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I don't follow, sorry - what's the problem of unique assignment of solutions in fluid dynamics and what's the connection to the post?


How are you setting  when ? I might be totally misunderstanding something but   at  - feels like you need to push  up towards like 2k to get something reasonable? (and the argument in 1.4 for using  clearly doesn't hold here because it's not greater than for this range of values).


Yeah I'd expect some degree of interference leading to >50% success on XORs even in small models.


Huh, I'd never seen that figure, super interesting! I agree it's a big issue for SAEs and one that I expect to be thinking about a lot. Didn't have any strong candidate solutions as of writing the post, wouldn't even able to be able to say any thoughts I have on the topic now, sorry. Wish I'd posted this a couple of weeks ago.


Well the substance of the claim is that when a model is calculating lots of things in superposition, these kinds of XORs arise naturally as a result of interference, so one thing to do might be to look at a small algorithmic dataset of some kind where there's a distinct set of features to learn and no reason to learn the XORs and see if you can still probe for them. It'd be interesting to see if there are some conditions under which this is/isn't true, e.g. if needing to learn more features makes the dependence between their calculation higher and the XORs more visible. 

Maybe you could also go a bit more mathematical and hand-construct a set of weights which calculates a set of features in superposition so you can totally rule out any model effort being expended on calculating XORs and then see if they're still probe-able.

Another thing you could do is to zero-out or max-ent the neurons/attention heads that are important for calculating the  feature, and see if you can still detect an  feature. I'm less confident in this because it might be too strong and delete even a 'legitimate'  feature or too weak and leave some signal in.

This kind of interference also predicts that the  and  features should be similar and so the degree of separation/distance from the category boundary should be small. I think you've already shown this to some extent with the PCA stuff though some quantification of the distance to boundary would be interesting. Even if the model was allocating resource to computing these XORs you'd still probably expect them to be much less salient though so not sure if this gives much evidence either way.


My hypothesis about what's going on here, apologies if it's already ruled out, is that we should not think of it separately computing the XOR of A and B, but rather that features A and B are computed slightly differently when the other feature is off or on. In a high dimensional space, if the vector  and the vector  are slightly different, then as long as this difference is systematic, this should be sufficient to successfully probe for .

For example, if A and B each rely on a sizeable number of different attention heads to pull the information over, they will have some attention heads which participate in both of them, and they would 'compete' in the softmax, where if head C is used in both writing features A and B, it will contribute less to writing feature A if it is also being used to pull across feature B, and so the representation of A will be systematically different depending on the presence of B.

It's harder to draw the exact picture for MLPs but I think similar interdependencies can occur there though I don't have an exact picture of how, interested to discuss and can try and sketch it out if people are curious. Probably would be like, neurons will participate in both, neurons which participate in A and B will be more saturated if B is active than if B is not active, so the output representation of A will be somewhat dependent on B.

More generally, I expect the computation of features to be 'good enough' but still messy and somewhat dependent on which other features are present because this kludginess allows them to pack more computation into the same number of layers than if the features were computed totally independently.


What assumptions is this making about scaling laws for these benchmarks? I wouldn't know how to convert laws for losses into these kind of fuzzy benchmarks.


There had been various clashes between Altman and the board. We don’t know what all of them were. We do know the board felt Altman was moving too quickly, without sufficient concern for safety, with too much focus on building consumer products, while founding additional other companies. ChatGPT was a great consumer product, but supercharged AI development counter to OpenAI’s stated non-profit mission.

Does anyone have proof of the board's unhappiness about speed, lack of safety concern and disagreement with founding other companies. All seem plausible but have seen basically nothing concrete.


Could you elaborate on what it would mean to demonstrate 'savannah-to-boardroom' transfer? Our architecture was selected for in the wilds of nature, not our training data. To me it seems that when we use an architecture designed for language translation for understanding images we've demonstrated a similar degree of transfer.

I agree that we're not yet there on sample efficient learning in new domains (which I think is more what you're pointing at) but I'd like to be clearer on what benchmarks would show this. For example, how well GPT-4 can integrate a new domain of knowledge from (potentially multiple epochs of training on) a single textbook seems a much better test and something that I genuinely don't know the answer to.


Do you know why 4x was picked? I understand that doing evals properly is a pretty substantial effort, but once we get up to gigantic sizes and proto-AGIs it seems like it could hide a lot. If there was a model sitting in training with 3x the train-compute of GPT4 I'd be very keen to know what it could do!

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