Senior research analyst at Open Philanthropy. Recently completed a doctorate in philosophy at the University of Oxford. Opinions my own.
Joe Carlsmith
Karma: 3,759
Mostly personal interest on my part (I was working on a blog post on the topic, now up), though I do think that the topic has broader relevance.
I really like this post. It’s a crisp, useful insight, made via a memorable concrete example (plus a few others), in a very efficient way. And it has stayed with me.
(Partly re-hashing my response from twitter.)
I’m seeing your main argument here as a version of what I call, in section 4.4, a “speed argument against schemers”—e.g., basically, that SGD will punish the extra reasoning that schemers need to perform.
(I’m generally happy to talk about this reasoning as a complexity penalty, and/or about the params it requires, and/or about circuit-depth—what matters is the overall “preference” that SGD ends up with. And thinking of this consideration as a different kind of counting argument *against* schemers seems like it might well be a productive frame. I do also think that questions about whether models will be bottlenecked on serial computation, and/or whether “shallower” computations will be selected for, are pretty relevant here, and the report includes a rough calculation in this respect in section 4.4.2 (see also summary here).)
Indeed, I think that maybe the strongest single argument against scheming is a combination of
“Because of the extra reasoning schemers perform, SGD would prefer non-schemers over schemers in a comparison re: final properties of the models” and
“The type of path-dependence/slack at stake in training is such that SGD will get the model that it prefers overall.”
My sense is that I’m less confident than you in both (1) and (2), but I think they’re both plausible (the report, in particular, argues in favor of (1)), and that the combination is a key source of hope. I’m excited to see further work fleshing out the case for both (including e.g. the sorts of arguments for (2) that I took you and Nora to be gesturing at on twitter—the report doesn’t spend a ton of time on assessing how much path-dependence to expect, and of what kind).
Re: your discussion of the “ghost of instrumental reasoning,” “deducing lots of world knowledge ‘in-context,’ and “the perspective that NNs will ‘accidentally’ acquire such capabilities internally as a convergent result of their inductive biases”—especially given that you only skimmed the report’s section headings and a small amount of the content, I have some sense, here, that you’re responding to other arguments you’ve seen about deceptive alignment, rather than to specific claims made in the report (I don’t, for example, make any claims about world knowledge being derived “in-context,” or about models “accidentally” acquiring flexible instrumental reasoning). Is your basic thought something like: sure, the models will develop flexible instrumental reasoning that could in principle be used in service of arbitrary goals, but they will only in fact use it in service of the specified goal, because that’s the thing training pressures them to do? If so, my feeling is something like: ok, but a lot of the question here is whether using the instrumental reasoning in service of some other goal (one that backchains into getting-reward) will be suitably compatible with/incentivized by training pressures as well. And I don’t see e.g. the reversal curse as strong evidence on this front.
Re: “mechanistically ungrounded intuitions about ‘goals’ and ‘tryingness’”—as I discuss in section 0.1, the report is explicitly setting aside disputes about whether the relevant models will be well-understood as goal-directed (my own take on that is in section 2.2.1 of my report on power-seeking AI here). The question in this report is whether, conditional on goal-directedness, we should expect scheming. That said, I do think that what I call the “messyness” of the relevant goal-directedness might be relevant to our overall assessment of the arguments for scheming in various ways, and that scheming might require an unusually high standard of goal-directedness in some sense. I discuss this in section 2.2.3, on “‘Clean’ vs. ‘messy’ goal-directedness,” and in various other places in the report.
Re: “long term goals are sufficiently hard to form deliberately that I don’t think they’ll form accidentally”—the report explicitly discusses cases where we intentionally train models to have long-term goals (both via long episodes, and via short episodes aimed at inducing long-horizon optimization). I think scheming is more likely in those cases. See section 2.2.4, “What if you intentionally train the model to have long-term goals?” That said, I’d be interested to see arguments that credit assignment difficulties actively count against the development of beyond-episode goals (whether in models trained on short episodes or long episodes) for models that are otherwise goal-directed. And I do think that, if we could be confident that models trained on short episodes won’t learn beyond-episode goals accidentally (even irrespective of mundane adversarial training—e.g., that models rewarded for getting gold coins on the episode would not learn a goal that generalizes to caring about gold coins in general, even prior to efforts to punish it for sacrificing gold-coins-on-the-episode for gold-coins-later), that would be a significant source of comfort (I discuss some possible experimental directions in this respect in section 6.2).
Hi David—it’s true that I don’t engage your paper (there’s a large literature on infinite ethics, and the piece leaves out a lot of it—and I’m also not sure I had seen your paper at the time I was writing), but re: your comments here on the ethical relevance of infinities: I discuss the fact that the affectable universe is probably finite—“current science suggests that our causal influence is made finite by things like lightspeed and entropy”—in section 1 of the essay (paragraph 5), and argue that infinites are still
relevant in practice due to (i) the remaining probability that current physical theories are wrong about our causal influence (and note also related possibilities like having causal influence on whether you go to an infinite-heaven/hell etc, a la pascal) and (ii) due to the possibility of having infinite acausal influence conditional on various plausible-in-my-view decision theories, and
relevant to ethical theory, even if not to day-to-day decision-making, due to (a) ethical theory generally aspiring to cover various physically impossible cases, and (b) the existence of intuitions about infinite cases (e.g., heaven > hell, pareto, etc) that seem prima facie amenable to standard attempts at systematization.
Glad you liked it :). I haven’t spent much time engaging with UDASSA — or with a lot other non-SIA/SSA anthropic theories — at this point, but UDASSA in particular is on my list to understand better. Here I wanted to start with the first-pass basics.
Hi Daniel,
Thanks for reading. I think estimating p(doom) by different dates (and in different take-off scenarios) can be a helpful consistency check, but I disagree with your particular “sanity check” here—and in particular, premise (2). That is, I don’t think that conditional on APS-systems becoming possible/financially feasible by 2035, it’s clear that we should have at least 50% on doom (perhaps some of disagreement here is about what it takes for the problem to be “real,” and to get “solved”?). Nor do I see 10% on “Conditional it being both possible and strongly incentivized to build APS systems, APS systems will end up disempowering approximately all of humanity” as obviously overconfident (though I do take some objections in this vein seriously). I’m not sure exactly what “10% on nuclear war” analog argument you have in mind: would you be able to sketch it out, even if hazily?
Rohin is correct. In general, I meant for the report’s analysis to apply to basically all of these situations (e.g., both inner and outer-misaligned, both multi-polar and unipolar, both fast take-off and slow take-off), provided that the misaligned AI systems in question ultimately end up power-seeking, and that this power-seeking leads to existential catastrophe.
It’s true, though, that some of my discussion was specifically meant to address the idea that absent a brain-in-a-box-like scenario, we’re fine. Hence the interest in e.g. deployment decisions, warning shots, and corrective mechanisms.
Cool, these comments helped me get more clarity about where Ben is coming from.
Ben, I think the conception of planning I’m working with is closest to your “loose” sense. That is, roughly put, I think of planning as happening when (a) something like simulations are happening, and (b) the output is determined (in the right way) at least partly on the basis of those simulations (this definition isn’t ideal, but hopefully it’s close enough for now). Whereas it sounds like you think of (strict) planning as happening when (a) something like simulations are happening, and (c) the agent’s overall policy ends up different (and better) as a result.
What’s the difference between (b) and (c)? One operationalization could be: if you gave an agent input 1, then let it do its simulations thing and produce an output, then gave it input 1 again, could the agent’s performance improve, on this round, in virtue of the simulation-running that it did on the first round? On my model, this isn’t necessary for planning; whereas on yours, it sounds like it is?
Let’s say this is indeed a key distinction. If so, let’s call my version “Joe-planning” and your version “Ben-planning.” My main point re: feedforward neural network was that they could do Joe-planning in principle, which it sounds like you think at least conceivable. I agree that it seems tough for shallow feedforward networks to do much of Joe-planning in practice. I also grant that when humans plan, they are generally doing Ben-planning in addition to Joe-planning (e.g., they’re generally in a position to do better on a given problem in virtue of having planned about that same problem yesterday).
Seems like key questions re: the connection to AI X-risk include:
Is there reason to think a given type of planning especially dangerous and/or relevant to the overall argument for AI X-risk?
Should we expect that type of planning to be necessary for various types of task performance?
Re: (1), I do think Ben-planning poses dangers that Joe-planning doesn’t. Notably, Ben planning does indeed allow a system to improve/change its policy “on its own” and without new data, whereas Joe planning need not — and this seems more likely to yield unexpected behavior. This seems continuous, though, with the fact that a Ben-planning agent is learning/improving its capabilities in general, which I flag separately as an important risk factor.
Another answer to (1), suggested by some of your comments, could appeal to the possibility that agents are more dangerous when you can tweak a single simple parameter like “how much time they have to think” or “search depth” and thereby get better performance (this feels related to Eliezer’s worries about “turning up the intelligence dial” by “running it with larger bounds on the for-loops”). I agree that if you can just “turn up the intelligence dial,” that is quite a bit more worrying than if you can’t — but I think this is fairly orthogonal to the Joe-planning vs. Ben-planning distinction. For example, I think you can have Joe-planning agents where you can increase e.g. their search depth by tweaking a single parameter, and you can have Ben-planning agents where the parameters you’d need to tweak aren’t under your control (or the agent’s control), but rather are buried inside some tangled opaque neural network you don’t understand.
The central reason I’m interested in Joe-planning, though, is that I think the instrumental convergence argument makes the most sense if Joe-planning is involved—e.g., if the agent is running simulations that allow it to notice and respond to incentives to seek power (there are versions of the argument that don’t appeal to Joe-planning, but I like these less—see discussion in footnote 87 here). It’s true that you can end up power-seeking-ish via non-Joe-planning paths (for example, if in training you developed sphex-ish heuristics that favor power-seeking-ish actions); but when I actually imagine AI systems that end up power-seeking, I imagine it happening because they noticed, in the course of modeling the world in order to achieve their goals, that power-seeking (even in ways humans wouldn’t like) would help.
Can this happen without Ben-planning? I think it can. Suppose, for example, that none of your previous Joe-planning models were power-seeking. Then, you train a new Joe-planner, who can run more sophisticated simulations. On some inputs, this Joe-planner realizes that power-seeking is advantageous, and goes for it (or starts deceiving you, or whatever).
Re: (2), for the reasons discussed in section 3.1, I tend to see Joe-planning as pretty key to lots of task-performance — though I acknowledge that my intuitions are surprised by how much it looks like you can do via something more intuitively “sphexish.” And I acknowledge that some of those arguments may apply less to Ben-planning. I do think this is some comfort, since agents that learn via planning are indeed scarier. But I am separately worried that ongoing learning will be very useful/incentivized, too.
Thanks for explaining where you’re coming from.
Yet I experience that computation as the qualia of “blueness.” How can that be? How can any computation of any kind create, or lead to qualia of any kind? You can say that it is just a story my brain is telling me that “I am seeing blue.” I must not understand what is being claimed, because I agree with it and yet it doesn’t remove the problem at all. Why does that story have any phenomenology to it? I can make no sense of the claim that it is an illusion.
As I understand it, the idea would be that, as weird as it may sound, there isn’t any phenomenology to it. Rather: according to the story that your brain is telling, there is some phenomenology to it. But there isn’t. That is, your brain’s story doesn’t create, lead to, or correlate with phenomenal blueness; rather, phenomenal blueness is something that the story describes, but which doesn’t exist, in the same way that a story can describe unicorns without bringing them to life.
Thanks for these comments.
that suggests that CrystalNights would work, provided we start from something about as smart as a chimp. And arguably OmegaStar would be about as smart as a chimp—it would very likely appear much smarter to people talking with it, at least.
“starting with something as smart as a chimp” seems to me like where a huge amount of the work is being done, and if Omega-star --> Chimp-level intelligence, it seems a lot less likely we’d need to resort to re-running evolution-type stuff. I also don’t think “likely to appear smarter than a chimp to people talking with it” is a good test, given that e.g. GPT-3 (2?) would plausibly pass, and chimps can’t talk.
“Do you not have upwards of 75% credence that the GPT scaling trends will continue for the next four OOMs at least? If you don’t, that is indeed a big double crux.”—Would want to talk about the trends in question (and the OOMs—I assume you mean training FLOP OOMs, rather than params?). I do think various benchmarks are looking good, but consider e.g. the recent Gopher paper:
On the other hand, we find that scale has a reduced benefit for tasks in the Maths, Logical Reasoning, and Common Sense categories. Smaller models often perform better across these categories than larger models. In the cases that they don’t, larger models often don’t result in a performance increase. Our results suggest that for certain flavours of mathematical or logical reasoning tasks, it is unlikely that scale alone will lead to performance breakthroughs. In some cases Gopher has a lower performance than smaller models– examples of which include Abstract Algebra and Temporal Sequences from BIG-bench, and High School Mathematics from MMLU.
(Though in this particular case, re: math and logical reasoning, there are also other relevant results to consider, e.g. this and this.)
It seems like “how likely is it that continuation of GPT scaling trends on X-benchmarks would result in APS-systems” is probably a more important crux, though?
Re: your premise 2, I had (wrongly, and too quickly) read this as claiming “if you have X% on +12 OOMs, you should have at least 1/2*X% on +6 OOMs,” and log-uniformity was what jumped to mind as what might justify that claim. I have a clearer sense of what you were getting at now, and I accept something in the vicinity if you say 80% on +12 OOMs (will edit accordingly). My +12 number is lower, though, which makes it easier to have a flatter distribution that puts more than half of the +12 OOM credence above +6.
The difference between 20% and 50% on APS-AI by 2030 seems like it could well be decision-relevant to me (and important, too, if you think that risk is a lot higher in short-timelines worlds).
I appreciated this, especially given how challenging this type of exercise can be. Thanks for writing.
I agree that it’s a useful heuristic, and the “baby steps” idealization you describe seems to me like a reasonable version to have in mind and to defer to over ourselves (including re: how to continue idealizing). I also appreciate that your 2012 post actually went through sketched a process in that amount of depth/specificity.
Cool (though FWIW, if you’re going to lean on the notion of policies being aligned with humans, I’d be inclined to define that as well, in addition to defining what it is for agents to be aligned with humans. But maybe the implied definition is clear enough: I’m assuming you have in mind something like “a policy is aligned with humans if an agent implementing that policy is aligned with humans.”).
Regardless, sounds like your definition is pretty similar to: “An agent is intent aligned if its behavioral objective is such that an arbitrarily powerful and competent agent pursuing this objective to arbitrary extremes wouldn’t act in ways that humans judge bad”? If you see it as importantly different from this, I’d be curious.
Thanks for writing this up. Quick question re: “Intent alignment: An agent is intent aligned if its behavioral objective is aligned with humans.” What does it mean for an objective to be aligned with humans, on your view? You define what it is for an agent to be aligned with humans, e.g.: “An agent is aligned (with humans) if it doesn’t take actions that we would judge to be bad/problematic/dangerous/catastrophic.” But you don’t say explicitly what it is for an objective to be aligned: I’m curious if you have a preferred formulation.
Is it something like: “the behavioral objective is such that, when the agent does ‘well’ on this objective, the agent doesn’t act in a way we would view as bad/problematic/dangerous/catastrophic.” If so, it seems like a lot might depend on exactly how “well” the agent does, and what opportunities it has in a given context. That is, an “aligned” agent might not stay aligned if it becomes more powerful, but continues optimizing for the same objective (for example, a weak robot optimizing for beating me at chess might be “aligned” because it only focuses on making good chess moves, but a stronger one might not be, because it figures out how to drug my tea). Is that an implication you’d endorse?
Or is the thought something like: “the behavioral objective such that, no matter how powerfully the agent optimizes for it, and no matter its opportunities for action, it doesn’t take actions we would view as bad/problematic/dangerous/catastrophic”? My sense is that something like this is often the idea people have in mind, especially in the context of anticipating things like intelligence explosions. If this is what you have in mind, though, maybe worth saying so explicitly, since intent alignment in this sense seems like a different constraint than intent alignment in the sense of e.g. “the agent’s pursuit of its behavioral objective does not in fact give rise to bad actions, given the abilities/contexts/constraints that will in fact be relevant to its behavior.”
The point of that part of my comment was that insofar as part of Nora/Quintin’s response to simplicity argument is to say that we have active evidence that SGD’s inductive biases disfavor schemers, this seems worth just arguing for directly, since even if e.g. counting arguments were enough to get you worried about schemers from a position of ignorance about SGD’s inductive biases, active counter-evidence absent such ignorance could easily make schemers seem quite unlikely overall.
There’s a separate question of whether e.g. counting arguments like mine above (e.g., “A very wide variety of goals can prompt scheming; By contrast, non-scheming goals need to be much more specific to lead to high reward; 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; 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”) do enough evidence labor to privilege schemers as a hypothesis at all. But that’s the question at issue in the rest of my comment. And in e.g. the case of “there are 1000 chinese restaurants in this, and only ~100 non-chinese restaurants,” the number of chinese restaurants seems to me like it’s enough to privilege “Bob went to a chinese restaurant” as a hypothesis (and this even without thinking that he made his choice by sampling randomly from a uniform distribution over restaurants). Do you disagree in that restaurant case?
The probability I give for scheming in the report is specifically for (goal-directed) models that are trained on diverse, long-horizon tasks (see also Cotra on “human feedback on diverse tasks,” which is the sort of training she’s focused on). I agree that various of the arguments for scheming could in principle apply to pure pre-training as well, and that folks (like myself) who are more worried about scheming in other contexts (e.g., RL on diverse, long-horizon tasks) have to explain what makes those contexts different. But I think there are various plausible answers here related to e.g. the goal-directedness, situational-awareness, and horizon-of-optimization of the models in questions (see e.g. here for some discussion, in the report, for why goal-directed models trained on longer episode seem more likely to scheme; and see here for discussion of why situational awareness seems especially likely/useful in models performing real-world tasks for you).
Re: “goal optimization is a good way to minimize loss in general”—this isn’t a “step” in the arguments for scheming I discuss. Rather, as I explain in the intro to report, the arguments I discuss condition on the models in question being goal-directed (not an innocuous assumptions, I think—but one I explain and argue for in section 3 of my power-seeking report, and which I think important to separate from questions about whether to expect goal-directed models to be schemers), and then focus on whether the goals in question will be schemer-like.
I agree that AIs only optimizing for good human ratings on the episode (what I call “reward-on-the-episode seekers”) have incentives to seize control of the reward process, that this is indeed dangerous, and that in some cases it will incentivize AIs to fake alignment in an effort to seize control of the reward process on the episode (I discuss this in the section on “non-schemers with schemer-like traits”). However, I also think that reward-on-the-episode seekers are also substantially less scary than schemers in my sense, for reasons I discuss here (i.e., reasons to do with what I call “responsiveness to honest tests,” the ambition and temporal scope of their goals, and their propensity to engage in various forms of sandbagging and what I call “early undermining”). And this especially for reward-on-the-episode seekers with fairly short episodes, where grabbing control over the reward process may not be feasible on the relevant timescales.
Agents that end up intrinsically motivated to get reward on the episode would be “terminal training-gamers/reward-on-the-episode seekers,” and not schemers, on my taxonomy. I agree that terminal training-gamers can also be motivated to seek power in problematic ways (I discuss this in the section on “non-schemers with schemer-like traits”), but I think that schemers proper are quite a bit scarier than reward-on-the-episode seekers, for reasons I describe here.
Really appreciated this sequence overall, thanks for writing.
Thanks for writing this—I’m very excited about people pushing back on/digging deeper re: counting arguments, simplicity arguments, and the other arguments re: scheming I discuss in the report. Indeed, despite the general emphasis I place on empirical work 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. But the report also discusses two arguments that don’t make this assumption – namely, the “training-game independent proxy goals story” (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.” 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). 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:
A very wide variety of goals can prompt scheming.
By contrast, non-scheming goals need to be much more specific to lead to high reward.
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.
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. 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). And I think they’re weak for other reasons too (in particular, the extra cognitive faff scheming involves 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 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:
Michael Huemer says that it’s sometimes OK to use the principle of indifference if you’re applying it to explanatorily fundamental variables.
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—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.
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.