AI Safety Researcher, my website is here.
ojorgensen
Karma: 199
Yeah I think we have the same understanding here (in hindsight I should have made this more explicit in the post / title).
I would be excited to see someone empirically try to answer the question you mention at the end. In particular, given some direction and a LayerNormed vector , one might try to quantify how smoothly rotating from towards changes the output of the MLP layer. This seems like a good test of whether the Polytope Lens is helpful / necessary for understanding the MLPs of Transformers (with smooth changes corresponding to your ‘random jostling cancels out’ corresponding to not needing to worry about Polytope Lens style issues).
It would save me a fair amount of time if all lesswrong posts had an “export BibTex citation” button, exactly like the feature on arxiv. This would be particularly useful for alignment forum posts!
One central criticism of this post is its pessimism towards enumerative safety. (i.e. finding all features in the model, or at least all important features). I would be interested to hear how the author / others have updated on the potential of enumerative safety in light of recent progress on dictionary learning, and finding features which appear to correspond to high-level concepts like truth, utility and sycophancy. It seems clear that there should be some positive update here, but I would be interested in understanding issues which these approaches will not contribute to solving.
But this does not hold for tiny cosine similarities (e.g. 0.01 for , which gives a lower bound of 2 using the formula above). I’m not aware of a lower bound better than for tiny angles.
Unless I’m misunderstanding, a better lower bound for almost orthogonal vectors when cosine similarity is approximately is just , by taking an orthogonal basis for the space.
My guess for why the formula doesn’t give this is because it is derived by covering a sphere with non-intersecting spherical caps, which is sufficient for almost orthogonality but not necessary. This is also why the lower bound of vectors makes sense when we require cosine similarity to be approximately , since then the only way you can fit two spherical caps onto the surface of a sphere is by dividing it into hemispheres.This doesn’t change the headline result (still exponentially much room for almost orthogonal vectors), but the actual numbers might be substantially larger thanks to almost orthogonal vectors being a weaker condition than spherical cap packing.
(Potential spoilers!)
There is some relevant literature which explores this phenomenon, also looking at the cosine similarity between words across layers of transformers. I think the most relevant is (Cai et. al 2021), where they also find this higher than expected cosine similarity between residual stream vectors in some layer for BERT, D-BERT, and GPT. (Note that they use some somewhat confusing terminology: they define inter-type cosine similarity to be cosine similarity between embeddings of different tokens in the same input; and intra-type cosine similarity to be cosine similarity of the same token in different inputs. Inter-type cosine similarity is the one that is most relevant here).
They find that the residual stream vectors for GPT-2 small tend to lie in two distinct clusters. Once you re-centre these clusters, the average cosine similarity between residual stream vectors falls to close to 0 throughout the layers of the model, as you might expect.
Problem: we want to make it hard for ML systems (trained via SGD) to perform naive gradient hacking. By naive gradient hacking, I mean “being able to keep some weights of the network constant for an arbitrary step of SGD”.
Solution: do “stochastic” regularisation, e.g. sample the amount of regularisation we perform randomly (could use quantum stuff if we want true randomness). This seems like it should make naive gradient hacking almost impossible—in order to keep some target weights unchanged, you’d have to match their +ve contribution to the loss to the degree of regularisation. If the degree of regularisation is stochastic, the loss contribution must also be stochastic, which is not possible with a determinstic NN!
The question of how useful this is from preventing any gradient hacking depends on how stable the loss landscape around some “deceptive / gradient hacking minimum is”. Seems possible the surrounding loss landscape could be pretty unstable to random pertubations?
Just a nit-pick but to me “AI growth-rate” suggests economic growth due to progress in AI, as opposed to simply techincal progress in AI. I think “Excessive AI progress yields little socio-economic benefit” would make the argument more immediately clear.
Rando et al. (2022)
This link is broken btw!
Didn’t get that impression from your previous comment, but this seems like a good strategy!
This seems like a bad rule of thumb. If your social circle is largely comprised of people who have chosen to remain within the community, ignoring information from “outsiders” seems like a bad strategy for understanding issues with the community.
Even if OpenAI don’t have the option to stop Bing Chat being released now, this would surely have been discussed during investment negotiations. It seems very unlikely this is being released without approval from decision-makers at OpenAI in the last month or so. If they somehow didn’t foresee that something could go wrong and had no mitigations in place in case Bing Chat started going weird, that’s pretty terrible planning.
This seems very similar to recent work that has come out of the Stanford AI Lab recently, linked to here.
Great post! This helps to clarify and extend lots of fuzzy intuitions I had around gradient hacking, so thanks! If anyone is interested in a different perspective / set of intuitions for how some properties of gradient descent affect gradient hacking, I wrote a small post about this here: https://www.lesswrong.com/posts/Nnb5AqcunBwAZ4zac/extremely-naive-gradient-hacking-doesn-t-work
I’d expect this to mainly be of use if the properties of gradient descent labelled 1, 4, 5 were not immediately obvious to you.
Hey! Not currently working on anything related to this, but would be excited to read anything related to this you are writing :))
I went through the paper for a reading group the other day, and I think the video really helped me to understand what is going on in the paper. Parts I found most useful were indications which parts of the paper / maths were most important to be able to understand, and which were not (tensor products).
I had made some effort to read the paper before with little success, but now feel like I understand the overall results of the paper pretty well. I’m very positive about this video, and similar things like this being made in the future!
Personal context: I also found the intro to IB video series similarly useful. I’m an AI masters student who has some pre-existing knowledge about AI alignment. I have a maths background.
Firstly, thanks for reading the post! I think you’re referring mainly to realisability here which I’m not that clued up on tbh, but I’ll give you my two cents because why not.
I’m not sure to what extent we should focus on unrealisability when aligning systems. I think I have a similar intuition to you that the important question is probably “how can we get good abstractions of the world, given that we cannot perfectly model it”. However, I think better arguments for why unrealisability is a core problem in alignment than I have laid out probably do exist, I just haven’t read that much into it yet. I’ll link again to this video series on IB (which I’m yet to finish) as I think there are probably some good arguments here.
I’m not sure if this is what you’re looking for, but Hofstadter gives a great analogy using record players which I find useful in terms of thinking about how changing the situation changes our results (which is paraphrased here).
A (hi-fi) record player that tries to playing every possible sound can’t actually play its own self-breaking sound, so it is incomplete by virtue of its strength.
A (low-fi) record player that refuses to play all sounds (in order to avoid destruction from its self-breaking sound) is incomplete by virtue of its weakness.
We may think of the hi-fi record player as a formal system like Peano Arithmetic: the incompleteness arises precisely because it is strong enough to be able to capture number theory. This is what allows us to use Gödel Numbering, which then allows PA to do meta-reasoning about itself.
The only way to fix it is to make a system that is weaker than PA, so that we cannot do Gödel Numbering. But then we have a system that isn’t even trying to express what we mean by number theory. This is the low-fi record player: as soon as we fix the one issue of self-reference, we fail to capture the thing we care about (number theory).
I think an example of a weaker formal system is Propositional Calculus. Here we do actually have completeness, but that is only because Propositional Calculus is too weak to be able to capture number theory.
I found this post really interesting, thanks for sharing it!
It doesn’t seem obvious to me that the methods of understanding a model given a high path-dependence world become significantly less useful if we are in a low path-dependence world. I think I see why low path-dependence would give us the opportunity to use different methods of analysis, but I don’t see why the high path-dependence ones would no longer be useful.
For example, here is the reasoning behind “how likely is deceptive alignment” in a high path-dependence world (quoted from the slide).
We start with a proxy-aligned model
In early training, SGD jointly focuses on improving the model’s understanding of the world along with improving its proxies
The model learns about the training process from its input data
SGD makes the model’s proxies into more long-term goals, resulting in it instrumentally optimizing for the training objective for the purposes of staying around
The model’s proxies “crystallize”, as they are no longer relevant to performance, and we reach an equilibrium
Let’s suppose that this reasoning, and the associated justification of why this is likely to arise due to SGD seeking the largest possible marginal performance improvements, are sound for a high path-dependence world. Why does it no longer hold in a low path-dependence world?
Strong upvote!
One thing I’d emphasise is that there’s a pretty big overhead to submitting a single application (getting recommendation letters, writing a generic statement of purpose), but it doesn’t take much effort to apply to more after that (you can rejig your SOP quite easily to fit different universities). Given the application process is noisy and competitive, if you’re submitting one application you should probably submit loads if you can afford the application costs. Good luck to everyone applying! :))