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Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

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Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#671

Post by Normal_gaussian »

xyzsparetimexyz wrote: post #633
Normal_gaussian wrote: post #366

Earlier quoted context omitted.

Commands like /goal and similar are the more complex version of this; you write a prompt like it was a singular iteration, it runs one iteration, then runs an "evaluator" to determine if the goal has been reached, then runs the prompt again with a little extra to make it go again - and so on. The evaluator is just an LLM with most of the result or context looking at the original goal and the state and answering the q…

Sounds overengineered to me

I was surprised at how little improvement they could eek out of tuning it; but it is a non-trivial improvement which is much less likely to wastefully spin if your validation is more expensive than you realise.

Makes sense that its in the major harnesses and not the self-built ones.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#672

Post by vatsachak »

eru wrote: post #448
vatsachak wrote: post #399

Earlier quoted context omitted.

How could they? That's why the free market works, millions of agents in parallel beats any planned economy (by humans)

The free market is mostly the glue that binds lots of tiny and not so tiny planned economies together. (I mean companies and even family budgets.)

But each company itself is composed of multiple agents. It's just that companies are a scale of consolidation.

The exact same thing happens in the cortex, 10s of thousands of cortical columns coalesce into a single action.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#673

Post by jameshart »

com2kid wrote: post #650
jameshart wrote: post #412

Earlier quoted context omitted.

Wow and TCP sends a stream of those microscopic memory cells?

Over a wire it sends pulses of electricity which you can see with an oscilloscope. Heck there is a standard for tcp/ip over short wave if you want to hear the bytes being transmitted. More widespread, those of us familiar with dial up modems are also aware that network traffic can be carried as actual sound. Or fiber optics where network traffic is flashes of light. Or IR transmissions, use your phone camera and you…

All of these are, actually, a long way removed from the ‘stream of octets’ which TCP delivers between applications.

All the Wikipedia actually means by ‘stream of octets’ is ‘sequence of numbers between 0 and 255’. TCP is a protocol concerned with sending a message encoded as a sequence of such numbers from one computer to another, over a packet-based network (i.e. one where it can only send limited bursts of information at a time); and it helps make sure that the original number sequence is able to be reassembled, in the right order, and makes sure that all the pieces have arrived.

The fact that people have tried to explain ‘octet’ concretely by pointing to RAM chips or flashes of light in a fiber really points to the fact that a lot of computer people just mentally gloss over a lot of the things that are virtualized at lower levels in the stack.

Yes, those are physical manifestations of ‘bits’. But not necessarily the ones TCP is concerned with.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#674

Post by blodir »

WarmWash wrote: post #224
minraws wrote: post #151

Earlier quoted context omitted.

This is also true for almost every other field, even within computer science. The only difference is that a lot of people operate at a very surface level without realizing just how much background knowledge they have accumulated. Think about the number of keywords your average SWE is expected to know. It is rather insane. Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, dea…

> https://en.wikipedia.org/wiki/Transmission_Control_Protocol compare to > https://en.wikipedia.org/wiki/Rees_algebra Most people, especially non-tech technical people, could crash through the TCP article and come out the other side with at least a high level understanding of it. Most people, even technical ones, could not even get through the first line of the rees article, heck the first statement of the article. A…

I agree with you, math is the most abstract study and therefore the most impenetrable. Anyway, for the sake of argument here's a counterexample: https://en.wikipedia.org/wiki/Courcelle%27s_theorem

Something like TCP is an engineering concept rather than a CS concept. It's not entirely surprising that it's easier to grok. There's also certainly no shortage of hard to understand stuff in eg. Physics

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#675

Post by Shocka1 »

daynthelife wrote: post #508
WarmWash wrote: post #224

Earlier quoted context omitted.

> https://en.wikipedia.org/wiki/Transmission_Control_Protocol compare to > https://en.wikipedia.org/wiki/Rees_algebra Most people, especially non-tech technical people, could crash through the TCP article and come out the other side with at least a high level understanding of it. Most people, even technical ones, could not even get through the first line of the rees article, heck the first statement of the article. A…

As mathematician, I actually agree. We could do a lot more to communicate ideas in a way non-experts can understand. For instance, most people are familiar with polynomials. Take a polynomial in x (with integer coefficients) and substitute x for 5t everywhere. So for instance, 2x^3 - 8x + 3 becomes 250t^3 - 40t + 3. The Rees algebra Z[5t] (here Z is the integers) is then just the set of all polynomials you can get th…

A mathematics book that was once on the front page here said the same. Mathematica by David Bessis.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#676

Post by raz32dust »

eitally wrote: post #642
raz32dust wrote: post #424

Earlier quoted context omitted.

The top comment has a counter example though https://x.com/DmitryRybin1/status/2079904005652893709 I think it's not even about the ability to steer the AI. Just the ability to ask the right questions

I am not impressed with that steering of the AI. In the case of Terry Tao, he clearly held a solid understanding of the problem domain and could also understand the outputs of the LLM at an expert level. He asked astute, topical questions that specifically probed areas of the problem that were either unclear or insufficiently specified, and ultimately ended up at a place where (presumably) he both understood the Jaco…

I know but the point is that it worked too. You could argue one problem is harder than the other, I am not and expert so I wouldn't know. But at least it's clear the second result is also impressive, and didn't require much expertise. So it's wrong to say that you need expertise to get hard and impressive things done with AI.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#677

Post by LoganDark »

djmips wrote: post #654
LoganDark wrote: post #414

Earlier quoted context omitted.

GPT-3.5 was so nice because the safeguards were so easy to bypass and it wasn't lobotomized by RLHF. Newer models really don't hit the same spot and I'm not sure what I liked so much about that initial release. I look back at conversation logs I saved and I just can't replicate them nowadays.

have you experimente with https://huggingface.co/HauhauCS/Qwen3.5-9B-Uncensored-Hauhau... to test that conjecture? It's very easy to try.

It looks like the practical limit for that on my hardware is ~130 t/s, which is just okay. Makes reasoning mode quite painful though.

(llama.cpp can't seem to exceed 30 t/s, I had Fable make me custom inference. that's why it took me a day to get back to you)

GPT-3.5 would repeat my prompt back in its own words for me to confirm. This model immediately runs with it and generates a lot of output. I would definitely need to use a harness that allows editing / cutting off generations.

Something I've noticed about models that have been specifically uncensored or trained to generate content is that they aren't very engaging to chat with. Maybe this is just because they weren't trained to chat at all (base models) but, it's hard to find a chat model that's been trained properly.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#680

Post by ProllyInfamous »

mettamage wrote: post #487
ProllyInfamous wrote: post #463

Earlier quoted context omitted.

Von Neumann is an interesting historical character that nobody has ever heard of , e.g: for such an accomplished inventor, that so few minutes of video footage exist of him. >I sometimes wondered if he used the same principle when he talked to the rest of us. I can come pretty close to a humbler example of this, as the more-extroverted "bad twin," of an identical set: my own genetic equal is bored to tears interactin…

Fascinating. I mean that.

Ours has been exceptionally unique sets of experiences.

One of my lifelong goals is to publish something witty about my perceptions on the nature vs nurture debate, given that I have both a genetic clone (i.e. same DNA)... but we're also the result of a late-split zygote, which resulted in us developing as mirror images (using the same genetic code).

https://en.wikipedia.org/wiki/Twin#Mirror_image_twins>

So we're actually chiral, in almost all aspects (handedness, lens prescription, some anatomical pathways, dominant "brain"ness).

https://en.wikipedia.org/wiki/Chirality>

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Motivation for my writing this is lacking, most likely due to decades of my very different life choices and experiences (see my previous comment). Were Twin's volition driving this article's composition (and eventual publication), it would have been done over a decade ago =D

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Love you, Brobro.

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