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OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

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Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#781

Post by _emna »

AgentMatt wrote: post #758
_emna wrote: post #697

Earlier quoted context omitted.

Sorry, can you explain this? To me, it makes sense to define abs(x) = sqrt(x^2) i.e. ignoring the negative solution enforces the positive result. Using that definition, abs(i+1) = sqrt((i+1)^2) = sqrt(i^2 + 2i + 1) = sqrt(-1 + 2i + 1) = sqrt(2i) != sqrt(2). The second example seems off in the same way (i.e. the answer should be sqrt(8i) instead of sqrt(8)). Am I missing something? Also, abs(i+2) = sqrt((i+2)^2) = sqr…

> To me, it makes sense to define abs(x) = sqrt(x^2) i.e. ignoring the negative solution enforces the positive result. Why does this make sense to you? You have some notion of what an absolute value should be, on an intuitive or conceptual level, and the mathematical definition you give is consistent with that (in the one dimensional case). Now taking this valid definition for the 1-d case and generalizing that to hi…

> Why does this make sense to you? You have some notion of what an absolute value should be, on an intuitive or conceptual level, and the mathematical definition you give is consistent with that (in the one dimensional case).

In my mind abs(x) = x*sign(x) which is why the above formulation seems correct. This formulation is useful, for example, in formulating reflections.

> Instead, you can go back to the conceptual idea of the absolute value and generate a definition for higher dimensional cases from there.

This is an interesting idea...how would you define sign(x) in a higher dimension? Wouldnt sign in a higher dimension be a component-wise function? E.g. the reflection would happen on one axis but not the other.

> Interpreting absolute value as the distance from the origin

This seems to make sense in that it is a different interpretation of abs which seems simpler than reflection in higher dimensions, but seems like a different definition.

I know that there are applications of complex numbers in real systems. In such systems, the complex definition seems to not be as valuable. E.g. if I'm solving a laplace transform, the real number definition seems more applicable than the complex number definition, right?

I've asked wolfram alpha to solve the equation and it lists both answers: one using the formulation of sqrt(x^2) and the other using sqrt(re(x)^2 + im(x)^2) so it seems like there is merit to both...

I suppose in the laplace example, we are actually operating in one dimension and the imaginary component is approximating something non-real, but doesnt actually exist. I.e. any real/observable effect only happens when the imaginary component disappears meaning that this is still technically one dimension. So, since we're still in one dimension, the one dimensional formula still applies. Is that correct?

Your explanation has been the most helpful though, thanks.

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#782

Post by seanhunter »

ben_w wrote: post #770
qsort wrote: post #761

Earlier quoted context omitted.

As someone with a CS background myself, I don't think this is what GP was talking about. Let's forget for a moment that stuff has to run on an actual machine. If you had to represent a quadratic equation, would you rather write: (a) x^2 + 5x + 4 = 0 (b) the square of the variable plus five times the variable plus four equals zero When you are trying to solve problems with a level of sophistication beyond the toy stuf…

I assumed seanhunter was suggesting getting the LLM to convert x^2 + 5x + 4 = 0 to a short bit of source code to solve for x. IIRC Wolfram Alpha has (or had, hard to keep up) a way to connect with ChatGPT.

It does. This is the plugins methodology described in the toolformers paper which I've linked elsewhere[1]. The model learns that for certain types of problems certain specific "tools" are the best way to solve the problem. The problem is of course it's simple to argue that the LLM learns to use the tool(s) and can't reason itself about the underlying problem. The question boils down to whether you're more interested in machines which can think (whatever that means) or having a super-powered co-pilot which can help with a wide variety of tasks. I'm quite biased towards the second so I have the wolfram alpha plugin enabled in my chat gpt. I can't say it solves all the math-related hallucinations I see but I might not be using it right.

[1] But here it is again https://arxiv.org/abs/2302.04761

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#783

Post by CGamesPlay »

While we're all wildly speculating about what Q* is and if GPT-5 will be able to do grade-school maths, I stumbled upon this interesting paper that discusses mixing classic RL algorithms (MCTS, like from AlphaGo), with LLMs. Q* is typically used to refer to the search for the optimal policy in these algorithms.

Paper: "Everything of Thoughts: Defying the Law of Penrose Triangle for Thought Generation " - https://arxiv.org/abs/2311.04254

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#784

Post by seanhunter »

chipsambos wrote: post #765
seanhunter wrote: post #716

Earlier quoted context omitted.

Actual reasoning shows the understanding and use of a model of the key features of the underlying problem/domain. As a simple example that you can replicate using chatgpt, ask it to solve some simple maths problem. Very frequently you will get a solution that looks like reasoning but is not, and reveals that it does not have an actual model of the underlying maths but is in fact doing text prediction based on a histo…

I generally agree with what you're saying and the first half of your answer makes perfect sense but I think the second is unfair (i.e. "[is it] easier to balance a barrel on a plank or a plank on a barrel"). It's a trick question and "it" tried to answer in good faith. If you were to ask the same question of a real person and they replied with the exact same answer you could not conclude that person was not capable o…

I didn't make up this methodology and it's genuinely not a trick question (or not intended as such), it's a simple example of an actual class of questions that researchers ask when trying to determine whether a model of the world exists. The paper I linked uses a ball and a plank iirc. Often they use a much wider range of objects eg: something like "Suggest a stable way of stacking a laptop, a book, 4 wine classes, a wine bottle and an orange" is one that I've seen in a paper for example.

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#785

Post by mkl »

_emna wrote: post #757
lovasoa wrote: post #740

Earlier quoted context omitted.

No, there is just one definition, and it's his son's: https://en.m.wikipedia.org/wiki/Absolute_value#Complex_numbe...

The article you linked literally says that there are two definitions: one for real numbers and another for complex numbers. Thanks for the info.

There is one definition: the distance to 0. There are several (more than two) different ways to calculate it in different situations.

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#786

Post by LASR »

_emna wrote: post #757
lovasoa wrote: post #740

Earlier quoted context omitted.

No, there is just one definition, and it's his son's: https://en.m.wikipedia.org/wiki/Absolute_value#Complex_numbe...

The article you linked literally says that there are two definitions: one for real numbers and another for complex numbers. Thanks for the info.

That’s not what it says. It says that there is a single definition that can be generalized to both real and complex numbers.

A special cases of the general definition where im(z)==0 yields an expression where some parts are multiplied by zero, and can then be omitted entirely.

This means that there is one definition. You can mentally ignore some parts of this when dealing with reals.

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#787

Post by cactusplant7374 »

ShamelessC wrote: post #486
cactusplant7374 wrote: post #291

Earlier quoted context omitted.

Yes: > This article, predictably, tells us almost nothing about the actual capabilities involved. The article tells us all we need to know.

I've gotta say it really does seem like you didn't read their comment or are responding in bad faith.

Questioning if one has read an article is against the rules on HN. Why do you think it’s any different for comments.

You’re both incredibly rude and arrogant.

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#788

Post by Gud »

aidaman wrote: post #629
raincole wrote: post #567

Earlier quoted context omitted.

But he also has the incentive to exaggerate the AI's ability. The whole idea of double-blind test (and really, the whole scientific methodology) is based on one simple thing: even the most experienced and informed professionals can be comfortably wrong. We'll only know when we see it. Or at least when several independent research groups see it.

Unlikely. We'll know when OpenAI has declared itself ruler of the new world, imposes martial law, and takes over.

Why would you ever know? Why would the singularity reveal itself in such an obvious way(until it's too late to stop it)?

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#789

Post by RamblingCTO »

sgt101 wrote: post #774
nostrademons wrote: post #593

Earlier quoted context omitted.

What I wonder, as a computer scientist: If you want to solve grade school math problems, why not use an 'add' instruction? It's been around since the 50s, runs a billion times faster than an LLM, every assembly-language programmer knows how to use it, every high-level language has a one-token equivalent, and doesn't hallucinate answers (other than integer overflow). We also know how to solve complex reasoning chains…

Can LLM's compute any computable function? I thought that an LLM can approximate any computable function, if the function is within the distribution that it is are trained on. I think it's jolly interesting to think about different axiomizations in this context. Also we know that LLM's can't do a few things - arithmetic, inference & planning are in there. They look like they can because they retrieve discussions from…

I still believe that A(G)I will consist of subsystems and different network architectures (if NN's are the path to that), just like we humans have.

Re: OpenAI researchers warned board of AI breakthrough ahead of CEO ouster

#790

Post by dustypotato »

cduzz wrote: post #316

I was talking to my (12 year old) son about parts of math he finds boring. He said that he thinks absolute value is absurdly easy and extremely boring. I asked him if there was anything that might make it more interesting, he said "maybe complex numbers". So I asked him "what would the absolute value of i+1 be?" he thinks for a little bit and says "square root of 2" and I ask him "what about the absolute value of 2i…

> To what degree can these large language models arrive at these same conclusions, and by what process?

By having visual understanding more deeply integrated in the thought process, in my opinion. Then they wouldn't be Large Language Models, of course. There are several concepts I remember and operate on by visualizing them , even visualizing motion. If i want to add numbers, i visualize the carry jumping on top of the next number. If i don't trust one of the additions , I go back , but I can't say if it's because i "mark" the uncertainty somehow.

When I think about my different groups of friends, in the back of my mind a visual representation forms.

Thinking about my flight route forms a mini map somehow, and i can compare distances between places, and all.

This helps incredibly in logical tasks like programming and math.

I think it's something that we all learned growing up and by playing with objects around us.

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