Maybe-Mathematical Musings — nostalgebraist: Although there isn’t evidence in...

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Sounds perfect Wahhhh, I don’t wanna
nostalgebraist
nostalgebraist

Although there isn’t evidence in the fact that the statistician reached the stopping time, there is (statistical) evidence in the amount of time it took them to reach it.

I haven’t worked it out formally, but maybe this explains the “paradox” about the beliefs of the statistician vs. the beliefs of a Bayesian watching them.  Learning that they stopped eventually tells you nothing.  Learning that they stopped at time N as opposed to N/10000 or N*10000 does tell you something.  So the outsider can update on that information, and update further if they get to see the data.  (This solves the problem of “I knew you were going to produce some data set leading you to have that posterior, so the data set you have doesn’t move me closer to believing that posterior” – you didn’t know the amount of time it would take to produce that data set.)

I’m not sure this makes sense at all.  (Exactly what information do you learn from the stopping time alone?  I’d have to work it out.)

jadagul

This is what I’d kind of been thinking. The stronger the effect, the longer you’d expect to have to run the trial before getting a positive result.

Like, the odds of getting a positive after 500 trials is what it is. And if we say do another 100 trials every time we don’t get a positive, then if we have 2000 trials that tells us it failed fifteen times.

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I really liked this Sarah Constantin article on why current AI approaches fundamentally aren’t going to lead to AGI.

Her discussion of ontological robustness reminded me of the point I was making the other day, about how GPT on a deep level can’t learn.

And for the agent to be able to conceive of [the possibility that its fundamental model might be wrong] and count it as something to avoid, for it to be able to say I don’t want my loss function to be spoofed by something that kills me, it needs to have a “goal” or a “value” that goes beyond its loss function.

AKA, not a static terminal goal. A way to distinguish the “true real-world goal” from one’s mere current specification of it, and update the specification as necessary.

AKA, cross-ontological transfer of goals.

GPT-like systems just…can’t do this. They have their training weights, and that’s what they have; nothing ever updates.

And of course there are ways to retrain them and fine-tune them, but that’s awkward, and manual, and not feeding off of any of the AI capabilities that GPT has. There’s no iterative improvement; and there’s no obvious or even really suggested path for how to get there.

Sarah says no one is even really working on this, and I believe her. I haven’t encountered anyone genuinely working on this; and it doesn’t seem terribly commercially useful, while it does seem super hard. And this is part of why I’m just not terribly worried about the AI apocalypse.

ai gpt ml

More generally, Yudkowsky has long been

  1. Correct that a powerful optimization agent that we don’t understand the inner workings of would be extremely scary, and
  2. Wrong in his belief that creating such a thing would be easy.

If you grant that a super-powerful uncontrolled optimization process is about to be launched, you should in fact worry quite a lot. But it’s not.

In particular, the successes of GPT and the Transformer should reduce the credibility of Yudkowskian arguments, not raise it. Yudkowsky was arguing from a premise that any recognizable AI would necessarily have a certain collection of capabilities. GPT either does, or probably will soon, satisfy the conditions of a “recognizable AI”, but it doesn’t have those capabilities.

And the Yudkowskian conclusion is basically, therefore it must have those capabilities somewhere.

ai ml gpt yudkowsky

bulbous-oar

We don’t know that no possible large neural network implements an optimizer. If one does, we could stumble into it via gradient descent, just as we’ve stumbled into large neural networks that have world models.

Sure, we don’t know that no possible neural network implements an optimizer. In fact, I’ll go farther: it seems like if it’s possible to write one, which it probably is, we should probably be able to encode one in a large neural network. It’s just a very flexible framework for a model.

(Of course that flexibility is also the weakness: if it could be anything it has no strong pressure to be a specific thing.)

But I can say something stronger and also dumber than that, right? If an optimizer exists, then it’s possible that if I have my computer spit out 10TB of random bits and then interpret that as the source code to a C program, it will compile to that optimizer. It’s just…unlikely.

Large neural networks like GPT are not attempting to create optimizing agents. The training process is (outer-)optimizing for something, and the thing it’s optimizing for is very much not an (inner-)optimizer.

So this argument is something like, maybe writing an extremely powerful optimizer is so easy that we’ll do it by accident. And then not only will we create one, but it will be so powerful that it can out-optimize us, even if we’re trying to stop it, even though that’s if anything counterproductive to what we were training the model to do. That’s not impossible but it seems extremely unlikely.

(In contrast, I don’t think we “stumbled into” world models exactly; they are something we were more or less explicitly trying to get for the past couple years. This is part of Sarah’s point: people are trying to get world models, but they aren’t trying to get ontological stability or train inner optimizing loops basically at all.)

ai ml gpt
jaydaigle.net

A Fictional History of Numbers, Part 2: Measurement, Estimation, Completeness, and Reality

This week we continue our exploration of what numbers are, and where mathematicians keep finding weird ones. We start by asking for the area of a circle, get exhausted by Archimedes's method for finding the answer, and take a tour through the idea of limits to construct the complete field of real numbers. We resolve one of the oldest mathematical flame war topics on the internet, and finish by worrying the real numbers are just too weird to actually use.
Jay Daigle

A new post up on my blog!  Last time we talked about the algebraic numbers, and how just wanting to solve simple equations can create a ton of different numbers.  But they don’t get us everything.

So this time we start off with the idea of measurement, and wind up inventing the real numbers.  The real numbers are weird.  Real weird.  But they show up when we start asking questions about size or measurement.  And in part 3, we’ll see they’re exactly the right way to do calculus.

blog math number theory calculus analysis
youzicha
raginrayguns

ok this is dumb and not important BUT neural networks are not piles of linear algebra, they're piles of matrix multiplications. Linear algebra is the name of the mathematical theory we use to prove theorems about matrix multiplications.

This is the same pedantic losing battle as me objecting to the use of "biology" to mean "life", "chemistry" to mean "chemical reactions", etc

youzicha

My main complaint with this phrase is that they are not linear. Like, that's exactly what makes them more powerful than the linear regression models and factor analysis models that people were using in the 20th century, right? That's a pretty significant thing that happened...

jadagul

Well, unless you’re using floating point operations.

But yeah, it’s a pile of linear operations with mildly nonlinear buffers in between.

ml ai linear algebra
jaydaigle.net

Evaluating Students is Important, Too

Adam Mastroianni wrote a very interesting essay on his substack about how the difference between teaching and grading, and how much he dislikes the latter and all the problems with it. And I don't really disagree, but I don't agree either. So here's my response. Grading sucks, but it's important.
Jay Daigle

I have a new post up on my blog.  Trying to experiment with writing faster and shorter so I can get more regular content out—which in this case means it’s only two thousand words and only took me a week to publish.

blog I profess grading
loki-zen
transgenderer

its an interesting choice that link is mute from the players perspective but clearly conveying ifnromation, seemingly verbally, to other characters. i think the implicaiton is that link is speaking, we just dnt know what hes saying. i guess to make him more of a "blank slate". im not sure.

max1461

Mario does this also. Nintendo thing. Very interesting I actually like it a lot.

jadagul

It’s a pretty common video game thing! Especially in earlier games. Link and Mario are always mute. But like Crono is also mute. In the Golden Sun games, whichever character is the protagonist at the time is mute. (And the Pokemon protagonists are mute, but that’s Nintendo again.)

In general if you want one character to be a standin for the player, it can be helpful for them to have no literal dialogue; the menu selections the player makes are “your dialogue”. That’s why modern pokemon games give you a bunch of dialog prompts where you can choose between “yes” and “of course” or some shit—the point is not to give you a choice, it’s to give you a line.

That doesn’t work well with modern voice-acted games, so it’s died out of those. But with a purely text-based interface it’s often the most reasonable choice.

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