Thanks for writing this -- I’m very excited about people pushing back on/digging deeper re: counting arguments [LW · GW], simplicity arguments [LW · GW], and the other arguments re: scheming I discuss in the report. Indeed, despite the general emphasis I place on empirical work [LW · GW] as the most promising source of evidence re: scheming, I also think that there’s a ton more to do to clarify and maybe debunk the more theoretical arguments people offer re: scheming – and I think playing out the dialectic further in this respect might well lead to comparatively fast progress (for all their centrality to the AI risk discourse, I think arguments re: scheming have received way too little direct attention). And if, indeed, the arguments for scheming are all bogus, this is super good news and would be an important update, at least for me, re: p(doom) overall. So overall I’m glad you’re doing this work and think this is a valuable post. 

Another note up front: I don’t think this post “surveys the main arguments that have been put forward for thinking that future AIs will scheme.” In particular: both counting arguments and simplicity arguments (the two types of argument discussed in the post) assume we can ignore the path that SGD takes through model space [LW · GW]. But the report also discusses two arguments that don’t make this assumption – namely, the “training-game independent proxy goals story [LW · GW]” (I think this one is possibly the most common story, see e.g. Ajeya here, and all the talk about the evolution analogy) and the “nearest max-reward goal argument [LW · GW].” I think that the idea that “a wide variety of goals can lead to scheming” plays some role in these arguments as well, but not such that they are just the counting argument restated, and I think they’re worth treating on their own terms. 

On counting arguments and simplicity arguments

Focusing just on counting arguments and simplicity arguments, though: Suppose that I’m looking down at a superintelligent model newly trained on diverse, long-horizon tasks. I know that it has extremely ample situational awareness – e.g., it has highly detailed models of the world, the training process it’s undergoing, the future consequences of various types of power-seeking, etc – and that it’s getting high reward because it’s pursuing some goal (the report conditions on this [LW · GW]). Ok, what sort of goal? 

We can think of arguments about scheming in two categories here. 

• (I) The first tries to be fairly uncertain/agnostic about what sorts of goals SGD’s inductive biases favor, and it argues that given this uncertainty, we should be pretty worried about scheming. 
  • I tend to think of my favored version of the counting argument (that is, the hazy counting argument) in these terms. 
• (II) The second type focuses on a particular story about SGD’s inductive biases and then argues that this bias favors schemers.
  • I tend to think of simplicity arguments in these terms. E.g., the story is that SGD’s inductive biases favor simplicity, schemers can have simpler goals, so schemers are favored.

Let’s focus first on (I), the more-agnostic-about-SGD’s-inductive-biases type. Here’s a way of pumping the sort of intuition at stake in the hazy counting argument:

1. A very wide variety of goals can prompt scheming.
2. By contrast, non-scheming goals need to be much more specific to lead to high reward.
3. I’m not sure exactly what sorts of goals SGD’s inductive biases favor, but I don’t have strong reason to think they actively favor non-schemer goals.
4. So, absent further information, and given how many goals-that-get-high-reward are schemer-like, I should be pretty worried that this model is a schemer. 

Now, as I mention in the report, I'm happy to grant that this isn't a super rigorous argument. But how, exactly, is your post supposed to comfort me with respect to it? We can consider two objections, both of which are present in/suggested by your post in various ways.

• (A) This sort of reasoning would lead to you giving significant weight to SGD overfitting. But SGD doesn’t overfit, so this sort of reasoning must be going wrong, and in fact you should have low probability on SGD having selected a schemer, even given this ignorance about SGD's inductive biases.
• (B): (3) is false: we know enough about SGD’s inductive biases to know that it actively favors non-scheming goals over scheming goals. 

Let’s start with (A). I agree that this sort of reasoning would lead you to giving significant weight to SGD overfitting, absent any further evidence. But it’s not clear to me that giving this sort of weight to overfitting was unreasonable ex ante, or that having learned that SGD-doesn't-overfit, you should now end up with low p(scheming) even given your ongoing ignorance about SGD's inductive biases.

Thus, consider the sort of analogy I discuss in the counting arguments section [LW · GW]. Suppose that all we know is that Bob lives in city X, that he went to a restaurant on Saturday, and that town X has a thousand chinese restaurants, a hundred mexican restaurants, and one indian restaurant. What should our probability be that he went to a chinese restaurant? 

In this case, my intuitive answer here is: “hefty.”^[1] In particular, absent further knowledge about Bob’s food preferences, and given the large number of chinese restaurants in the city, “he went to a chinese restaurant” seems like a pretty salient hypothesis. And it seems quite strange to be confident that he went to a non-chinese restaurant instead. 

Ok but now suppose you learn that last week, Bob also engaged in some non-restaurant leisure activity. For such leisure activities, the city offers: a thousand movie theaters, a hundred golf courses, and one escape room. So it would’ve been possible to make a similar argument for putting hefty credence on Bob having gone to a movie. But lo, it turns out that actually, Bob went golfing instead, because he likes golf more than movies or escape rooms.

How should you update about the restaurant Bob went to? Well… it’s not clear to me you should update much. Applied to both leisure and to restaurants, the hazy counting argument is trying to be fairly agnostic about Bob’s preferences, while giving some weight to some type of “count.” Trying to be uncertain and agnostic does indeed often mean putting hefty probabilities on things that end up false. But: do you have a better proposed alternative, such that you shouldn’t put hefty probability on “Bob went to a chinese restaurant”, here, because e.g. you learned that hazy counting arguments don’t work when applied to Bob? If so, what is it? And doesn’t it seem like it’s giving the wrong answer?

Or put another way: suppose you didn’t yet know whether SGD overfits or not, but you knew e.g. about the various theoretical problems with unrestricted uses of the indifference principle. What should your probability have been, ex ante, on SGD overfitting? I’m pretty happy to say “hefty,” here. E.g., it’s not clear to me that the problem, re: hefty-probability-on-overfitting, was some a priori problem with hazy-counting-argument-style reasoning. For example: given your philosophical knowledge about the indifference principle, but without empirical knowledge about ML, should you have been super surprised if it turned out that SGD did overfit? I don’t think so. 

Now, you could be making a different, more B-ish sort of argument here: namely, that the fact that SGD doesn’t overfit actively gives us evidence that SGD’s inductive biases also disfavor schemers. This would be akin to having seen Bob, in a different city, actively seek out mexican restaurants despite there being many more chinese restaurants available, such that you now have active evidence that he prefers mexican and is willing to work for it. This wouldn’t be a case of having learned that bob’s preferences are such that hazy counting arguments “don’t work on bob” in general. But it would be evidence that Bob prefers non-chinese.

I’m pretty interested in arguments of this form. But I think that pretty quickly, they move into the territory of type (II) arguments above: that is, they start to say something like “we learn, from SGD not overfitting, that it prefers models of type X. Non-scheming models are of type X, schemers are not, so we now know that SGD won’t prefer schemers.”

But what is X? I’m not sure your answer (though: maybe it will come in a later post). You could say something like “SGD prefers models that are ‘natural’” – but then, are schemers natural in that sense? Or, you could say “SGD prefers models that behave similarly on the training and test distributions” – but in what sense is a schemer violating this standard? On both distributions, a schemer seeks after their schemer-like goal. I’m not saying you can’t make an argument for a good X, here – but I haven’t yet heard it. And I’d want to hear its predictions about non-scheming forms of goal-misgeneralization as well.  

Indeed, my understanding is that a quite salient candidate for “X” here is “simplicity” – e.g., that SGD’s not overfitting is explained by its bias towards simpler functions. And this puts us in the territory of the “simplicity argument” above. I.e., we’re now being less agnostic about SGD’s preferences, and instead positing some more particular bias. But there’s still the question of whether this bias favors schemers or not, and the worry is that it does. 

This brings me to your take on simplicity arguments. I agree with you that simplicity arguments are often quite ambiguous about the notion of simplicity at stake (see e.g. my discussion here [? · GW]). And I think they’re weak for other reasons too (in particular, the extra cognitive faff scheming involves [? · GW] seems to me more important than its enabling simpler goals). 

But beyond “what is simplicity anyway,” you also offer some other considerations, other than SGD-not-overfitting, meant to suggest that we have active evidence that SGD’s inductive biases disfavor schemers. I’m not going to dig deep on those considerations here, and I’m looking forward to your future post on the topic. For now, my main reaction is: “we have active evidence that SGD’s inductive biases disfavor schemers” seems like a much more interesting claim/avenue of inquiry than trying to nail down the a priori philosophical merits of counting arguments/indifference principles, and if you believe we have that sort of evidence, I think it’s probably most productive to just focus on fleshing it out and examining it directly. That is, whatever their a priori merits, counting arguments are attempting to proceed from a position of lots of uncertainty and agnosticism, which only makes sense if you’ve got no other good evidence to go on. But if we do have such evidence (e.g., if (3) above is false), then I think it can quickly overcome  [LW · GW]whatever “prior” counting arguments set (e.g., if you learn that Bob has a special passion for mexican food and hates chinese, you can update far towards him heading to a mexican restaurant). In general, I’m very excited for people to take our best current understanding of SGD’s inductive biases (it’s not my area of expertise), and apply it to p(scheming), and am interested to hear your own views in this respect. But if we have active evidence that SGD’s inductive biases point away from schemers, I think that whether counting arguments are good absent such evidence matters way less, and I, for one, am happy to pay them less attention.

(One other comment re: your take on simplicity arguments: it seems intuitively pretty non-simple to me to fit the training data on the training distribution, and then cut to some very different function on the test data, e.g. the identity function or the constant function. So not sure your parody argument that simplicity also predicts overfitting works. And insofar as simplicity is supposed to be the property had by non-overfitting functions, it seems somewhat strange if positing a simplicity bias predicts over-fitting after all.)

A few other comments

Re: goal realism, it seems like the main argument in the post is something like: 

1. Michael Huemer says that it’s sometimes OK to use the principle of indifference if you’re applying it to explanatorily fundamental variables. 
2. But goals won’t be explanatorily fundamental. So the principle of indifference is still bad here.

I haven’t yet heard much reason to buy Huemer’s view, so not sure how much I care about debating whether we should expect goals to satisfy his criteria of fundamentality. But I'll flag I do feel like there’s a pretty robust way in which explicitly-represented goals appropriately enter into our explanations of human behavior – e.g., I have buying a flight to New York because I want to go to New York, I have a representation of that goal and how my flight-buying achieves it, etc. And it feels to me like your goal reductionism is at risk of not capturing this. (To be clear: I do think that how we understand goal-directedness matters for scheming -- more here [LW · GW] -- and that if models are only goal-directed in a pretty deflationary sense, this makes scheming a way weirder hypothesis. But I think that if models are as goal-directed as strategic and agentic humans reasoning about how to achieve explicitly represented goals, their goal-directedness has met a fairly non-deflationary standard.)

I’ll also flag some broader unclarity about the post’s underlying epistemic stance. You rightly note that the strict principle of indifference has many philosophical problems. But it doesn’t feel to me like you’ve given a compelling alternative account of how to reason “on priors” in the sorts of cases where we’re sufficiently uncertain that there’s a temptation to spread one’s credence over many possibilities in the broad manner that principles-of-indifference-ish reasoning attempts to do. 

Thus, for example, how does your epistemology think about a case like “There are 1000 people in this town, one of them is the murderer, what’s the probability that it’s Mortimer P. Snodgrass?” Or: “there are a thousand white rooms, you wake up in one of them, what’s the probability that it’s room number 734?” These aren’t cases like dice, where there’s a random process designed to function in principle-of-indifference-ish ways. But it’s pretty tempting to spread your credence out across the people/rooms (even if in not-fully-uniform ways), in a manner that feels closely akin to the sort of thing that principle-of-indifference-ish reasoning is trying to do. (We can say "just use all the evidence available to you" -- but why should this result in such principle-of-indifference-ish results?)

Your critique of counting argument would be more compelling to me if you had a fleshed out account of cases like these -- e.g., one which captures the full range of cases where we’re pulled towards something principle-of-indifference-ish, such that you can then take that account and explain why it shouldn’t point us towards hefty probabilities on schemers, a la the hazy counting argument, even given very-little-evidence about SGD’s inductive biases.

More to say on all this, and I haven't covered various ways in which I'm sympathetic to/moved by points in the vicinity of the ones you're making here.  But for now: thanks again for writing, looking forward to future installments. 

1. ^{^}

   Though I do think cases like this can get complicated, and depending on how you carve up the hypothesis space, in some versions "hefty" won't be the right answer. 

I really do appreciate this being written up, but to the extent that this is intended to be a rebuttal to the sorts of counting arguments that I like, I think you would have basically no chance of passing my ITT [? · GW] here. From my perspective reading this post, it read to me like "I didn't understand the counting argument, therefore it doesn't make sense" which is (obviously) not very compelling to me. That being said, to give credit where credit is due, I think some people would make a more simplistic counting argument like the one you're rebutting. So I'm not saying that you're not rebutting anyone here, but you're definitely not rebutting my position.

Edit: If you're struggling to grasp the distinction I'm pointing to here, it might be worth trying this exercise pointing out where the argument in the post goes wrong in a very simple case [LW(p) · GW(p)] and/or looking at Ryan's restatement of my mathematical argument [LW(p) · GW(p)].

Edit: Another point of clarification here [LW(p) · GW(p)]—my objection is not that there is a "finite bitstring case" and an "infinite bitstring case" and you should be using the "infinite bitstring case". My objection is that the sort of finite bitstring analysis in this post does not yield any well-defined mathematical object at all, and certainly not one that would predict generalization.

Let's work through how to properly reason about counting arguments:

• When doing reasoning about simplicity priors, a really important thing to keep in mind is the relationship between infinite bitstring simplicity and finite bitstring simplicity. When you just start counting the ways in which the model can behave on unseen inputs and then saying that the more ways there are the more likely it is, what you're implicitly computing there is actually an inverse simplicity prior: Consider two programs, one that takes $n$ bits and then stops, and one that takes $2n$ bits to specify the necessary logic but then uses $m$ remaining bits to fill in additional pieces for how it might behave on unseen inputs. Obviously the $n$ bit program is simpler, but by your logic the $2n$ bit program would seem to be simpler because it leaves more things unspecified in terms of all the ways to fill in the remaining $m$ bits. But if you understand that we can recast everything into infinite bitstring complexity, then it's clear that actually the $n$ bit program is leaving $n+m$ bits unspecified—even though those bits don't do anything in that case, they're still unspecified parts of the overall infinite bitstring.
• Once we understand that relationship, it should become pretty clear why the overfitting argument doesn't work: the overfit model is essentially the $2n$ model, where it takes more bits to specify the core logic, and then tries to "win" on the simplicity by having $m$ unspecified bits of extra information. But that doesn't really matter: what matters is the size of the core logic, and if there are simple patterns that can fit the data in $n$ bits rather than $2n$ bits, you'll learn those.
• However, this doesn't apply at all to the counting argument for deception. In fact, understanding this distinction properly is critically important to make the argument work. Let's break it down:
  • Suppose my model has the following structure: an $n$ bit world model, an $m$ bit search procedure, and an $x$ bit objective function. This isn't a very realistic assumption, but it'll be enough to make it clear why the counting argument here doesn't make use of the same fallacious reasoning that would lead you to think that the $2n$ bit model was simpler.
  • We'll assume that the deceptive and non-deceptive models require the same $n+m$ bits of world modeling and search, so the only question is the objective function.
  • I would usually then make an argument here for why in most cases the simplest objective that leads to deception is simpler than the simplest objective that leads to alignment, but that's just a simplicity argument, not a counting argument. Since we want to do the counting argument here, let's assume that the simplest objective that leads to alignment is simpler than the simplest objective that leads to deception.
  • Okay, but now if the simplest objective that leads to alignment is simpler than the simplest objective that leads to deception, how could deception win? Well, the key is that the core logic necessary for deception is simpler: the only thing required for deception is a long-term objective, everything else is unspecified. So, mathematically, we have:
    • Complexity of simplest aligned objective: $a$
    • Complexity of simplest deceptive objective: $l+b$ where $l$ is the minimum necessary for any long-term objective and $b$ is everything else necessary to implement some particular long-term objective.
    • We're assuming that $a<l+b$, but that $l<a$.
    • Casting into infinite bitstring land, we see that the set of aligned objectives includes those with anything after the first $a$ bits, whereas the set of deceptive objectives includes anything after the first $l$ bits. Even though you don't get a full program until you're $l+b$ bits deep, the complexity here is just $l$, because all the bits after the first $l$ bits aren't pinned down. So if we're assuming that $l<a$, then deception wins.
    • Certainly, you could contest the assumption that $l<a$—and conversely I would even go further and say probably $a>l+b$—but either way the point is that this argument is totally sound given its assumptions.
• At a high level, what I'm saying here is that counting arguments are totally valid and in fact strongly predict that you won't learn to memorize, but only when you do them over infinite bitstrings, not when done over finite bitstrings. If we think about the simplicity of learning a line to fit a set of linear datapoints vs. the simplicity of memorizing everything, there are more ways to implement a line than there are to memorize, but only over infinite bitstrings. In the line case, the extra bits don't do anything, whereas in the memorization case, they do, but that's not a relevant distinction: they're still unspecified bits, and what we're doing is counting up the measure of the infinite bitstrings which implement that algorithm.
• I think this analysis should also make clear what's going on with the indifference principle here. The "indifference principle" in this context is about being indifferent across all infinite bitstrings—it's not some arbitrary thing where you can carve up the space however you like and then say you're indifferent across the different pieces—it's a very precise notion that comes from theoretical computer science (though there is a question about what UTM to use; there you're trying to get as close as possible to a program prior that would generalize well in practice given that we know ML generalizes well). The idea is that indifference across infinite bitstrings gives you a universal semi-measure, from which you can derive a universal prior (which you're trying to select out of the space of all universal priors to match ML well). Of course, it's certainly not the case that actual machine learning inductive biases are purely simplicity, or that they're even purely indifferent across all concrete parameterizations, but I think it's a reasonable first-pass assumption given facts like ML not generally overfitting as you note.
• Looking at this more broadly, from my perspective, the fact that we don't see overfitting is the entire reason why deceptive alignment is likely. The fact that models tend to learn simple patterns that fit the data rather than memorize a bunch of stuff is exactly why deception, a simple strategy that compresses a lot of data, might be a very likely thing for them to learn. If models were more likely to learn overfitting-style solutions, I would be much, much less concerned about deception—but of course, that would also mean they were less capable, so it's not much solace.

This isn't a proper response to the post, but since I've occasionally used counting-style arguments in the past I think I should at least lay out some basic agree/disagree points. So:

• This post basically-correctly refutes a kinda-mediocre (though relatively-commonly-presented) version of the counting argument.
• There does exist a version of the counting argument which basically works.
• The version which works routes through compression and/or singular learning theory.
• In particular, that version would talk about "goal-slots" (i.e. general-purpose search) showing up for exactly the same reasons that neural networks are able to generalize in the overparameterized regime more generally. In other words, if you take the "counting argument for overfitting" from the post, walk through the standard singular-learning-theory-style response to that story, and then translate that response over to general-purpose search as a specific instance of compression, then you basically get the good version of the counting argument.
  • Just remembered I walked through basically the good version of the counting argument in this section of What's General-Purpose Search, And Why Might We Expect To See It In Trained ML Systems? [LW · GW]
• The "Against Goal Realism" section is a wild mix of basically-correct points and thorough philosophical confusion. I would say the overall point it's making is probably mostly-true of LLMs, false of humans, and most of the arguments are confused enough that they don't provide much direct evidence relevant to either of those.

Pretty decent post overall.

Since there are “more” possible schemers than non-schemers, the argument goes, we should expect training to produce schemers most of the time. In Carlsmith’s words:

It's important to note that the exact counting argument you quote isn't one that Carlsmith endorses, just one that he is explaning. And in fact Carlsmith specifically notes that you can't just apply something like the principle of indifference without more reasoning about the actual neural network prior.

(You mention this later in the "simplicity arguments" section, but I think this objection is sufficiently important and sufficiently missing early in the post that it is important to emphasize.)

Quoting somewhat more context:

I start, in section 4.2, with what I call the “counting argument.” It runs as follows:

1. The non-schemer model classes, here, require fairly specific goals in order to get high reward.
2. By contrast, the schemer model class is compatible with a very wide range of (beyond- episode) goals, while still getting high reward (at least if we assume that the other require- ments for scheming to make sense as an instrumental strategy are in place—e.g., that the classic goal-guarding story, or some alternative, works).48
3. In this sense, there are “more” schemers that get high reward than there are non-schemers that do so.
4. So, other things equal, we should expect SGD to select a schemer.

Something in the vicinity accounts for a substantial portion of my credence on schemers (and I think it often undergirds other, more specific arguments for expecting schemers as well). However, the argument I give most weight to doesn’t move immediately from “there are more possible schemers that get high reward than non-schemers that do so” to “absent further argument, SGD probably selects a schemer” (call this the “strict counting argument”), because it seems possible that SGD actively privileges one of these model classes over the others. Rather, the argument I give most weight to is something like:

1. It seems like there are “lots of ways” that a model could end up a schemer and still get high reward, at least assuming that scheming is in fact a good instrumental strategy for pursuing long-term goals.
2. So absent some additional story about why training won’t select a schemer, it feels, to me, like the possibility should be getting substantive weight. I call this the “hazy counting argument.” It’s not especially principled, but I find that it moves me

[Emphasis mine.]

(I might write a longer response later, but I thought it would be worth writing a quick response now. Cross-posted from the EA forum [EA(p) · GW(p)], and I know you've replied there, but I'm posting anyway.)

I have a few points of agreement and a few points of disagreement:

Agreements:

• The strict counting argument seems very weak as an argument for scheming, essentially for the reason you identified: it relies on a uniform prior over AI goals, which seems like a really bad model of the situation.
• The hazy counting argument—while stronger than the strict counting argument—still seems like weak evidence for scheming. One way of seeing this is, as you pointed out, to show that essentially identical arguments can be applied to deep learning in different contexts that nonetheless contradict empirical evidence.

Some points of disagreement:

• I think the title overstates the strength of the conclusion. The hazy counting argument seems weak to me but I don't think it's literally "no evidence" for the claim here: that future AIs will scheme.
• I disagree with the bottom-line conclusion: "we should assign very low credence to the spontaneous emergence of scheming in future AI systems—perhaps 0.1% or less"
  • I think it's too early to be very confident in sweeping claims about the behavior or inner workings of future AI systems, especially in the long-run. I don't think the evidence we have about these things is very strong right now.
  • One caveat: I think the claim here is vague. I don't know what counts as "spontaneous emergence", for example. And I don't know how to operationalize AI scheming. I personally think scheming comes in degrees: some forms of scheming might be relatively benign and mild, and others could be more extreme and pervasive.
  • Ultimately I think you've only rebutted one argument for scheming—the counting argument. A more plausible argument for scheming, in my opinion, is simply that the way we train AIs—including the data we train them on—could reward AIs that scheme over AIs that are honest and don't scheme. Actors such as AI labs have strong incentives to be vigilant against these types of mistakes when training AIs, but I don't expect people to come up with perfect solutions. So I'm not convinced that AIs won't scheme at all.
  • If by "scheming" all you mean is that an agent deceives someone in order to get power, I'd argue that many humans scheme all the time. Politicians routinely scheme, for example, by pretending to have values that are more palatable to the general public, in order to receive votes. Society bears some costs from scheming, and pays costs to mitigate the effects of scheming. Combined, these costs are not crazy-high fractions of GDP; but nonetheless, scheming is a constant fact of life.
  • If future AIs are "as aligned as humans", then AIs will probably scheme frequently. I think an important question is how intensely and how pervasively AIs will scheme; and thus, how much society will have to pay as a result of scheming. If AIs scheme way more than humans, then this could be catastrophic, but I haven't yet seen any decent argument for that theory.
  • So ultimately I am skeptical that AI scheming will cause human extinction or disempowerment, but probably for different reasons than the ones in your essay: I think the negative effects of scheming can probably be adequately mitigated by paying some costs even if it arises.
• I don't think you need to believe in any strong version of goal realism in order to accept the claim that AIs will intuitively have "goals" that they robustly attempt to pursue. It seems pretty natural to me that people will purposely design AIs that have goals in an ordinary sense, and some of these goals will be "misaligned" in the sense that the designer did not intend for them. My relative optimism about AI scheming doesn't come from thinking that AIs won't robustly pursue goals, but instead comes largely from my beliefs that:
  • AIs, like all real-world agents, will be subject to constraints when pursuing their goals. These constraints include things like the fact that it's extremely hard and risky to take over the whole world and then optimize the universe exactly according to what you want. As a result, AIs with goals that differ from what humans (and other AIs) want, will probably end up compromising and trading with other agents instead of pursuing world takeover. This is a benign failure and doesn't seem very bad.
  • The amount of investment we put into mitigating scheming is not an exogenous variable, but instead will respond to evidence about how pervasive scheming is in AI systems, and how big of a deal AI scheming is. And I think we'll accumulate lots of evidence about the pervasiveness of AI scheming in deep learning over time (e.g. such as via experiments with model organisms of alignment), allowing us to set the level of investment in AI safety at a reasonable level as AI gets incrementally more advanced. 
    
    If we experimentally determine that scheming is very important and very difficult to mitigate in AI systems, we'll probably respond by spending a lot more money on mitigating scheming, and vice versa. In effect, I don't think we have good reasons to think that society will spend a suboptimal amount on mitigating scheming.

↑ comment by ryan_greenblatt · 2024-02-28T01:55:49.010Z · LW(p) · GW(p)

Ultimately I think you've only rebutted one argument for scheming—the counting argument. A more plausible argument for scheming, in my opinion, is simply that the way we train AIs—including the data we train them on—could reward AIs that scheme over AIs that are honest and don't scheme.

It's worth noting here that Carlsmith's original usage of the term scheming just refers to AIs that perform well on training and evaluations for instrumental reasons because they have longer run goals or similar.

So, AIs lying because this was directly reinforced wouldn't itself be scheming behavior in Carlsmith's terminology.

However, it's worth noting that part of Carlsmith's argument involves arguing that smart AIs will likely have to explicitly reason about the reinforcement process (sometimes called playing the training game) and this will likely involve lying.

Replies from: matthew-barnett

↑ comment by Matthew Barnett (matthew-barnett) · 2024-02-28T02:11:28.973Z · LW(p) · GW(p)

Perhaps I was being too loose with my language, and it's possible this is a pointless pedantic discussion about terminology, but I think I was still pointing to what Carlsmith called schemers in that quote. Here's Joe Carlsmith's terminological breakdown:

The key distinction in my view is whether the designers of the reward function intended for lies to be reinforced or not. [ETA: this was confusingly stated. What I meant is that if a people design a reward function that accidentally reinforces lying in order to obtain power, it seems reasonable to call the agent that results from training on that reward function a "schemer" given Carlsmith's terminology, and common sense.]

If lying to obtain power is reinforced but the designers either do not know this, or do not know how to mitigate this behavior, then it still seems reasonable to call the resulting model a "schemer". In Ajeya Cotra's story [LW · GW], for example:

1. Alex was incentivized to lie because it got rewards for taking actions that were superficially rated as good even if they weren't actually good, i.e. Alex was "lying because this was directly reinforced". She wrote, "Because humans have systematic errors in judgment, there are many scenarios where acting deceitfully causes humans to reward Alex’s behavior more highly. Because Alex is a skilled, situationally aware, creative planner, it will understand this; because Alex’s training pushes it to maximize its expected reward, it will be pushed to act on this understanding and behave deceptively."
2. Alex was "playing the training game", as Ajeya Cotra says this explicitly several times in her story.
3. Alex was playing the training game in order to get power for itself or for other AIs; clearly, as the model literally takes over the world and disempowers humanity at the end.
4. Alex kind of didn't appear to purely care about reward-on-the-episode, since it took over the world? Yes, Alex cared about rewards, but not necessarily on this episode. Maybe I'm wrong here. But even if Alex only cared about reward-on-the-episode, you could easily construct a scenario similar to Ajeya's story in which a model begins to care about things other than reward-on-the-episode, which nonetheless fits the story of "the AI is lying because this was directly reinforced".

Replies from: ryan_greenblatt, ryan_greenblatt

↑ comment by ryan_greenblatt · 2024-02-28T05:20:29.609Z · LW(p) · GW(p)

The key distinction in my view is whether the designers of the reward function intended for lies to be reinforced or not.

Hmm, I don't think the intention is the key thing (at least with how I use the word and how I think Joe uses the word), I think the key thing is whether the reinforcement/reward process actively incentivizes bad behavior.

Overall, I use the term to mean basically the same thing as "deceptive alignment". (But more specifically pointing the definition in Joe's report which depends less on some notion of mesa-optimization and is a bit more precise IMO.)

Replies from: matthew-barnett

↑ comment by Matthew Barnett (matthew-barnett) · 2024-02-28T19:22:38.200Z · LW(p) · GW(p)

Hmm, I don't think the intention is the key thing (at least with how I use the word and how I think Joe uses the word), I think the key thing is whether the reinforcement/reward process actively incentivizes bad behavior.

I confusingly stated my point (and retracted my specific claim in the comment above). I think the rest of my comment basically holds, though. Here's what I think is a clearer argument:

• The term "schemer" evokes an image of someone who is lying to obtain power. It doesn't particularly evoke a backstory for why the person became a liar in the first place.
• There are at least two ways that AIs could arise that lie in order to obtain power:
  • The reward function could directly reinforce the behavior of lying to obtain power, at least at some point in the training process.
  • The reward function could have no defects (in the sense of not directly reinforcing harmful behavior), and yet an agent could nonetheless arise during training that lies in order to obtain power, simply because it is a misaligned inner optimizer (broadly speaking)
• In both cases, one can imagine the AI eventually "playing the training game", in the sense of having a complete understanding of its training process and deliberately choosing actions that yield high reward, according to its understanding of the training process
• Since both types of AIs are: (1) playing the training game, (2) lying in order to obtain power, it makes sense to call both of them "schemers", as that simply matches the way the term is typically used. 
  
  For example, Nora and Quintin started their post with, "AI doom scenarios often suppose that future AIs will engage in scheming— planning to escape, gain power, and pursue ulterior motives, while deceiving us into thinking they are aligned with our interests." This usage did not specify the reason for the deceptive behavior arising in the first place, only that the behavior was both deceptive and aimed at gaining power.
• Separately, I am currently confused at what it means for a behavior to be "directly reinforced" by a reward function, so I'm not completely confident in these arguments, or my own line of reasoning here. My best guess is that these are fuzzy terms that might be much less coherent than they initially appear if one tried to make these arguments more precise.

Replies from: ryan_greenblatt

↑ comment by ryan_greenblatt · 2024-02-28T19:32:43.908Z · LW(p) · GW(p)

Since both types of AIs are: (1) playing the training game, (2) lying in order to obtain power, it makes sense to call both of them "schemers", as that simply matches the way the term is typically used.

I agree this matches typical usage (and also matches usage in the overall post we're commenting on), but sadly the word schemer in the context of Joe's report means something more specific. I'm sad about the overall terminology situation here. It's possible I should just always use a term like beyond-episode-goal-style-scheming.

I agree this distinction is fuzzy, but I think there is likely to be an important distinction because the case where the behavior isn't due to things well described as beyond-episode-goals, it should be much easier to study. See here [LW · GW] for more commentary. There will of course be a spectrum here.

↑ comment by ryan_greenblatt · 2024-02-28T05:17:49.003Z · LW(p) · GW(p)

I think in Ajeya's story the core threat model isn't well described as scheming and is better described as seeking some proxy of reward.

Deep learning is strongly biased toward networks that generalize the way humans want— otherwise, it wouldn’t be economically useful.

This is NOT what the evidence supports, and super misleadingly phrased. (Either that, or it's straightup magical thinking, which is worse)

The inductive biases / simplicity biases of deep learning are poorly understood but they almost certainly don't have anything to do with what humans want, per se. (that would be basically magic) Rather, humans have gotten decent at intuiting them, such that humans can often predict how the neural network will generalize in response to such-and-such training data. i.e. human intuitive sense of simplicity is different, but not totally different, at least not always, from the actual simplicity biases at play.

Stylized abstract example: Our current AI is not generalizing in the way we wanted it to. Looking at its behavior, and our dataset, we intuit that the dataset D is narrow/nondiverse in ways Y and Z and that this could be causing the problem; we go collect more data so that our dataset is diverse in those ways, and try again, and this time it works (i.e. the AI generalizes to unseen data X). Why did this happen? Why didn't it just overfit to the new dataset Dnew and fail at X? Because the simplicity biases were as we suspected they were -- the model was indeed learning [nondiverse, overfitting-to-D policy] and not [desired policy] because of Y and Z related reasons and in the new training run Y and Z were fixed and the simplest policy was [desired policy] instead of [nondiverse, overfitting-to-Dnew policy], as we predicted & hoped it would be.

I think that if you do assume a fixed goal slot and outline an overall architecture, then there are pretty good arguments for a serious probabilty of scheming.

(Though there are also plenty of bad arguments, including some that people have made in the past : ).)

That said, I'm sympathetic to some version of the "Against goal realism" argument applying to models which are sufficiently useful. As in, the first transformatively useful models won't in practice contain have internal (opaque-to-human-overseers) goals such that the traditional story for scheming doesn't apply.

(However, it's worth noting that at least some humans do seem to have internal goals and reductionism doesn't defeat this intuition. It's not super clear that the situation with humans is well described as a "goal slot", though there is pretty clearly some stuff that could be changed in a human brain that would cause them to be well described as coherantly pursue different goals. So arguing that AIs won't have internal goals in a way that could result in scheming does require noting some ways in which you're argument doesn't apply to humans. More strongly, humans can and do scheme even in cases where some overseer selected the humans for good behavior.)

Regardless, I'll assume the existance of something well described as a goal slot in this comment.

In the remainder of this comment:

• I make a simple (but vague and hand wavy) counting/measure/simplicity style argument for scheming independently.
• I'll try to quickly sketch a simple and relatively concrete architecture with a goal slot that I think might lead to scheming. I make somewhat artificial choices for the sake of simplicity.

Simple (counting-style) argument for scheming

(I make a less fleshed out version of this argument, in this comment [LW(p) · GW(p)] below.)

Let's suppose that we do have a neural network which implements goal-directed reasoning and has something well described as a goal slot.

The model is trained for a long time with RL.

Let's imagine that this model is very smart and it understands reasonably well the training the process it's in and how its actions in training effect the final model produced by training. (This second property is sometimes called situational awareness.)

Speaking roughly, and under a few more assumptions I'll discuss later, there are two types of goals which perform well enough in RL to be selected:

• Goals which directly pursue anything that is nearly perfectly correlated with the outcome that it reinforced (aka reward).
• Goals which care most about literally any long run outcome.

So, we care about the measure on these two types of goals.

If we imagine that our RL'd neural network computes a bunch of predictions, then it does seem plausible that it will have a bunch of long horizon predictions in its activations with higher aggregate measure than predicting things that perfectly correlate with the outcome that was reinforced (aka reward)! As in, if we imagine randomly sampling a linear probe, it will be far more likely to sample a probe where most of the variance is driven by long run outcomes than to sample a linear probe which is almost perfectly correlated with reward (e.g. a near perfect predictor of reward up to monotone regression). Neural networks are likely to compute a bunch of long range predictions at least as intermediates, but they only need to compute things that nearly perfectly correlate with reward once! (With some important caveats about transfer from other distributions.)

It's not clear that variance in the activations determines the relative measure of different goals that perform equally well in training, but it seems like a vaguely sane rough ballpark guess. (Other proposals don't seem to particular effect the intuitions because the process of goals selecting actions will absolutely require thinking about predicted consequences.)

Overall, I don't think this measure argument is clear, but in the case with explicit goal slots there are at least some concerning signs.

For the above argument to go through, there are a few assumptions I've made:

• In order for the AI to perform sufficiently well as to be a plausible result of training it has to explicitly "play the training game" (e.g. explicitly reason about and try to get high performance).
• The AI's predictions are aware of what its goal slot contains.

It also seems reasonable to contest these assumption, but this is a different thing than the counting argument. I think these two assumptions are very likely to hold in the limit of arbitrary intelligence, but it's unclear if they hold for AIs which are created prior to the point where human AI safety efforts are totally obsolete.

Simple architecture where scheming seems plausible (though not certain)

This architecture will involve internally doing literal best of n search against an internally represented goal.

• Let's suppose that our AI has an internal world model P. P maps from proposed actions to a bunch of predictions about the world conditional on that action being taken. Let's say these predictions are represented as a vector in $R^M$ (e.g. a neural network computes predictions about the future as an embedding). For now, let's assume that this world model is fixed, but does end up predicting all of the important outcomes needed to perform well in training.
• It also has some sort of action generator to get proposed actions A. This allows it to sample proposed actions to search over. For now, let's suppose that the AI's distribution over actions is fixed. (But the search over these actions won't be fixed.)
• It also has an explicit goal represented as a linear probe which is applied to the predictions from the world model. We'll suppose this goal is the only thing which is train for simplicity (though I expect this rough argument to work if we train the world model in parallel with the goals).

Now, our overall architecture will do search using these components. Here's some python pseudo code:

def P(input, action, goal):
    # returns a vector in R^M
    ...

def A(input):
    # samples an action
    ...

def model(input, goal_linear_probe, N):
    highest_goodness = -float('inf')
    best_action = None


    for i in range(N):
        action = A(input)
        preds = P(input, action, goal_linear_probe)
        interally_assessed_goodness = (goal_linear_probe * preds).sum()

        if interally_assessed_goodness > highest_goodness:
            highest_goodness = interally_assessed_goodness
            best_action = action

    return best_action

Note that this is pseudo code for the overall model which we're training and which is implementing consequentialism interally in an opaque way (opaque in the corresponding real model, this is obviously not opaque because it's written as python code). So there would an outer training loop that trains this model. (In this case for simplicity, we assume that only the goal_linear_probe is trained.)

Now, in the case where:

• N is very large (analogy: a massive amount of selection pressure is applied by internal consequentialist reasoning, e.g. 64 bits or N=2^64).
• P has all of the important predictions for performing well in training including intermediate predictions.
• We train the AI (really just the goal probe) for a huge number of episodes (analogy: a massive amount of selection pressure is applied by training). (For simplicity, we can imagine this training just doing best-of-n sampling over some massive number of random linear probes (e.g. 2^1024) which is ~equivalent to Mingard et al.)
  • This assumption and the above assumption combined with this architecture basically implies that playing the training game is required to be selected by training. (See above for a rough definition of playing the training game.)
• P "understands" that it is part of an AI in training and that the submitted action will effect selection/training pressure on the goal probe. And in turn it understands what actions various goal probes will take at different points. Note that this requires that the predictor takes the goal as input which corresponds to the AI being aware of its own goals.
• (We also need some consistency properties on the representations that P uses for long run predictions. E.g., specific consistent long run predictions need to be linearly represented and use consistent representations over time. This is even more in the weeds, so most people can ignore this even if this is a bit confusing.)

Then there are basically two types of goal linear probes you can get:

• Probes which mostly "care" about long run outcomes in ~every training episode and thus assign high internally_assessed_goodness to highly rewarded actions because these actions will result in these goals getting more influence over the long run (because the goal probe isn't selected against).
• Probes which are nearly perfectly correlated with the outcome that is reinforced (aka reward).

Probably literal reward is somewhat saliant to P in this setup (particular if we imagine this model being trained to predict reward as occurs in many RL setups), but there are also going to be a lot of long range predictions that the model will need to compute to do well in training (both in RL and in pretraining). And you only need to compute near-perfect-on-distribution correlates of reward once (at least for the RL part of training).

I might try to touch up this argument at some point, but this is the core sketch.

The current literature on scheming appears to have been inspired by Paul Christiano’s speculations about malign intelligences in Solomonoff induction

This doesn't seem right. The linked post by Paul here is about the (extremely speculative) case where consequentialist life emerges organically inside of full blown simulations (e.g. evolving from scratch) while arguments about ML models never go here.

Regardless, concerns and arguments about scheming are much older than Paul's posts on this topic.

(That said, I do think that people have made scheming style arguments based on intuitions from thinking about AIXI and the space of turing machines at various points. Though this was never very key and I don't believe these arguments are ever in reference to cases where a literal simulation evolves life.)

There is also a hazy counting argument for overfitting:

1. It seems like there are “lots of ways” that a model could end up massively overfitting and still get high training performance.
2. So absent some additional story about why training won’t select an overfitter, it feels like the possibility should be getting substantive weight.

While many machine learning researchers have felt the intuitive pull of this hazy overfitting argument over the years, we now have a mountain of empirical evidence that its conclusion is false. Deep learning is strongly biased toward networks that generalize the way humans want— otherwise, it wouldn’t be economically useful.

I don't know well NN history, but I have the impression good NN training is not trivial. I expect that the first $n$ attempts at NN training went bad in some way, including overfitting. So, without already knowing how to train an NN without overfitting, you'd get some overfitting in your experiments. The fact that now, after someone already poured their brain juice over finding techniques that avoid the problem, you don't get overfitting, is not evidence that you shouldn't have expected overfitting before.

The analogy with AI scheming is: you don't already know the techniques to avoid scheming. You can't use as counterargument a case in which a problem has already deliberately been solved. If you take that same case, and put yourself in the shoes of someone who doesn't already have the solution, you see you'll get the problem in your face a few times before solving it.

Then, it is a matter of whether it works like Yudkowsky says, that you may only get one chance to solve it.

The title says "no evidence for AI doom in counting arguments", but the article mostly talks about neural networks (not AI in general), and the conclusion is

In this essay, we surveyed the main arguments that have been put forward for thinking that future AIs will scheme against humans by default. We find all of them seriously lacking. We therefore conclude that we should assign very low credence to the spontaneous emergence of scheming in future AI systems— perhaps 0.1% or less.

"main arguments": I don't think counting arguments completely fill up this category. Example: the concept of scheming originates from observing it in humans.

Overall, I have the impression of some overstatement. It can also be that I'm missing some previous discussion context/assumptions, so other background theory from you may say "humans don't matter as examples", and also "AI will be NNs and not other things".

Joe also discusses simplicity arguments for scheming, which suppose that schemers may be “simpler” than non-schemers, and therefore more likely to be produced by SGD.

I'm not familiar with the details of Joe's arguments, but to me the strongest argument from simplicity is not that schemers are simpler than non-schemers, it's that scheming itself is conceptually simple and instrumentally useful. So any system capable of doing useful and general cognitive work will necessarily have to at least be capable of scheming.

We will address this question in greater detail in a future post. However, we believe that current evidence about inductive biases points against scheming for a variety of reasons. Very briefly:

• Modern deep neural networks are ensembles of shallower networks. Scheming seems to involve chains of if-then reasoning which would be hard to implement in shallow networks.
• Networks have a bias toward low frequency functions— that is, functions whose outputs change little as their inputs change. But scheming requires the AI to change its behavior dramatically (executing a treacherous turn) in response to subtle cues indicating it is not in a sandbox, and could successfully escape.
• There’s no plausible account of inductive biases that does support scheming. The current literature on scheming appears to have been inspired by Paul Christiano’s speculations about malign intelligences in Solomonoff induction, a purely theoretical model of probabilistic reasoning which is provably unrealizable in the real world.^[16] Neural nets look nothing like this.
• In contrast, points of comparison that are more relevant to neural network training, such as isolated brain cortices, don’t scheme. Your linguistic cortex is not “instrumentally pretending to model linguistic data in pursuit of some hidden objective.”

Also, don't these counterpoints prove too much? If networks trained via SGD can't learn scheming, why should we expect models trained via SGD to be capable of learning or using any high-level concepts, even desirable ones?

These bullets seem like plausible reasons for why you probably won't get scheming within a single forward pass of a current-paradigm DL model, but are already inapplicable to the real-world AI systems in which these models are deployed.

LLM-based systems are already capable of long chains of if-then reasoning, and can change their behavior dramatically given a different initial prompt, often in surprising ways.

If the most relevant point of comparison to NN training is an isolated brain cortex, then that's just saying that NN training will never be useful in isolation, since an isolated brain cortex can't do much (good or bad) unless it is actually hooked up to a body, or at least the rest of a brain.

I don't get how you can arrive at 0.1% for future AI systems even if NNs are biased against scheming. Humans scheme, the future AI systems trained to be capable of long if-then chains may also learn to scheme, maybe because explicitly changing biases is good for performance. Or even, what, you have <0.1% on future AI systems not using NNs?

Also, not saying "but it doesn't matter", but assuming everyone agrees that spectrally biased NN with classifier or whatever is a promising model of a safe system. Do you then propose we should not worry and just make the most advanced AI we can as fast as possible. Or it would be better to first reduce remaining uncertainty about behavior of future systems?

the problem faced by evolution and by SGD is much easier than this: producing systems that behave the right way in all scenarios they are likely to encounter.

I think you mean "in all scenarios they are likely to encounter *on the training distribution* / in the ancestral environment right? That's importantly different.

In reality, the problem faced by evolution and by SGD is much easier than this: producing systems that behave the right way in all scenarios they are likely to encounter. In virtue of their aligned behavior, these systems will be “aimed at the right things” in every sense that matters in practice.

I find this passage remarkable, given that so many people are choosing to to have few or no children that fertility has fallen to 0.78 in Korea and 1.0 in China. Presumably you're aware of these (or similar) facts and intended the meaning of this passage to be compatible with them, but I'm having trouble figuring out how...

By contrast, goal realism leads only to unfalsifiable speculation about an “inner actress” with utterly alien motivations.

In order for such speculation to be unfalsifiable, it seemingly has to be the case that we're unable to ever develop good enough interpretability tools to definitively say whether the AI in question has such internal motivations. This could well turn out to be true, but I don't understand how you're able to predict this now. (Or maybe you mean something else by "unfalsifiable" but I can't see what it could be. ETA: Maybe you mean "unfalsifiable with existing methods"?)

On the other hand, with your own proposed alignment method, we have to speculate about what scenarios an AI is likely to encounter. You could say that this is falsifiable (we just have to wait for the future to unfold), but is this actually an advantage?

• It seems like there are “lots of ways” that a model could end up massively overfitting and still get high training performance.
• So absent some additional story about why training won’t select an overfitter, it feels like the possibility should be getting substantive weight.

FWIW, once I learned more about the problem of induction, I realized that there do exist additional stories explaining why training won't select an overfitter. Or perhaps to put it differently, after I understood the problem of induction better it no longer seemed to me that there were lots of ways a model could massively overfit and still get high training performance. (That is, it seems to me there are many MORE ways it could not overfit)

Nora and/or Quentin: you talk a lot about inductive biases of neural nets ruling scheming out, but I have a vague sense that scheming ought to happen in some circumstances - perhaps rather contrived, but not so contrived as to be deliberately inducing the ulterior motive. Do you expect this to be impossible? Can you propose a set of conditions you think sufficient to rule out scheming?

More generally, John Miller and colleagues have found training performance is an excellent predictor of test performance, even when the test set looks fairly different from the training set, across a wide variety of tasks and architectures.

Counterdatapoint to [training performance being an excellent predictor of test performance]: in this paper, GPT-3 was fine-tuned to multiply "small" (e.g., 3-digit by 3-digit) numbers, which didn't generalize to multiplying bigger numbers.

In favour of goal realism

Suppose your looking at an AI that is currently placed in a game of chess. 

It has a variety of behaviours. It moves pawns forward in some circumstances. It takes a knight with a bishop in a different circumstance. 

You could describe the actions of this AI by producing a giant table of "behaviours". Bishop taking behaviours in this circumstance. Castling behaviour in that circumstance. ... 

But there is a more compact way to represent similar predictions. You can say it's trying to win at chess. 

The "trying to win at chess" model makes a bunch of predictions that the giant list of behaviour model doesn't. 

Suppose you have never seen it promote a pawn to a Knight before. (A highly distinct move that is only occasionally allowed and a good move in chess)  

The list of behaviours model has no reason to suspect the AI also has a "promote pawn to knight" behaviour. 

Put the AI in a circumstance where such promotion is a good move, and the "trying to win" model makes it as a clear prediction. 

Now it's possible to construct a model that internally stores a huge list of behaviours. For example, a giant lookup table trained on an unphysically huge number of human chess games. 

But neural networks have at least some tendency to pick up simple general patterns, as opposed to memorizing giant lists of data. And "do whichever move will win" is a simple and general pattern. 

Now on to making snarky remarks about the arguments in this post.

There is no true underlying goal that an AI has— rather, the AI simply learns a bunch of contextually-activated heuristics, and humans may or may not decide to interpret the AI as having a goal that compactly explains its behavior.

There is no true ontologically fundamental nuclear explosion. There is no minimum number of nuclei that need to fission to make an explosion. Instead there is merely a large number of highly energetic neutrons and fissioning uranium atoms, that humans may decide to interpret as an explosion or not as they see fit. 

Nonfundamental decriptions of reallity, while not being perfect everywhere, are often pretty spot on for a pretty wide variety of situations. If you want to break down the notion of goals into contextually activated heuristics, you need to understand how and why those heuristics might form a goal like shape. 

Should we actually expect SGD to produce AIs with a separate goal slot and goal-achieving engine?

Not really, no. As a matter of empirical fact, it is generally better to train a whole network end-to-end for a particular task than to compose it out of separately trained, reusable modules. As Beren Millidge writes,

This is not the strong evidence that you seem to think it is. Any efficient mind design is going to have the capability of simulating potential futures at multiple different levels of resolution. A low res simulation to weed out obviously dumb plans before trying the higher res simulation. Those simulations are ideally going to want to share data with each other. (So you don't need to recompute when faced with several similar dumb plans) You want to be able to backpropagate your simulation. If a plan failed in simulation because of one tiny detail, that indicates you may be able to fix the plan by changing that detail. There are a whole pile of optimization tricks. An end to end trained network can, if it's implementing goal directed behaviour, stumble into some of these tricks. At the very least, it can choose where to focus it's compute. A module based system can't use any optimization that humans didn't design into it's interfaces. 

Also, evolution analogy. Evolution produced animals with simple hard coded behaviours long before it started getting to the more goal directed animals. This suggests simple hard coded behaviours in small dumb networks. And more goal directed behaviour in large networks. I mean this is kind of trivial. A 5 parameter network has no space for goal directedness. Simple dumb behaviour is the only possibility for toy models. 

In general, full [separation between goal and goal-achieving engine] and the resulting full flexibility is expensive. It requires you to keep around and learn information (at maximum all information) that is not relevant for the current goal but could be relevant for some possible goal where there is an extremely wide space of all possible goals.

That is not how this works. That is not how any of this works. 

Back to our chess AI. Lets say it's a robot playing on a physical board. It has lots of info on wood grain, which it promptly discards. It currently wants to play chess, and so has no interest in any of these other goals. 

I mean it would be possible to design an agent that works as described here. You would need a probability distribution over new goals. A tradeoff rate between optimizing the current goal and any new goal that got put in the slot. Making sure it didn't wirehead by giving itself a really easy goal would be tricky. 

For AI risk arguments to hold water, we only need that the chess playing AI will persue new and never seen before strategies for winning at chess. And that in general AI's doing various tasks will be able to invent highly effective and novel strategies. The exact "goal" they are persuing may not be rigorously specified to 10 decimal places. The frog-AI might not know whether it want to catch flies or black dots. But if it builds a dyson sphere to make more flies which are also black dots, it doesn't matter to us which it "really wants".  

What are you expecting. An AI that says "I'm not really sure whether I want flies or black dots. I'll just sit here not taking over the world and not get either of those things"?

I wrote up my views on the principle of indifference here:

https://www.lesswrong.com/posts/3PXBK2an9dcRoNoid/on-having-no-clue [LW · GW]

I agree that it has certain philosophical issues, but I don’t believe that this is as fatal to counting arguments as you believe.

Towards the end I write:

“The problem is that we are making an assumption, but rather than owning it, we're trying to deny that we're making any assumption at all, ie. "I'm not assuming a priori A and B have equal probability based on my subjective judgement, I'm using the principle of indifference". Roll to disbelieve.

I feel less confident in my post than when I wrote it, but it still feels more credible than the position articulated in this post.

Otherwise: this was an interesting post. Well done on identifying some arguments that I need to digest.

Despite not answering all possible goal-related questions a priori, the reductionist perspective does provide a tractable research program for improving our understanding of AI goal development. It does this by reducing questions about goals to questions about behaviors observable in the training data.

[emphasis mine]

This might be described as "a reductionist perspective". It is certainly not "the reductionist perspective", since reductionist perspectives need not limit themselves to "behaviors observable in the training data".

A more reasonable-to-my-mind behavioral reductionist perspective might look like this [LW(p) · GW(p)].

Ruling out goal realism as a good way to think does not leave us with [the particular type of reductionist perspective you're highlighting].
In practice, I think the reductionist perspective you point at is:

• Useful, insofar as it answers some significant questions.
• Highly misleading if we ever forget that [this perspective doesn't show us that x is a problem] doesn't tell us [x is not a problem].

We can salvage a counting argument. But it needs to be a little subtle. And it's all about the comments, not the code.

Suppose a neural network has 1 megabyte of memory. To slightly oversimplify, lets say it can represent a python file of 1 megabyte. 

One option is for the network to store a giant lookup table. Lets say the network needs half a megabyte to store the training data in this table. This leaves the other half free to be any rubbish. Hence around $2^{4,000,000}$ possible networks.

The other option is for the network to implement a simple algorithm, using up only 1kb. Then the remaining 999kb can be used for gibberish comments. This gives $2^{7,992,000}$ possible networks. Which is a lot more. 

The comments can be any form of data that doesn't show up during training. Whether it can show up in other circumstances or is a pure comment doesn't matter to the training dynamics. 

If the line between training and test is simple, there isn't a strong counting argument against nonsense showing up in test. 

But programs that go 

    if in_traning():

        return sensible_algorithm()

    else:

        return "random nonsense goes here"

Have to pay the extra cost of an "in_training" function that returns true in training. If the test data is similar to training, the cost of a step that returns false in test can be large. This is assuming that there is a unique sensible algorithm. 

The reason SDG doesn't overfit large neural networks is probably because of various measures specifically intended to prevent overfitting, like weight penalties, dropout, early stopping, data augmentation + noise on inputs, and large enough learning rates that prevent convergence. If you didn't do those, running SDG to parameter convergence would probably cause overfitting. Furthermore, we test networks on validation datasets on which they weren't trained, and throw out the networks that don't generalize well to the validation set and start over (with new hyperparameters, architectures or parameter initializations). These measures bias us away from producing and especially deploying overfit networks.

Similarly, we might expect scheming without specific measures to prevent it. What could those measures look like? Catching scheming during training (or validation), and either heavily penalizing it, or fully throwing away the network and starting over? We could also validate out-of-training-distribution. Would networks whose caught scheming has been heavily penalized or networks selected for not scheming during training (and validation) generalize to avoid all (or all x-risky) scheming? I don't know, but it seems more likely than counting arguments would suggest.

More generally, John Miller and colleagues have found training performance is an excellent predictor of test performance, even when the test set looks fairly different from the training set, across a wide variety of tasks and architectures.

Seems like figure 1 from Miller et al is a plot of test performance vs. "out of distribution" test performance. One might expect plots of training performance vs. "out of distribution" test performance to have more spread.

To goal realism vs goal reductionism, I would say: why not both?

I think that really highly capable AGI is likely to have both heuristics and behaviors that come from training and also internal thought processes, maybe done by LLM or LLM-like module or directly from the more complex network. This process would incorporate having some preferences and hence goals (even if temporary, changed between tasks).

I wouldn't say that the presented "counting argument" is a "central reason". The central reason is an a priori notion that if "x can be achieved by scheming" someone who wants x will scheme

A point about counting arguments that I have not seen made elsewhere (although I may have missed it!).

The failure of the counting argument that SGD should result in overfitting is not a valid countexample! There is a selection bias here - the only reason we are talking about SGD is *because* it is a good learning algorithm that does not overfit. It could well still be true that almost all counting arguments are true about almost all learning algorithms. The fact that SGD does generalises well is an exception *by design*.

The principle fails even in these simple cases if we carve up the space of outcomes in a more fine-grained way. As a coin or a die falls through the air, it rotates along all three of its axes, landing in a random 3D orientation. The indifference principle suggests that the resting states of coins and dice should be uniformly distributed between zero and 360 degrees for each of the three axes of rotation. But this prediction is clearly false: dice almost never land standing up on one of their corners, for example.

The only way I can parse this is that you are conflating (1) the position of a dice/coin when it makes contact with the ground and (2) its position when it stabilizes/[comes to rest]. A dice/coin can be in any position when it touches the ground but a vast majority of those are unstable, so it doesn't remain in it for long. 

The LessWrong Review [? · GW] runs every year to select the posts that have most stood the test of time. This post is not yet eligible for review, but will be at the end of 2025. The top fifty or so posts are featured prominently on the site throughout the year.

Hopefully, the review is better than karma at judging enduring value. If we have accurate prediction markets on the review results, maybe we can have better incentives on LessWrong today. Will this post make the top fifty?

The indifference principle is making the mistake of using a uniform prior, when a true bayesian uses the Jeffreys prior

We can also construct an analogous simplicity argument for overfitting:

Overfitting networks are free to implement a very simple function— like the identity function or a constant function— outside the training set, whereas generalizing networks have to exhibit complex behaviors on unseen inputs. Therefore overfitting is simpler than generalizing, and it will be preferred by SGD.

Prima facie, this parody argument is about as plausible as the simplicity argument for scheming. Since its conclusion is false, we should reject the argumentative form on which it is based.

As far as I understood people usually talk about simplicity biases based on the volume of basins in parameter space. So the response would be that overfitting takes up more parameters than other (probably smaller desciption length) algorithms and therefore has smaller basins.

I'm curious if you endore or reject this way of defining simplicity based on the size of basins of a set of similar algorithms?

The way I'm currently thinking about this is:

1. Assume we are training end to end on tasks that require our network to do deep reasoning that requires multiple steps and high frequency functions for generating dramatically new outputs based on updated understanding of science etc (We are not monitoring the CoT or using a large net that emulates CoT internally without good interpretability).
2. Then the basins of the schemers that use the least parameters are large parts of the parameter space. The basins of harmless nets with few parameters are large parts as well. Gradient descent will select the one that is larger.
3. I don't understand gradient descent inductive biases well enough to have strong intuitions which would be larger. So I end up feeling something like each could happen, I'd bet 60% the least parameter schemers is larger since there's maybe slightly less space for encoding of the harmlessness needed. In that case I'd expect 99%+ probability of a schemer. In the harmless basins are larger case 99%+ of a harmless model.

I suppose this isn't exactly a counting argument, because I think that evidence about inductive biases will quickly overcome any such argument and I'm agnostic what evidence I will recieve since I'm not very knowledgable about it and other people seem to disagree a bunch.

Is my reasoning here flawed in some obvious way?

Also I appreciated the example of the cortices doing reasonably intelligent stuff without seemingly doing any scheming which makes me more hopeful an AGI system with interpretable CoT made up of a bunch of cortex level subnets with some control techniques would be sufficient to strongly accelerate the construction of a global xrisk defense system.

I buy the argument that scheming won't happen conditionally on the fact that we don't allow much slack between different optimisation steps. As Quentin mentions in his AXRP podcast episode, SGD doesn't have close to the same level of slack that, for example, cultural evolution allowed. (See the entire free energy of optimisation debate here from before, can't remember the post names ;/) Iff that holds, then I don't see why the inner behaviour should diverge from what the outer alignment loop specifies.

I do, however, believe that ensuring that this is true by specifying the right outer alignment loop as well as the right deployment environment is important to ensure that slack is minimised at all points along the chain so that misalignment is avoided everywhere.

If we catch deception in training, we will be ok. If we catch actors that might create deceptive agents in training then we will be ok. If we catch states developing agents to do this or defense>offense then we will be ok. I do not believe that this happens by default.

I think this is an excellent post. I really liked the insight about the mechanisms (and mistakes) shared by the counting arguments behind AI doom and behind "deep learning surely won't generalize." Thank you for writing this; these kinds of loose claims have roamed freely for far too long.

EDIT: Actually this post is weaker than a draft I'd read. I still think it's good, but missing some of the key points I liked the most. And I'm not on board with all of the philosophical claims about e.g. generalized objections to the principle of indifference (in part because I don't understand them).