Maybe-Mathematical Musings — nostalgebraist: Now that I think about it, I...

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See, that’s what the app is perfect for.

Sounds perfect Wahhhh, I don’t wanna
nostalgebraist
nostalgebraist

Now that I think about it, I think probabilistic Newcomb still has the problem that perfect predictor Newcomb has: you are not told how the predictor achieves its predictions, only that it always has a certain success rate.  This leaves you to conclude that it has that success rate even when you do strange things like run a copy of it and do the opposite of what the copy says.

All of the trippy aspects of the thought experiment have to do with this assumption.  The predictor is a black box that somehow anticipates everything you could possibly think about it.  (Even in the probabilistic version, it achieves the same success rate no matter what you think, which is sort of the same thing.)

Once you specify what the predictor is actually doing, the problem dissolves.  If it is using some sort of detailed simulation that actually takes into account all of your thoughts about it, then that means something like backwards causation really is happening (and also means that the predictor cannot be accurate in the infinite regress case – you cannot ask it to faithfully simulate a copy of itself*).  That situation is weird, but also very unlike the situations we tend to face in the real world.  On the other hand, if the predictor is just using demographics or the like, it does not have the detailed information that you have about your decision procedure, and you don’t have to worry about your decision now “causing” suboptimal box fillings in the past.

(You do have to worry about ideas like “most people end up two-boxing because they think it can’t influence the result, which leads the predictor to think you’ll two-box, which you don’t want.”  This is a real problem, but it’s more of a coordination problem than a trippy retro-causality problem.  It’s analogous to a coordination problem with any kind of actuarial prediction, e.g. “insurance for my demographic will cost less if people in my demographic take fewer risks, but since the demographic trait is unchangeable, everyone figures they can’t affect the insurance price themselves, and end up taking a lot of risks that drive the price up for everyone.”  Standard free rider problem.)

*(although if the <100% probabilistic accuracy were achieved by some sort of simplification, it’s possible that an infinite regress of simplified predictors could converge)

jadagul

I think this is basically right.  Relevant facts:

1. Yudkowsky is working in the hypothetical where the predictor is always, 100% of the time, right.

2. From this he concludes it can’t be doing anything boring and demographic, and must instead be completely simulating your thought process (because otherwise it wouldn’t be right 100% of the time regardless of what you do).

2a. As a subpoint, he’s assuming that the predictor has computational capacity that from your perspective might as well be infinite; the predictor can simulate anything you can do, but not necessarily anything the predictor can do.  

3. Yudkowsky is worrying about strong general artificial intelligence, and believes that such entities are actually plausible.

yudkowsky newcomb

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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.

video games
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