Earlier quoted context omitted.
I believe it's a reference to a joke meme that goes something like "Write Windows 12 from scratch. Make no mistakes." At least that's the first context I heard it in.
Precisely
A digestion of the Jacobian conjecture counterexample
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Re: A digestion of the Jacobian conjecture counterexample
#32Earlier quoted context omitted.
Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?
It's a meme. Telling it to "make no mistakes" doesn't do anything because LLMs don't have an inherent concept of a mistake and they are already RLHFed to code correctly. However , if you tell it to not do particular behaviors explicitly—some of which would be considered mistakes—it will not do said behaviors and with enough checks and balances, you'll get output without "mistakes". One example of this from the OpenAI…
Re: A digestion of the Jacobian conjecture counterexample
#33Okay. So what does this overturn, intuitively? Can we no longer assume that functions are differentiable at certain points, or something?
https://www.math.columbia.edu/~woit/wordpress/?p=105
it is about a purported (though incorrect) positive proof of the Jacobian conjecture in 2 dimemnsions. It is true in 1 dimension. The Fable proof is that it is false in >= 3 dimensions. 2 dimensions is still open.
Anyway, in that post it says
> It now seems that a proof has been found by Carolyn Dean of the University of Michigan, for the case of polynomials in two complex variables *(for more variables, many people believe it is not even true)*
so the resolution of this is a "surprise" in that it is a very long open with many failed proof attempts. But the direction it resolved was not surprising.
Re: A digestion of the Jacobian conjecture counterexample
#34Can we audit the CoT and work the AI did to generate such a remarkable cancellation?
I think a reasonable assumption is that there is an interaction between an LLM, a https://en.wikipedia.org/wiki/Computer_algebra_system tool, a human prompting with deep math expertise, and lots of compute that explains hitting upon the remarkable cancellation.
Re: A digestion of the Jacobian conjecture counterexample
#35Re: A digestion of the Jacobian conjecture counterexample
#36Earlier quoted context omitted.
He’s famous, but I don’t believe he is a celebrity, as he is not famous for his persona.
I just mean, anything Tao writes that is related to AI will get on the front page, because Tao represents the authoritative voice of reason using AI tools. And this website is primarily for AI news.
Re: A digestion of the Jacobian conjecture counterexample
#37Can we audit the CoT and work the AI did to generate such a remarkable cancellation?
I doubt Anthropic will share the details (or at least the full true details). The mystery of the magic makes for much better marketing. I think a reasonable assumption is that there is an interaction between an LLM, a https://en.wikipedia.org/wiki/Computer_algebra_system tool, a human prompting with deep math expertise, and lots of compute that explains hitting upon the remarkable cancellation.
The original tweet implied that the whole thing was done while the author was watching the World Cup final.
I know it’s tempting to hope that a human did the “real” work here, but if some special insight was put into prompting, the author kept it to himself, and there is no reason why they would hide this since it would elevate their own status.
Re: A digestion of the Jacobian conjecture counterexample
#38reading through this I eventually realized a situation similar to my experience of it is what my dog sees if I attempt to explain Python programming to him.
And chances are that humanity at large will be soon trying to follow ai inventions and discoveries not unlike your dog follows your Python code.
Re: A digestion of the Jacobian conjecture counterexample
#39Can we audit the CoT and work the AI did to generate such a remarkable cancellation?
I doubt Anthropic will share the details (or at least the full true details). The mystery of the magic makes for much better marketing. I think a reasonable assumption is that there is an interaction between an LLM, a https://en.wikipedia.org/wiki/Computer_algebra_system tool, a human prompting with deep math expertise, and lots of compute that explains hitting upon the remarkable cancellation.