We're trying to address cases where the human isn't actually able to update on all of D and form a posterior based on that. We're trying to approximate 'what the human posterior would be if they had been able to look at all of D'. So to do that, we learn the human prior, and we learn the human likelihood, then have the ML do the computationally-intensive part of looking at all of D and updating based on everything in there.

Does that make sense?

Starting with amplification as a baseline; am I correct to infer that imitative generalisation only boosts capabilities, and doesn't give you any additional safety properties?

I think the distinction isn't actually super clear, because you can usually trade off capabilities problems and safety problems. I think of it as expanding the range of questions you can get aligned answers to in a reasonable number of steps. If you're just doing IDA/debate, and you try to get your model to give you answers to questions where the model only knows the answer because of updating on a big dataset, you can either keep going through the big dataset when any question of this type comes up (very slow, so capability limitation), or not trust these answers (capability limitation), or just hope they're correct (safety problem).

Bonus question: Is the intention only to boost efficiency, or do you think that IA will fundamentally allow amplification to solve more problems? (Ie., solve more problems with non-ridiculous amounts of compute – I'd be happy to count an exponential speedup as the latter.)

The latter :)

I think the only way to get debate to be able to answer all the questions that debate+IG can answer is to include subtrees that are the size of your whole training dataset at arbitrary points in your debate tree, which I think counts as a ridiculous amount of compute

That is a concern, but only in the case where there's no answer that has an argument tree that bottoms out in depth<D. As long as there exists an answer that is supported by a depth<D tree, this answer will beat the answers only supported by depth>D argument trees.

So there is a case where the debaters are not incentivised to be honest; the case where the debaters know something but there's no human-understandable argument for it that bottoms out in <D steps. This is where we get the PSPACE constraint.

If we include discussion of cross-examination (which the analysis there did not include), then we can get rid of this constraint: each debater commits to an argument tree, then each debater points out the weakest node in the tree (or points out that some part of the tree doesn't bottom out).

(we can only handle really large trees if we assume debaters are computationally unbounded in general though. If we don't assume this, even if we still assume they have oracles for some specific problems, we still probably can't supervise anything that's not in NP, because of the obfuscated argument problem)

I don't think 'assuming one player is honest' and 'not trusting answers by default' are in contradiction. if the judge assumes one player is honest, then if they see two different answers they don't know which one to trust, but if they only see one answer (the debaters agree on an answer/the answer is not challenged by the opposing debater) then they can trust that answer.

I was trying to describe something that's the same as the judging procedure in that doc! I might have made a mistake, but I'm pretty sure the key piece about recursion payments is the same. Apologies that things are unclear. I'm happy to try to clarify, if there were particular aspects that seem different to you.

Yeah, I think the infinite tree case should work just the same - ie an answer that's only supported by an infinite tree will behave like an answer that's not supported (it will lose to an answer with a finite tree and draw with an answer with no support)

It seems possible that the proposal you're discussing very significantly addresses concerns I've had about debate.

That's exciting!

In the ball-attached-to-a-pole example, the honest debater has assigned probabilities that are indistinguishable from what you would do if you knew noting except that the claim is false. (I.e., assign probabilities that doubt each component equally.) I'm curious how difficult it is to find the flaw in this argument structure. Have you done anything like showing these transcripts to other experts and seeing if they will be able to answer it?

Not systematically; I would be excited about people doing these experiments. One tricky thing is that you might think this is a strategy that's possible for ML models, but that humans aren't naturally very good.

If I had to summarize this finding in one sentence, it would be "it seems like an expert can generally find a set of arguments for a false claim that is flawed such that an equally competent expert can't identify the flawed component, and the set of arguments doesn't immediately look suspect". This seems surprising, and I'm wondering whether it's unique to physics. (The cryptographic example was of this kind, but there, the structure of the dishonest arguments was suspect.)

Yeah, this is a great summary. One thing I would clarify is that it's sufficient that the set of arguments don't look suspicious to the judge. The arguments might look suspicious to the expert, but unless they have a way to explain to the judge why it's suspicious, we still have a problem.

If this finding holds, my immediate reaction is "okay, in this case, the solution for the honest debater is to start a debate about whether the set of arguments from the dishonest debater has this character". I'm not sure how good this sounds. I think my main issue here is that I don't know enough physics understand why the dishonest arguments are hard to identify

Yeah, I think that is the obvious next step. The concern is that the reasons the argument is suspicious may be hard to justify in a debate, especially if they're reasons of the form 'look, I've done a bunch of physics problems, and approaching it this way feels like it will makes things messy, whereas approaching it this way feels cleaner'. Debate probably doesn't work very well for supervising knowledge that's gained through finding patterns in data, as opposed to knowledge that's gained through step-by-step reasoning. Something like imitative generalisation (AKA 'learning the prior') is trying to fill this gap.

It seems like the only thing stopping z from primarily containing object-level knowledge about the world is the human prior about the unlikelihood of object-level knowledge. But humans are really bad at assigning priors even to relatively simple statements - this is the main reason that we need science.

Agree that humans are not necessarily great at assigning priors. The main response to this is that we don't have a way to get better priors than an amplified human's best prior. If amplified humans think the NN prior is better than their prior, they can always just use this prior. So in theory this should be both strictly better than the alternative, and the best possible prior we can use.

Science seems like it's about collecting more data and measuring the likelihood, not changing the prior. We still need to use our prior - there are infinite scientific theories that fit the data, but we prefer ones that are simple and elegant.

z will consist of a large number of claims, but I have no idea how to assign a prior to the conjunction of many big claims about the world, even in theory. That prior can't calculated recursively, because there may be arbitrarily-complicated interactions between different components of z.

One thing that helps a bit here is that we can use an amplified human. We also don't need the human to calculate the prior directly, just to do things like assess whether some change makes the prior better or worse. But I'm not sure how much of a roadblock this is in practice, or what Paul thinks about this problem.

Consider the following proposal: "train an oracle to predict the future, along with an explanation of its reasoning. Reward it for predicting correctly, and penalise it for explanations that sound fishy". Is there an important difference between this and imitative generalisation?

Yeah, the important difference is that in this case there's nothing that constrains the explanations to be the same as the actual reasoning the oracle is using, so the explanations you're getting are not necessarily predictive of the kind of generalisation that will happen. In IG it's important that the quality of z is measured by having humans use it to make predictions.

An agent can "generalise badly" because it's not very robust, or because it's actively pursuing goals that are misaligned with those of humans. It doesn't seem like this proposal distinguishes between these types of failures. Is this distinction important in motivating the proposal?

I'm not sure exactly what you're asking. I think the proposal is motivated by something like: having the task be IID/being able to check arbitrary outputs from our model to make sure it's generalising correctly buys us a lot of safety properties. If we have this guarantee, we only have to worry about rare or probabilistic defection, not that the model might be giving us misleading answers for every question we can't check.

Thanks for the post, I'm excited that you're thinking about debate!

I think I disagree with the claim you're making about being able to avoid requiring the judge to assume that one player is honest (but I might be confused about what you're proposing). 
Basically, it sounds like you're saying that we can get good answers by just running the whole debate and throwing out answers that turn out to have a defeater, or a defeater-defeater-defeater, or whatever. But if this is the only guarantee we're providing, then we're going to need to run an extremely large number of debates to ever get a good answer (ie an exp number of debates for a question where the explanation for the answer is exp-sized)

It sounds like you're saying that we can not require that the judge assume one player is honest/trust the claims lower in the debate tree when evaluating the claims higher in the tree. But if we can't assume this, that presumably means that some reasonable fraction of all claims being made are dishonest (because if there were only a few dishonest claims, then they'd have honest defeaters and we'd have a clear training signal away from dishonesty, so after training for a bit we'd be able to trust the lower claims). This probably means that most debates will give us a bad answer (as you only need a few bad claims to invalidate the whole tree).  At this point, debate isn't really competitive, because it gives us dud answers almost all the time, and we're going to have to run an exponential number of debates before we happen on a correct one.

Are you suggesting we use debate more as a check on our AI systems, to help us discover that they're bad, rather than as a safe alternative? Ie debate never produces good answers, it just lets you see that bad answers are bad?

But also, the 'amplified judge consulting sub-debates' sounds like it's just the same thing as letting the judge assume that claims lower in the debate are correct when evaluating claims higher in the tree. 

The standard argument against having a non-zero-sum debate game is that then you may incentivise your debaters to collude.  

I don't know if you've seen our most recent debate rules and attempt at analysis of whether they provide the desired behavior - seems somewhat relevant to what you're thinking about here.