughly the same amount of time to make a coffee, and so someone uses it as a proxy stopwatch. But it can very well suddenly take more or less time, without anything being wrong about it – maybe different coffee brands, cleaned pipes, or whatnot.
ChatGPT is an algorithm designed to parrot language, not to perform mathematical reasoning based on logic rules.
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.
You are not wrong, but I think public perception is different. It doesn’t help, that OpenAI is pushing their models as problem solvers:
I didn’t know they made such claims. They’re borderline dangerous claims…