Introduction

This review is part of a project with Joe Collman and Jérémy Perret to try to get as close as possible to peer review when giving feedback on the Alignment Forum. Our reasons behind this endeavor are detailed in our original post asking for suggestions of works to review; but the gist is that we hope to bring further clarity to the following questions:

  • How many low-hanging fruits in terms of feedback can be plucked by getting into a review mindset and seeing the review as part of one’s job?
  • Given the disparate state of research in AI Alignment, is it possible for any researcher to give useful feedback on any other research work in the field?
  • What sort of reviews are useful for AI Alignment research?

Instead of thinking about these questions in the abstract, we simply make the best review we can, which answers some and gives evidence for others.

In this post, we review Fun with +12 OOMs of Compute by Daniel Kokotajlo. We start by summarizing the work, to ensure that we got it right. Then we review the value of the post in itself -- that it, by admitting its hypotheses. We follow by examining the relevance of the work to the field, which hinges on the hypotheses it uses. The last two sections respectively propose follow-up work that we think would be particularly helpful, and discuss how this work fits into the framing of AI Alignment research proposed here by one of us.

This post was written by Adam; as such, even if both Joe and Jérémy approve of its content, it’s bound to be slightly biased towards Adam’s perspective.

Summary

The post attempts to operationalize debates around timelines for Transformative AI using current ML techniques in two ways: by proposing a quantity of resources (compute, memory, bandwidth, everything used in computing) for which these techniques should create TAI with high probability (the +12 OOMs of the title), and by giving concrete scenarios of how the use of these resources could lead to TAI.

The operational number comes from Ajeya Cotra’s report on TAI timelines, and isn’t really examined or debated in the post. What is expanded upon are the scenarios proposed for leveraging these added resources.

  • OmegaStar, a bigger version of AlphaStar trained on every game in the Steam library, as well as on language-related “games” like “predict the next word in a web page” or “make a user engaged as a chatbot”. Note that these language-related games are played at the scale of the entire internet.
  • Amp(GPT-7), a scaled-up GPT model that is then amplified to be able to decompose any tasks into subtasks it can delegate to copies of itself, recursively.
  • Crystal Nights, a simulation of the whole of evolution, but done smartly enough (for example by selecting for abstract intelligence) to reduce the compute needed to fit within the budget of +12 OOMs
  • Skunkworks, a STEM AI system that uses incredibly detailed simulations to iterate over millions of design variations and test them, all without having to build the prototypes.
  • Neuromorph, a learning process to train brain-like models, starting with running the best brain model available right now at the correct biological scale, and then filling in the blanks and iterating on this process using standard ML techniques (like SGD).

In light of these scenarios, Daniel then argues that if one takes them seriously and considers their results as likely to be TAI, one should put the bulk of its probability mass about when TAI will happen at the point where such increase of compute is reached, or before. In comparison, Ajeya’s model from her report puts the median of her distribution at this point, which results in having quite a lot of probability mass after this point.

Daniel thus concludes that an important crux of timeline debates is how people think about scenarios like the ones he presented, and asks for proponents of long timelines to defend their positions along this line for a more productive discussion.

Does the post succeed on its own terms?

This work relies on one big hypothesis: we can get +12 OOMs of compute and other relevant resources in a short enough time frame to warrant the label “short timelines” to the scenario developed here. We found issues with this hypothesis, at least with how it is currently stated and defended. But before detailing those, we start by admitting this assumption and examining how the post fares in that context.

All three of us found Daniel’s scenarios worrying, in terms of potential for TAI. We also broadly agree with Daniel’s global point that the risk of TAI from these scenarios probably implies a shift in the probability mass that lies after this point to somewhere closer to this point (with the caveat that none of us actually studied Ajeya’s report in detail).

Thus the work makes its point successfully: why that amount of additional compute and resources might be enough for TAI, and what it should imply for the most detailed model that we have about TAI timelines.

That being said, we feel that each scenario isn’t as fleshed out as it could be for maximum convincingness. They tend to feel like “if you can apply this technique to a bigger model with every dataset in existence, it would become transformative”. Although that’s an intuition we are sympathetic to, there are many caveats that -- ironically -- the references deal with but Daniel doesn't discuss explicitly or in detail.

Some examples:

  • With OmegaStar, one of us thought he remembered that AlphaStar’s reward function was hand shaped, and so humans might prove a bottleneck. A bit more research revealed that AlphaStar used imitation learning to learn a reward function from human games -- an approach that solves at least some of the problems with scaling to “all games in the steam” library.
    Since the issue of humans as bottlenecks in training is pretty relevant, it would have been helpful to describe this line of thought in the post.
  • With Amp(GPT-7), we wondered why GPT-7 and not GPT-8 or GPT-9. More concretely, why should we expect progress on the tasks that are vital for Daniel’s scenario? We don’t have convincing arguments (as far as we know) for arguing that GPT-N will be good at a task for which GPT-3 showed no big improvement over the state of the art. So the tasks for which we can expect such a jump are the ones GPT-3 (or previous GPT) made breakthrough at.
    Daniel actually relies on such tasks, as shown in his reference to this extrapolation post that goes into more detail on this reasoning, and what we can expect from future versions of GPT models. But he fails to make this important matter explicit enough to help us think through the argument and decide whether we’re convinced. Instead the only way to find out is either to know already that line of reasoning, or to think very hard about his post and the references in that spec way specifically.

In essence, we find that in this post, almost all the information we would want for thinking about these scenarios exists in the references, but isn’t summarized in nearly enough detail in the post itself to make reading self-contained. Of course, we can’t ask of Daniel that he explains every little point about his references and assumptions. Yet we still feel like he could probably do a better job, given that he already has all the right pointers (as his references show).

Relevance of the post to the field

The relevance of this work appears to rely mostly on the hypothesis that the +12 OOMs of magnitude of compute and all relevant resources could plausibly be obtained in a short time frame. If not, then the arguments made by Daniel wouldn’t have the consequence of making people have shorter timelines.

The first problem we noted was that this hypothesis isn’t defended anywhere in the post. Arguments for it are not even summarized. This in turns means that if we read this post by itself, without being fully up to date with its main reference, there is no reason to update towards shorter timelines.

Of course, not having a defense of this position is hardly strong evidence against the hypothesis. Yet we all agreed that it was counterintuitive enough that the burden of proving at least plausibility laid on people defending it.

Another issue with this hypothesis is that it assumes, under the hood, exactly the kind of breakthrough that Daniel is trying so hard to remove from the software side. Our cursory look at Ajeya’s report (focused on the speed-up instead of the cost reduction) showed that almost all the hardware improvement forecasted came from breakthrough into currently not working (or not scalable) hardware. Even without mentioning the issue that none of these technologies look like they can provide anywhere near the improvement expected, there is still the fact that getting these orders of magnitude of compute requires many hardware breakthroughs, which contradicts Daniel’s stance on not needing new technology or ideas, just scaling.

(Very important note: we haven’t studied Ajeya’s report in full. It is completely possible that our issues are actually addressed somewhere in it, and that the full-fledged argument for why this increase in compute will be possible looks convincing. Also, she herself writes that at least the hardware forecasting part looks under-informed to her. We’re mostly highlighting the same problem as in the previous section -- Daniel not summarizing enough the references that are crucial to his point -- with the difference that this time, when looking quickly at the reference, we failed to find convincing enough arguments).

Lastly, Daniel edited his post to add that the +12 OOMs increase applied to every relevant resource, like memory and bandwidth. But bandwidth for example is known to increase far slower than compute. We understand that this edit was a quick one made to respond to critics that some of his scenarios would require a lot of other resources, but it considerably weakens his claim by making his hypothesis almost impossible to satisfy. That is, even if we could see an argument for that much short term increase in compute, a similar argument for bandwidth looks much less probable.

One counterargument is that the scenarios don’t need that much bandwidth, which sounds reasonable. But then what’s missing is a ballpark estimate of how much each type of resource is needed, and an argument for why that increase might be done in a short timeline scale.

To summarize, how we interpret this work depends on an hypothesis that is neither obvious nor defended in an easy-to-find argument. As such, we are unable to really judge what should be done following the argument in this post. If the hypothesis is indeed plausible and defended, then we feel that Daniel is making a good point for updating timelines towards shorter ones. If the hypothesis cannot be plausibly defended, then this post might even have the opposite effect: if the most convincing scenarios we have for TAI using modern ML looks like they require an amount of compute we won’t get anytime soon, some might update towards longer timelines (at least compared to Daniel’s very short ones).

Follow-up work we would be excited about

Most of our issues with this post come from its main premise. As such, we would be particularly excited by any further research arguing for it, be it by extracting the relevant part from sources like Ajeya’s report, or by making a whole new argument.

If the argument can only be made for a smaller increase in compute, then looking for scenarios using this much would be the obvious next step.

Less important but still valuable, fleshing out the scenarios and operationalizing them as much as possible (for example with the requirements in the various other resources, or the plausible bottlenecks) would be a good follow-up.

Fitness with framing on AI Alignment research

Finally, how does this work fit in the framing of AI Alignment research proposed by one of us (Adam) here? To refresh memories, this framing splits AI Alignment research into categories around 3 aspects of the field: studying which AIs we’re most likely to build, and thus which one we should try to align; studying what well-behaved means for AIs, that is, what we want; and based on at least preliminary answers from the previous two, studying how to solve the problem of making that kind of AIs well-behaved in that way.

Adam finds that Daniel’s post fits perfectly in the first category: it argues for the fact that scaled up current AI (à la prosaic AGI) is the kind of AI we should worry about and make well-behaved. And similarly, this post makes no contribution to the other two categories.

On the other hand, the other two reviewers are less convinced that this fully captures Daniel’s intentions. For example, they argue that it’s not that intuitive that an argument about timelines (when we’re going to build AI) fits into the “what kind of AI we’re likely to build” part. Or that the point of the post looks more like a warning for people expecting a need for algorithmic improvement than a defense of a specific kind of AI we’re likely to build. 

What do you think?

Conclusion

We find that this post is a well-written argument for short timelines, painting a vivid picture of possible transformative AIs with current ML technology, and operationalizing a crux for the timeline debate. That being said, the post also suffers from never defending his main premise, and not pointing to a source from which it can be extracted without a tremendous investment of work.

In that condition, we can’t be confident about how this work will be relevant to the field. But additional research and argument about that premise would definitely help convince us that this is crucial work for AI Alignment.

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18 comments, sorted by Highlighting new comments since Today at 3:39 AM
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Thanks for doing this! I'm honored that you chose my post to review and appreciate all the thought you put into this.

I have one big objection: The thing you think this post assumes, this post does not actually assume. In fact, I don't even believe it! In more detail:

You say:

The relevance of this work appears to rely mostly on the hypothesis that the +12 OOMs of magnitude of compute and all relevant resources could plausibly be obtained in a short time frame. If not, then the arguments made by Daniel wouldn’t have the consequence of making people have shorter timelines.

I disagree. This post works within Ajeya's framework, which works as follows: First, we come up with a distribution over how much extra compute we'd need given 2020's levels of knowledge. Then, we come up with projections for how knowledge will improve over time, and how compute will increase over time. Then we combine all three to get our timelines. (Compute increasing can be thought of as moving us rightward through the distribution, and knowledge improving can be thought of as shifting the entire distribution leftward.)

Ajeya's distribution has its median at +12 OOMs. This corresponds to answering "50%" to my Question Two. If you instead answer something higher, then you (all else equal) must have shorter timelines, because you put more mass in the lower region. Now, you could put all that extra mass in, say, the region from +9 to +12 OOMs, and in that case your credence in short timelines wouldn't go up, because in the short term we aren't going to cross more than (say) 6 OOMs. This is why I had the "all else equal" qualifier. If your distribution over the next 12 OOMs looks like Ajeya's except that it totals to 80% instead of 50%, then (I calculate) the median of your AI timelines should be somewhere in the late 2030's.

To put it another way: I don't actually believe we will get to +12 OOMs of compute, or anywhere close, anytime soon. Instead, I think that if we had +12 OOMs, we would very likely get TAI very quickly, and then I infer from that fact that the probability of getting TAI in the next 6 OOMs is higher than it would otherwise be (if I thought that +12 OOMs probably wasn't enough, then my credence in the next 6 OOMs would be correspondingly lower).

To some extent this reply also partly addresses the concerns you raised about memory and bandwidth--I'm not actually saying that we actually will scale that much; I'm using what would happen if we magically did as an argument for what we should expect if we (non-magically) scale a smaller amount.

You're welcome!

To put it another way: I don't actually believe we will get to +12 OOMs of compute, or anywhere close, anytime soon. Instead, I think that if we had +12 OOMs, we would very likely get TAI very quickly, and then I infer from that fact that the probability of getting TAI in the next 6 OOMs is higher than it would otherwise be (if I thought that +12 OOMs probably wasn't enough, then my credence in the next 6 OOMs would be correspondingly lower).

To some extent this reply also partly addresses the concerns you raised about memory and bandwidth--I'm not actually saying that we actually will scale that much; I'm using what would happen if we magically did as an argument for what we should expect if we (non-magically) scale a smaller amount.

(Talking only for myself here)

Rereading your post after seeing this comment:

What I’ve done in this post is present an intuition pump, a thought experiment that might elicit in the reader (as it does in me) the sense that the probability distribution should have the bulk of its mass by the 10^35 mark.

I personally misread this, and understood "the bulk of its mass at the 10^35 mark". The correct reading is more in line with what you're saying here. That's probably a reason why I personnally focused on the +12 OOMs mark (I mean, that's also in the title).

So I agree we misunderstood some parts of your post, but I still think our issue remains. Except that instead of being about justifying +12 OOMs of magnitude in the short term, it becomes about justifying why the +12 OOMs examples should have any impact on, let's say, +6 OOMs.

I personally don't feel like your examples give me an argument  for anywhere but the +12 OOMs mark. That's where they live, and those examples seem to require that much compute, or still a pretty big amount of it. So reading your post makes me feel like I should have more probability mass at this mark or very close to it, but I don't see any reason to update the probability at the +6OOMs mark say.

And if the +12 OOMs looks really far, as it does in my point of view, then that definitely doesn't make me update towards shorter timelines.

Thanks! Well, I agree that I didn't really do anything in my post to say how the "within 12 OOMs" credence should be distributed. I just said: If you distribute it like Ajeya does except that it totals to 80% instead of 50%, you should have short timelines.

There's a lot I could say about why I think within 6 OOMs should have significant probability mass (in fact, I think it should have about as much mass as the 7-12 OOM range). But for now I'll just say this: If you agree with me re Question Two, and put (say) 80%+ probability mass by +12 OOMs, but you also disagree with me about what the next 6 OOMs should look like and think that it is (say) only 20%, then that means your distribution must look something like this:

Probability distribution over how many extra OOMs of compute we need given current ideas

EDIT to explain: Each square on this graph is a point of probability mass. The far-left square represents 1% credence in the hypothesis "It'll take 1 more OOM." The second-from the left represents "It'll take 2 more OOM." The third-from-the-left is a 3% chance it'll take 3 more OOM, and so on. The red region is the region containing the 7-12 OOM hypotheses.

Note that I'm trying to be as charitable as I can when drawing this! I only put 2% mass on the far right (representing "not even recapitulating evolution would work!"). This is what I think the probability distribution of someone who answered 80% to my Question Two should look like if they really really don't want to believe in short timelines. Even on this distribution, there's a 20% chance of 6 or fewer OOMs being enough given current ideas/algorithms/etc. (And hence, about a 20% chance of AGI/TAI/etc. by 2030, depending on how fast you think we'll scale up and how much algorithmic progress we'll make.)

And even this distribution looks pretty silly to me. Like, why is it so much more confident that 11 OOMs will be how much we need, than 13 OOMs? Given our current state of ignorance about AI, I think the slope should not be that steep.

Let me try to make an analogy with your argument.

Say we want to make X. What you're saying is "with 10^12 dollars, we could do it that way". Why on earth would I update at all whether it can be done with 10^6 dollars? If your scenario works with that amount, then you should have described it using only that much money. If it doesn't, then you're not providing evidence for the cheaper case.

Similarly here, if someone starts with a low credence on prosaic AGI, I can see how your arguments would make them put a bunch of probability mass close to +10^12 compute. But they have no reason to put probability mass anywhere far from that point, since the scenarios you give are tailored to that. And lacking an argument for why you can get that much compute in a short timeline, then they probably end up thinking that if prosaic AGI ever happens, it's probably after every other option. Which seems like the opposite of the point you're trying to make.

I'm not sure, but I think that's not how updating works? If you have a bunch of hypotheses (e.g. "It'll take 1 more OOM," "It'll take 2 more OOMs," etc.) and you learn that some of them are false or unlikely (only 10% chance of it taking more than 12" then you should redistribute the mass over all your remaining hypotheses, preserving their relative strengths. And yes I have the same intuition about analogical arguments too. For example, let's say you overhear me talking about a bridge being built near my hometown, and you wonder how many tons of steel it will cost. You don't know much about bridge construction so your uncertainty ranges over several orders of magnitude -- say, from 10^2 to 10^9 tons. Then you do some googling and discover that 450,000 tons is how much it took to build the longest bridge in the world. OK, so clearly it almost certainly won't take more than 10^5 tons to build the bridge being built near my hometown. What do you do with all the probability mass you used to have above 10^5? Do you pile it all up on 10^4 and 10^5? No, you redistribute it evenly. You DO come to have a higher credence that it will be merely 10^2 or 10^3 as a result of learning about the longest bridge in the world, because you are Bayesian and you are deleting falsified hypotheses and renormalizing.

Of course, real life updates are never that simple, because they involve more information than the pure "it won't be more than X." For example, the fact that I chose to write about 12 OOMs instead of 6 should be suspicious; it's evidence that 6 OOMs isn't enough (otherwise I would have chosen to write about 6, right?). Also, the stuff I said about what you could do with 12 OOMs may have also contained information about what you can't do with 6 -- for example, my calculations for Crystal Nights probably also serve as evidence that an only-6-OOM version of Crystal Nights wouldn't work. You probably didn't think it would, but if you did, then reading my Crystal Nights thing may have convinced you it wouldn't.

To the first suspicion I'll say: I had good reasons for writing about 12 rather than 6 which I am happy to tell you about if you like. To the second I'll say: YMMV, but it doesn't feel to me that the scenarios I sketched at 12 OOMs provide much evidence either way about what happens at 6 OOMs. It feels to me that they really can be mostly characterized as providing evidence that it won't take more than 12.

...

Independently of the above though, what do you think about my graph-based argument? In a sentence, the argument is: If you answer 80% to Question Two but still have <20% credence in TAIby2030, your distribution must look at least as spiky and steep as the red-blue one I sketched, but that's implausible because overconfident--it seems unjustified to have so much more credence in +11 OOMs than in +13.

...

Independently of the above, I'm happy to provide more inside-view reasons to take "within 6 OOMs" seriously. It just wasn't the focus of the post. You might be right that it should have been the focus of the post--but like I said, I had reasons.

About the update

You're right, that's what would happen with an update.

I think that the model I have in mind (although I hadn't explicitly thought about it until know), is something like a distribution over ways to reach TAI (capturing how probable it is that they're the first way to reach AGI), and each option comes with its own distribution (let's say over years). Obviously you can compress that into a single distribution over years, but then you lose the ability to do fine grained updating.

For example, I imagine that someone with relatively low probability that prosaic AGI will be the first to reach AGI, upon reading your post, would have reasons to update the distribution for prosaic AGI in the way you discuss, but not to update the probability that prosaic AGI will be the first to reach TAI. On the other hand, if there was a argument centered more around an amount of compute we could plausibly get in a short timeframe (the kind of thing we discuss as potential follow-up work), then I'd expect that this same person, if convinced, would put more probability that prosaic AGI will be the first to reach TAI.

Graph-based argument

I must admit that I have trouble reading your graph because there's no scale (although I expect the spiky part is centered at +12 OOMs? As for the textual argument, I actually think it makes sense to put quite low probability to +13 OOMs if one agrees with your scenario.

Maybe my argument is a bit weird, but it goes something like this: based on your scenarios, it should be almost sure that we can reach TAI with +12 OOMs of magnitude. If it's not the case, then there's something fundamentally difficult about reaching TAI with prosaic AGI (because you're basically throwing all the compute we want at it), and so I expect very little probability of a gain from 1 OOMs.

The part about this reasoning that feels weird is that I reason about 13 OOMs based on what happens at 12 OOMs, and the idea that we care about 13 OOMs iff 12 OOMs is not enough. It might be completely wrong.

Reasons for 12 OOMs

To the first suspicion I'll say: I had good reasons for writing about 12 rather than 6 which I am happy to tell you about if you like.

I'm both interested, and (without knowing them), I expect that I will want you to have put them in the post, to deal with the implicit conclusion that you couldn't argue 6 OOMs.

Also interested by your arguments for 6 OOMs or pointers.

If you have a bunch of hypotheses (e.g. "It'll take 1 more OOM," "It'll take 2 more OOMs," etc.) and you learn that some of them are false or unlikely (only 10% chance of it taking more than 12" then you should redistribute the mass over all your remaining hypotheses, preserving their relative strengths.

This depends on the mechanism by which you assigned the mass initially - in particular, whether it's absolute or relative. If you start out with specific absolute probability estimates as the strongest evidence for some hypotheses, then you can't just renormalise when you falsify others.

E.g. consider we start out with these beliefs:
If [approach X] is viable, TAI will take at most 5 OOM; 20% chance [approach X] is viable.
If [approach X] isn't viable, 0.1% chance TAI will take at most 5 OOM.
30% chance TAI will take at least 13 OOM.

We now get this new information:
There's a 95% chance [approach Y] is viable; if [approach Y] is viable TAI will take at most 12 OOM.

We now need to reassign most of the 30% mass we have on >13 OOM, but we can't simply renormalise: we haven't (necessarily) gained any information on the viability of [approach X].
Our post-update [TAI <= 5OOM] credence should remain almost exactly 20%. Increasing it to ~26% would not make any sense.


For AI timelines, we may well have some concrete, inside-view reasons to put absolute probabilities on contributing factors to short timelines (even without new breakthroughs we may put absolute numbers on statements of the form "[this kind of thing] scales/generalises"). These probabilities shouldn't necessarily be increased when we learn something giving evidence about other scenarios. (the probability of a short timeline should change, but in general not proportionately)

Perhaps if you're getting most of your initial distribution from a more outside-view perspective, then you're right.

We now need to reassign most of the 30% mass we have on >13 OOM, but we can't simply renormalise: we haven't (necessarily) gained any information on the viability of [approach X].
Our post-update [TAI <= 5OOM] credence should remain almost exactly 20%. Increasing it to ~26% would not make any sense.

I don't see why this is. From a bayesian perspective, alternative hypotheses being ruled out == gaining evidence for a hypothesis. In what sense have we not gained any information on the viability of approach X? We've learned that one of the alternatives to X (the at least 13 OOM alternative) won't happen.

We do gain evidence on at least some alternatives, but not on all the factors which determine the alternatives. If we know something about those factors, we can't usually just renormalise. That's a good default, but it amounts to an assumption of ignorance.

Here's a simple example:
We play a 'game' where you observe the outcome of two fair coin tosses x and y.
You score:
1 if x is heads
2 if x is tails and y is heads
3 if x is tails and y is tails

So your score predictions start out at:
1 : 50%
2 : 25%
3 : 25%

We look at y and see that it's heads. This rules out 3.
Renormalising would get us:
1 : 66.7%
2 : 33.3%
3: 0%

This is clearly silly, since we ought to end up at 50:50 - i.e. all the mass from 3 should go to 2. This happens because the evidence that falsified 3 points was insignificant to the question "did you score 1 point?".
On the other hand, if we knew nothing about the existence of x or y, and only knew that we were starting from (1: 50%, 2: 25%, 3: 25%), and that 3 had been ruled out, it'd make sense to re-normalise.

In the TAI case, we haven't only learned that 12 OOM is probably enough (if we agree on that). Rather we've seen specific evidence that leads us to think 12 OOM is probably enough. The specifics of that evidence can lead us to think things like "This doesn't say anything about TAI at +4 OOM, since my prediction for +4 is based on orthogonal variables", or perhaps "This makes me near-certain that TAI will happen by +10 OOM, since the +12 OOM argument didn't require more than that".

Interesting, hmm.

In the 1-2-3 coin case, seeing that y is heads rules out 3, but it also rules out half of 1. (There are two 1 hypotheses, the yheads and the ytails version) To put it another way, terms P(yheads|1)=0.5. So we are ruling-out-and-renormalizing after all, even though it may not appear that way at first glance.

The question is, is something similar happening with the AI OOMs?

I think if the evidence leads us to think things like "This doesn't say anything about TAI at +4 OOM, since my prediction is based on orthogonal variables" then that's a point in my favor, right? Or is the idea that the hypotheses ruled out by the evidence presented in the post include all the >12OOM hypotheses, but also a decent chunk of the <6OOM hypotheses but not of the 7-12 OOM hypotheses such that overall the ratio of (our credence in 7-12 OOMs)/(our credence in 0 - 6 OOMs) increases?

"This makes me near-certain that TAI will happen by +10 OOM, since the +12 OOM argument didn't require more than that" also seems like a point in my favor. FWIW I also had the sense that the +12OOM argument didn't really require 12 OOMs, it would have worked almost as well with 10.

Yes, we're always renormalising at the end - it amounts to saying "...and the new evidence will impact all remaining hypotheses evenly". That's fine once it's true.

I think perhaps I wasn't clear with what I mean by saying "This doesn't say anything...".
I meant that it may say nothing in absolute terms - i.e. that I may put the same probability of [TAI at 4 OOM] after seeing the evidence as before.

This means that it does say something relative to other not-ruled-out hypotheses: if I'm saying the new evidence rules out >12 OOM, and I'm also saying that this evidence should leave p([TAI at 4 OOM]) fixed, I'm implicitly claiming that the >12 OOM mass must all go somewhere other than the 4 OOM case.

Again, this can be thought of as my claiming e.g.:
[TAI at 4 OOM] will happen if and only if zwomples work
There's a 20% chance zwomples work
The new 12 OOM evidence says nothing at all about zwomples

In terms of what I actually think, my sense is that the 12 OOM arguments are most significant where [there are no high-impact synergistic/amplifying/combinatorial effects I haven't thought of].
My credence for [TAI at < 4 OOM] is largely based on such effects. Perhaps it's 80% based on some such effect having transformative impact, and 20% on we-just-do-straightforward-stuff. [Caveat: this is all just ottomh; I have NOT thought for long about this, nor looked at much evidence; I think my reasoning is sound, but specific numbers may be way off]

Since the 12 OOM arguments are of the form we-just-do-straightforward-stuff, they cause me to update the 20% component, not the 80%. So the bulk of any mass transferred from >12 OOM, goes to cases where p([we-just-did-straightforward-stuff and no strange high-impact synergies occurred]|[TAI first occurred at this level]) is high.

I think I'm just not seeing why you think the >12 OOM mass must all go somewhere than the <4 OOM (or really, I would argue, <7 OOM) case. Can you explain more?

Maybe the idea is something like: There are two underlying variables, 'We'll soon get more ideas' and 'current methods scale.' If we get new ideas soon, then <7 are needed. If we don't but 'current methods scale' is true, 7-12 are needed. If neither variable is true then >12 is needed. So then we read my +12 OOMs post and become convinced that 'current methods scale.' That rules out the >12 hypothesis, but the renormalized mass doesn't go to <7 at all because it also rules out a similar-sized chunk of the <7 hypothesis (the chunk that involved 'current methods don't scale'). This has the same structure as your 1, 2, 3 example above.

Is this roughly your view? If so, nice, that makes a fair amount of sense to me. I guess I just don't think that the "current methods scale" hypothesis is confined to 7-12 OOMs; I think it is a probability distribution that spans many OOMs starting with mere +1, and my post can be seen as an attempt to upper-bound how high the distribution goes--which then has implications for how low it goes also, if you want to avoid the anti-spikiness objection. Another angle: I could have made a similar post for +9 OOMs, and a similar one for +6 OOMs, and each would have been somewhat less plausible than the previous. But (IMO) not that much less plausible; if you have 80% credence in +12 then I feel like you should have at least 50% by +9 and at least, idk, 25% by +6. If your credence drops faster than that, you seem overconfident in your ability to extrapolate from current data IMO (or maybe not, I'd certainly love to hear your arguments!)

[[ETA, I'm not claiming the >12 OOM mass must all go somewhere other than the <4 OOM case: this was a hypothetical example for the sake of simplicity. I was saying that if I had such a model (with zwomples or the like), then a perfectly good update could leave me with the same posterior credence on <4 OOM.
In fact my credence on <4 OOM was increased, but only very slightly]]

First I should clarify that the only point I'm really confident on here is the "In general, you can't just throw out the >12 OOM and re-normalise, without further assumptions" argument. 

I'm making a weak claim: we're not in a position of complete ignorance w.r.t. the new evidence's impact on alternate hypotheses.

My confidence in any specific approach is much weaker: I know little relevant data.

That said, I think the main adjustment I'd make to your description is to add the possibility for sublinear scaling of compute requirements with current techniques. E.g. if beyond some threshold meta-learning efficiency benefits are linear in compute, and non-meta-learned capabilities would otherwise scale linearly, then capabilities could scale with the square root of compute (feel free to replace with a less silly example of your own).

This doesn't require "We'll soon get more ideas" - just a version of "current methods scale" with unlucky (from the safety perspective) synergies.

So while the "current methods scale" hypothesis isn't confined to 7-12 OOMs, the distribution does depend on how things scale: a higher proportion of the 1-6 region is composed of "current methods scale (very) sublinearly".

My p(>12 OOM | sublinear scaling) was already low, so my p(1-6 OOM | sublinear scaling) doesn't get much of a post-update boost (not much mass to re-assign).
My p(>12 OOM | (super)linear scaling) was higher, but my p(1-6 OOM | (super)linear scaling) was low, so there's not too much of a boost there either (small proportion of mass assigned).

I do think it makes sense to end up with a post-update credence that's somewhat higher than before for the 1-6 range - just not proportionately higher. I'm confident the right answer for the lower range lies somewhere between [just renormalise] and [don't adjust at all], but I'm not at all sure where.

Perhaps there really is a strong argument that the post-update picture should look almost exactly like immediate renormalisation. My main point is that this does require an argument: I don't think its a situation where we can claim complete ignorance over impact to other hypotheses (and so renormalise by default), and I don't think there's a good positive argument for [all hypotheses will be impacted evenly].

OK, thanks.

1. I concede that we're not in a position of complete ignorance w.r.t. the new evidence's impact on alternate hypotheses. However, the same goes for pretty much any argument anyone could make about anything. In my particular case I think there's some sense in which, plausibly, for most underlying views on timelines people will have, my post should cause an update more or less along the lines I described. (see below)

2. Even if I'm wrong about that, I can roll out the anti-spikiness argument to argue in favor of <7 OOMs, though to be fair I don't make this argument in the post. (The argument goes: If 60%+ of your probability mass is between 7 and 12 OOMs, you are being overconfident.)


Argument that for most underlying views on timelines people will have, my post should cause an update more or less along the lines I described:

--The only way for your credence in <7 to go down relative to your credence in7-12 after reading my post and (mostly) ruling out >12 hypotheses, is for the stuff you learn to also disproportionately rule out sub-hypotheses in the <7 range compared to sub-hypotheses in the 7-12 range. But this is a bit weird; my post didn't talk about the <7 range at all, so why would it disproportionately rule out stuff in that range? Like I said, it seems like (to a first approximation) the information content of my post was "12 OOMs is probably enough" and not something more fancy like "12 OOMs is probably enough BUT 6 is probably not enough." I feel unsure about this and would like to hear you describe the information content of the post, in your terms.

--I actually gave an argument that this should increase your relative credence in <7 compared to 7-12, and it's a good one I think: The arguments that 12 OOMs are probably enough are pretty obviously almost as strong for 11 OOMs, and almost as strong as that for 10 OOMs, and so on. To put it another way, our distribution shouldn't have a sharp cliff at 12 OOMs; it should start descending several OOMs prior. What this means is that actually stuff in the 7-12 OOM range is disproportionately ruled out compared to stuff in the <7 OOM range, so we should actually be more confident in <7 OOMs than you would be if you just threw out >12 OOM and renormalized.

Taking your last point first: I entirely agree on that. Most of my other points were based on the implicit assumption that readers of your post don't think something like "It's directly clear that 9 OOM will almost certainly be enough, by a similar argument".

Certainly if they do conclude anything like that, then it's going to massively drop their odds on 9-12 too. However, I'd still make an argument of a similar form: for some people, I expect that argument may well increase the 5-8 range more (than proportionately) than the 1-4 range.

On (1), I agree that the same goes for pretty-much any argument: that's why it's important. If you update without factoring in (some approximation of) your best judgement of the evidence's impact on all hypotheses, you're going to get the wrong answer. This will depend highly on your underlying model.

On the information content of the post, I'd say it's something like "12 OOMs is probably enough (without things needing to scale surprisingly well)". My credence for low OOM values is mostly based on worlds where things scale surprisingly well.

But this is a bit weird; my post didn't talk about the <7 range at all, so why would it disproportionately rule out stuff in that range?

I don't think this is weird. What matters isn't what the post talks about directly - it's the impact of the evidence provided on the various hypotheses. There's nothing inherently weird about evidence increasing our credence in [TAI by +10OOM] and leaving our credence in [TAI by +3OOM] almost unaltered (quite plausibly because it's not too relevant to the +3OOM case).

Compare the 1-2-3 coins example: learning y tells you nothing about the value of x. It's only ruling out any part of the 1 outcome in the sense that it maintains [x_heads & something independent is heads], and rules out [x_heads & something independent is tails]. It doesn't need to talk about x to do this.

You can do the same thing with the TAI first at k OOM case - call that Tk. Let's say that your post is our evidence e and that e+ stands for [e gives a compelling argument against T13+].
Updating on e+ you get the following for each k:
Initial hypotheses: [Tk & e+], [Tk & e-]
Final hypothesis: [Tk & e+]

So what ends up mattering is the ratio p[Tk | e+] : p[Tk | e-]
I'm claiming that this ratio is likely to vary with k.

Specifically, I'd expect T1 to be almost precisely independent of e+, while I'd expect T8 to be correlated. My reason on the T1 is that I think something radically unexpected would need to occur for T1 to hold, and your post just doesn't seem to give any evidence for/against that.
I expect most people would change their T8 credence on seeing the post and accepting its arguments (if they've not thought similar things before). The direction would depend on whether they thought the post's arguments could apply equally well to ~8 OOM as 12.

Note that I am assuming the argument ruling out 13+ OOM is as in the post (or similar).
If it could take any form, then it could be a more or less direct argument for T1.

Overall, I'd expect most people who agree with the post's argument to update along the following lines (but smoothly):
T0 to Ta: low increase in credence
Ta to Tb: higher increase in credence
Tb+: reduced credence

with something like (0 < a < 6) and (4 < b < 13).
I'm pretty sure a is going to be non-zero for many people.

So what ends up mattering is the ratio p[Tk | e+] : p[Tk | e-]
I'm claiming that this ratio is likely to vary with k.

Wait, shouldn't it be the ratio p[Tk & e+] : p[Tk & e-]? Maybe both ratios work fine for our purposes, but I certainly find it more natural to think in terms of &.

Unless I've confused myself badly (always possible!), I think either's fine here. The | version just takes out a factor that'll be common to all hypotheses: [p(e+) / p(e-)]. (since p(Tk & e+) ≡ p(Tk | e+) * p(e+))

Since we'll renormalise, common factors don't matter. Using the | version felt right to me at the time, but whatever allows clearer thinking is the way forward.

I'm probably being just mathematically confused myself; at any rate, I'll proceed with the p[Tk & e+] : p[Tk & e-] version since that comes more naturally to me. (I think of it like: Your credence in Tk is split between two buckets, the Tk&e+ and Tk&e- bucket, and then when you update you rule out the e- bucket. So what matters is the ratio between the buckets; if it's relatively high (compared to the ratio for other Tx's) your credence in Tk goes up, if it's relatively low it goes down.

Anyhow, I totally agree that this ratio matters and that it varies with k. In particular here's how I think it should vary for most readers of my post:

for k>12, the ratio should be low, like 0.1.

for low k, the ratio should be higher.

for middling k, say 6<k<13, the ratio should be in between.

Thus, the update should actually shift probability mass disproportionately to the lower k hypotheses.

I realize we are sort of arguing in circles now. I feel like we are making progress though. Also, separately, want to hop on a call with me sometime to sort this out? I've got some more arguments to show you...