If you train on infinite data, I assume you'd not see a delay between training and testing, but you'd expect a non-monotonic accuracy curve that looks kind of like the test accuracy curve in the finite-data regime? So I assume infinite data is also cheating?

I've been using "delayed generalisation", which I think is more precise than "grokking", places the emphasis on the delay rather the speed of the transition, and is a short phrase.

I think the hyperlink for "conv nets without residual streams" is wrong? It's https://www.westernunion.com/web/global-service/track-transfer for me

This feels kind of like a semantic disagreement to me. To ground it, it's probably worth considering whether further research on the CCS-style work I posted would also be useful for self-driving cards (or other applications). I think that would depend on whether the work improves the robustness of the contrastive probing regardless of what is being probed for (which would be generically useful), or whether it improves the probing specifically for truthfulness in systems that have a conception of truthfulness , possibly by improving the constraints or adding additional constraints (less useful for other systems). I think both would be good, but I'm uncertain which would be more useful to pursue if one is motivated by reducing x-risk from misalignment.

I think that "don't kill humans" can't chain into itself because there's not a real reason for its action-bids to systematically lead to future scenarios where it again influences logits and gets further reinforced, whereas "drink juice" does have this property.

I'm trying to understand why the juice shard has this propety. Which of these (if any) are the the explanation for this:

• Bigger juice shards will bid on actions which will lead to juice multiple times over time, as it pushes the agent towards juice from quite far away (both temporally and spatially), and hence will be strongly reinforcement when the reward comes, even though it's only a single reinforcement event (actually getting the juice).
• Juice will be acquired more with stronger juice shards, leading to a kind of virtuous cycle, assuming that getting juice is always positive reward (or positive advantage/reinforcement, to avoid zero-point issues)

The first seems at least plausibly to also to apply to "avoid moldy food", if it requires multiple steps of planning to avoid moldy food (throwing out moldy food, buying fresh ingredients and then cooking them, etc.)

The second does seem to be more specific to juice than mold, but it seems to me that's because getting juice is rare, and is something we can better and better at, whereas avoiding moldy food is something that's fairly easy to learn, and past that there's not much reinforcement to happen. If that's the case, then I kind of see that as being covered by the rare-states explanation in my previous comment, or maybe an extension of that to "rare states and skills in which improvement leads to more reward".

Having just read tailcalled comment, I think that is in some sense another of phasing what I was trying to say, where rare (but not too rare) states are likely to mean that policy-caused variance is high on those decisions. Probably policy-caused variance is more fundamental/closer as an explanation to what's actually happening in the learning process, but maybe states of certain rarity which are high-reward/reinforcement is one possibly environmental feature that produces policy-caused variance.

So I struggle to think of an example of a tool that is good for finding insidious misaligning bugs but not others.

One example: A tool that is designed to detect whether a model is being truthful (correctly representing what it knows about the world to the user), perhaps based on specific properties of truthfulness (for example see https://www.alignmentforum.org/posts/L4anhrxjv8j2yRKKp/how-discovering-latent-knowledge-in-language-models-without) doesn't seem like it would be useful for improving the reliability of self-driving cars, as likely self-driving cars aren't misaligned in the sense that they could drive perfectly safely but choose not to, but rather are just unable to drive perfectly safely because some of their internal (learned) systems aren't sufficiently robust.

Not Paul, but some possibilities why ARC's work wouldn't be relevant for self-driving cars:

• The stuff Paul said about them aiming at understanding quite simple human values (don't kill us all, maintain our decision-making power) rather than subtle things. It's likely for self-driving cars we're more concerned with high reliability and hence would need to be quite specific. E.g., maybe ARC's approach could discern whether a car understands whether it's driving on the road or not (seems like a fairly simple concept), but not whether it's driving in a riskier way than humans in specific scenarios.
• One of the problems that I think ARC is worried about is ontology identification, which seems like a meaningfully different problem for sub-human systems (whose ontologies are worse than ours, so in theory could be injected into ours) than for human-level or super-human systems (where that may not hold). Hence focusing on the super-human case would look weird and possibly not helpful for the subhuman case, although it would be great if they could solve all the cases in full generality.
• Maybe once it works ARC's approach could inform empirical work which helps with self-driving cars, but if you were focused on actually doing the thing for cars you'd just aim directly at that, whereas ARC's approach would be a very roundabout and needlessly complex and theoretical way of solving the problem (this may or may not actually be the case, maybe solving this for self-driving cars is actually fundamentally difficult in the same way as for ASI, but it seems less likely).

I found it useful to compare a shard that learns to pursue juice (positive value) to one that avoids eating mouldy food (prohibition), just so they're on the same kind of framing/scale.

It feels like a possible difference between prohibitions and positive values is that positive values specify a relatively small portion of the state space that is good/desirable (there are not many states in which you're drinking juice), and hence possibly only activate less frequently, or only when parts of the state space like that are accessible, whereas prohibitions specify a large part of the state space that is bad (but not so much that the complement is a small portion - there are perhaps many potential states where you eat mouldy food, but the complement of that set is still not a similar size to the set of states of drinking juice). The first feels more suited to forming longer-term plans towards the small part of the state space (cf this definition of optimisation), whereas the second is less so. Then shards that start doing optimisation like this are hence more likely to become agentic/self-reflective/meta-cognitive etc.

In effect, positive values are more likely/able to self-chain because they actually (kind of, implicitly) specify optimisation goals, and hence shards can optimise them, and hence grow and improve that optimisation power, whereas prohibitions specify a much larger desirable state set, and so don't require or encourage optimisation as much.

As an implication of this, I could imagine that in most real-world settings "don't kill humans" would act as you describe, but in environments where it's very easy to accidentally kill humans, such that states where you don't kill humans are actually very rare, then the "don't kill humans" shard could chain into itself more, and hence become more sophisticated/agentic/reflective. Does that seem right to you?

Thanks for the answer! I feel uncertain whether that suggestion is an "alignment" paradigm/method though - either these formally specified goals don't cover most of the things we care about, in which case this doesn't seem that useful, or they do, in which case I'm pretty uncertain how we can formally specify them - that's kind of the whole outer alignment problem. Also, there is still (weaker) pressure to produce outputs that look good to humans, if humans are searching over goals to find those that produce good outputs. I agree it's further away, but that seems like it could also be a bad thing, if it makes it harder to pressure the models to actually do what we want in the first place.