Thanks for the responses! I think we qualitatively agree on a lot, just put emphasis on different things or land in different places on various axes. Responses to some of your points below:
The local/causal structure of our universe gives a very strong preferred way to “slice it up”; I expect that’s plenty sufficient for convergence of abstractions. [...]
Let me try to put the argument into my own words: because of locality, any “reasonable” variable transformation can in some sense be split into “local transformations”, each of which involve only a few variables. These local transformations aren’t a problem because if we, say, resample n variables at a time, then transforming m<n variables doesn’t affect redundant information.
I’m tentatively skeptical that we can split transformations up into these local components. E.g. to me it seems that describing some large number N of particles by their center of mass and the distance vectors from the center of mass is a very reasonable description. But it sounds like you have a notion of “reasonable” in mind that’s more specific then the set of all descriptions physicists might want to use.
I also don’t see yet how exactly to make this work given local transformations—e.g. I think my version above doesn’t quite work because if you’re resampling a finite number n of variables at a time, then I do think transforms involving fewer than n variables can sometimes affect redundant information. I know you’ve talked before about resampling any finite number of variables in the context of a system with infinitely many variables, but I think we’ll want a theory that can also handle finite systems. Another reason this seems tricky: if you compose lots of local transformations, for overlapping local neighborhoods, you get a transformation involving lots of variables. I don’t currently see how to avoid that.
I’d also offer this as one defense of my relatively low level of formality to date: finite approximations are clearly the right way to go, and I didn’t yet know the best way to handle finite approximations. I gave proof sketches at roughly the level of precision which I expected to generalize to the eventual “right” formalizations. (The more general principle here is to only add formality when it’s the right formality, and not to prematurely add ad-hoc formulations just for the sake of making things more formal. If we don’t yet know the full right formality, then we should sketch at the level we think we do know.)
Oh, I did not realize from your posts that this is how you were thinking about the results. I’m very sympathetic to the point that formalizing things that are ultimately the wrong setting doesn’t help much (e.g. in our appendix, we recommend people focus on the conceptual open problems like finite regimes or encodings, rather than more formalization). We may disagree about how much progress the results to date represent regarding finite approximations. I’d say they contain conceptual ideas that may be important in a finite setting, but I also expect most of the work will lie in turning those ideas into non-trivial statements about finite settings. In contrast, most of your writing suggests to me that a large part of the theoretical work has been done (not sure to what extent this is a disagreement about the state of the theory or about communication).
Existing work has managed to go from pseudocode/circuits to interpretation of inputs mainly by looking at cases where the circuits in question are very small and simple—e.g. edge detectors in Olah’s early work, or the sinusoidal elements in Neel’s work on modular addition. But this falls apart quickly as the circuits get bigger—e.g. later layers in vision nets, once we get past early things like edge and texture detectors.
I totally agree with this FWIW, though we might disagree on some aspects of how to scale this to more realistic cases. I’m also very unsure whether I get how you concretely want to use a theory of abstractions for interpretability. My best story is something like: look for good abstractions in the model and then for each one, figure out what abstraction this is by looking at training examples that trigger the abstraction. If NAH is true, you can correctly figure out which abstraction you’re dealing with from just a few examples. But the important bit is that you start with a part of the model that’s actually a natural abstraction, which is why this approach doesn’t work if you just look at examples that make a neuron fire, or similar ad-hoc ideas.
More generally, if you’re used to academia, then bear in mind the incentives of academia push towards making one’s work defensible to a much greater degree than is probably optimal for truth-seeking.
I agree with this. I’ve done stuff in some of my past papers that was just for defensibility and didn’t make sense from a truth-seeking perspective. I absolutely think many people in academia would profit from updating in the direction you describe, if their goal is truth-seeking (which it should be if they want to do helpful alignment research!)
On the other hand, I’d guess the optimal amount of precision (for truth-seeking) is higher in my view than it is in yours. One crux might be that you seem to have a tighter association between precision and tackling the wrong questions than I do. I agree that obsessing too much about defensibility and precision will lead you to tackle the wrong questions, but I think this is feasible to avoid. (Though as I said, I think many people, especially in academia, don’t successfully avoid this problem! Maybe the best quick fix for them would be to worry less about precision, but I’m not sure how much that would help.) And I think there’s also an important failure mode where people constantly think about important problems but never get any concrete results that can actually be used for anything.
It also seems likely that different levels of precision are genuinely right for different people (e.g. I’m unsurprisingly much more confident about what the right level of precision is for me than about what it is for you). To be blunt, I would still guess the style of arguments and definitions in your posts only work well for very few people in the long run, but of course I’m aware you have lots of details in your head that aren’t in your posts, and I’m also very much in favor of people just listening to their own research taste.
both my current work and most of my work to date is aimed more at truth-seeking than defensibility. I don’t think I currently have all the right pieces, and I’m trying to get the right pieces quickly.
Yeah, to be clear I think this is the right call, I just think that more precision would be better for quickly arriving at useful true results (with the caveats above about different styles being good for different people, and the danger of overshooting).
Being both precise and readable at the same time is hard, man.
Yeah, definitely. And I think different trade-offs between precision and readability are genuinely best for different readers, which doesn’t make it easier. (I think this is a good argument for separate distiller roles: if researchers have different styles, and can write best to readers with a similar style of thinking, then plausibly any piece of research should have a distillation written by someone with a different style, even if the original was already well written for a certain audience. It’s probably not that extreme, I think often it’s at least possible to find a good trade-off that works for most people, though hard).
We may disagree about how much progress the results to date represent regarding finite approximations. I’d say they contain conceptual ideas that may be important in a finite setting, but I also expect most of the work will lie in turning those ideas into non-trivial statements about finite settings. In contrast, most of your writing suggests to me that a large part of the theoretical work has been done (not sure to what extent this is a disagreement about the state of the theory or about communication).
Perhaps your instincts here are better than mine! Going to the finite case has indeed turned out to be more difficult than I expected at the time of writing most of the posts you reviewed.
Thanks for the responses! I think we qualitatively agree on a lot, just put emphasis on different things or land in different places on various axes. Responses to some of your points below:
Let me try to put the argument into my own words: because of locality, any “reasonable” variable transformation can in some sense be split into “local transformations”, each of which involve only a few variables. These local transformations aren’t a problem because if we, say, resample n variables at a time, then transforming m<n variables doesn’t affect redundant information.
I’m tentatively skeptical that we can split transformations up into these local components. E.g. to me it seems that describing some large number N of particles by their center of mass and the distance vectors from the center of mass is a very reasonable description. But it sounds like you have a notion of “reasonable” in mind that’s more specific then the set of all descriptions physicists might want to use.
I also don’t see yet how exactly to make this work given local transformations—e.g. I think my version above doesn’t quite work because if you’re resampling a finite number n of variables at a time, then I do think transforms involving fewer than n variables can sometimes affect redundant information. I know you’ve talked before about resampling any finite number of variables in the context of a system with infinitely many variables, but I think we’ll want a theory that can also handle finite systems. Another reason this seems tricky: if you compose lots of local transformations, for overlapping local neighborhoods, you get a transformation involving lots of variables. I don’t currently see how to avoid that.
Oh, I did not realize from your posts that this is how you were thinking about the results. I’m very sympathetic to the point that formalizing things that are ultimately the wrong setting doesn’t help much (e.g. in our appendix, we recommend people focus on the conceptual open problems like finite regimes or encodings, rather than more formalization). We may disagree about how much progress the results to date represent regarding finite approximations. I’d say they contain conceptual ideas that may be important in a finite setting, but I also expect most of the work will lie in turning those ideas into non-trivial statements about finite settings. In contrast, most of your writing suggests to me that a large part of the theoretical work has been done (not sure to what extent this is a disagreement about the state of the theory or about communication).
I totally agree with this FWIW, though we might disagree on some aspects of how to scale this to more realistic cases. I’m also very unsure whether I get how you concretely want to use a theory of abstractions for interpretability. My best story is something like: look for good abstractions in the model and then for each one, figure out what abstraction this is by looking at training examples that trigger the abstraction. If NAH is true, you can correctly figure out which abstraction you’re dealing with from just a few examples. But the important bit is that you start with a part of the model that’s actually a natural abstraction, which is why this approach doesn’t work if you just look at examples that make a neuron fire, or similar ad-hoc ideas.
I agree with this. I’ve done stuff in some of my past papers that was just for defensibility and didn’t make sense from a truth-seeking perspective. I absolutely think many people in academia would profit from updating in the direction you describe, if their goal is truth-seeking (which it should be if they want to do helpful alignment research!)
On the other hand, I’d guess the optimal amount of precision (for truth-seeking) is higher in my view than it is in yours. One crux might be that you seem to have a tighter association between precision and tackling the wrong questions than I do. I agree that obsessing too much about defensibility and precision will lead you to tackle the wrong questions, but I think this is feasible to avoid. (Though as I said, I think many people, especially in academia, don’t successfully avoid this problem! Maybe the best quick fix for them would be to worry less about precision, but I’m not sure how much that would help.) And I think there’s also an important failure mode where people constantly think about important problems but never get any concrete results that can actually be used for anything.
It also seems likely that different levels of precision are genuinely right for different people (e.g. I’m unsurprisingly much more confident about what the right level of precision is for me than about what it is for you). To be blunt, I would still guess the style of arguments and definitions in your posts only work well for very few people in the long run, but of course I’m aware you have lots of details in your head that aren’t in your posts, and I’m also very much in favor of people just listening to their own research taste.
Yeah, to be clear I think this is the right call, I just think that more precision would be better for quickly arriving at useful true results (with the caveats above about different styles being good for different people, and the danger of overshooting).
Yeah, definitely. And I think different trade-offs between precision and readability are genuinely best for different readers, which doesn’t make it easier. (I think this is a good argument for separate distiller roles: if researchers have different styles, and can write best to readers with a similar style of thinking, then plausibly any piece of research should have a distillation written by someone with a different style, even if the original was already well written for a certain audience. It’s probably not that extreme, I think often it’s at least possible to find a good trade-off that works for most people, though hard).
Perhaps your instincts here are better than mine! Going to the finite case has indeed turned out to be more difficult than I expected at the time of writing most of the posts you reviewed.