This is interesting to me for two reasons:
The speed prior still delegates to better search algorithms though. For example, suppose that someone is able to fill in a 1000 bit program using only 2^500 steps of local search. Then the local search algorithm has speed prior complexity 500 bits, so will beat the object-level program. And the prior we'd end up using is basically "2x longer = 2 more bits" instead of "2x longer = 1 more bit," i.e. we end up caring more about speed because we delegated.
The actual limit on how much you care about speed is given by whatever search algorithms work best. I think it's likely possible to "expose" what is going on to the outer optimizer (so that it finds a hypothesis like "This local search algorithm is good" and then uses it to find an object-level program, rather than directly finding a program that bundles both of them together). But I'd guess intuitively that it's just not even meaningful to talk about the "simplest" programs or any prior that cares less about speed than the optimal search algorithm.
In traditional settings, we are searching for a program M that is simpler than the property P. For example, the number of parameters in our model should be smaller than the size of the dataset we are trying to fit if we want the model to generalize. (This isn't true for modern DL because of subtleties with SGD optimizing imperfectly and implicit regularization and so on, but spiritually I think it's still fine..)
But this breaks down if we start doing something like imposing consistency checks and hoping that those change the result of learning. Intuitively it's also often not true for scientific explanations---even simple properties can be surprising and require explanation, and can be used to support theories that are much more complex than the observation itself.
The speed prior is calibrated such that this never happens if the learned optimizer is just using brute force---if it needs to search over 1 extra bit then it will take 2x longer, offsetting the gains.
That means that in the regime where P is simple, the speed prior is the "least you can reasonably care about speed"---if you care even less, you will just end up pushing the optimization into an inner process that is more concerned with speed and is therefore able to try a bunch of options.
(However, this is very mild, since the speed prior cares only a tiny bit about speed. Adding 100 bits to your program is the same as letting it run 2^100 times longer, so you are basically just optimizing for simplicity.)
To make this concrete, suppose that I instead used the kind-of-speed prior, where taking 4x longer is equivalent to using 1 extra bit of description complexity. And suppose that P is very simple relative to the complexities of the other objects involved. Suppose that the "object-level" program M has 1000 bits and runs in 2^2000 time, so has kind-of-speed complexity 2000 bits. A search that uses the speed prior will be able to find this algorithm in 2^3000 time, and so will have a kind-of-speed complexity of 1500 bits. So the kind-of-speed prior will just end up delegating to the speed prior.
Suppose I am interested in finding a program M whose input-output behavior has some property P that I can probabilistically check relatively quickly (e.g. I want to check whether M implements a sparse cut of some large implicit graph). I believe there is some simple and fast program M that does the trick. But even this relatively simple M is much more complex than the specification of the property P.
Now suppose I search for the simplest program running in time T that has property P. If T is sufficiently large, then I will end up getting the program "Search for the simplest program running in time T' that has property P, then run that." (Or something even simpler, but the point is that it will make no reference to the intended program M since encoding P is cheaper.)
I may be happy enough with this outcome, but there's some intuitive sense in which something weird and undesirable has happened here (and I may get in a distinctive kind of trouble if P is an approximate evaluation). I think this is likely to be a useful maximally-simplified example to think about.
We might be able to get similar advantages with a more general proposal like:
Fit a function f to a (Q, A) dataset with lots of questions about latent structure. Minimize the sum of some typical QA objective and the computational cost of verifying that f is consistent.
Then the idea is that matching the conditional probabilities from the human's model (or at least being consistent with what the human believes strongly about those conditional probabilities) essentially falls out of a consistency condition.
It's not clear how to actually formulate that consistency condition, but it seems like an improvement over the prior situation (which was just baking in the obviously-untenable requirement of exactly matching). It's also not clear what happens if this consistency condition is soft.
It's not clear what "verify that the consistency conditions are met" means. You can always do the same proposal as in the parent, though it's not really clear if that's a convincing verification. But I think that's a fundamental philosophical problem that both of these proposals need to confront.
It's not clear how to balance computational cost and the QA objective. But you are able to avoid most of the bad properties just by being on the Pareto frontier, and I don't think this is worse than the prior proposal.
Overall this approach seems like it could avoid making such strong structural assumptions about the underlying model. It also helps a lot with the overlapping explanations + uniformity problem. And it generally seems to be inching towards feeling plausible.
Here's another approach to "shortest circuit" that is designed to avoid this problem:
The "intended" circuit C just follows along with the computation done by Fθ and then translates its internal state into natural language.
What about the problem case where Fθ computes some reasonable beliefs (e.g. using the instrumental policy, where the simplicity prior makes us skeptical about their generalization) that C could just read off? I'll imagine those being written down somewhere on a slip of paper inside of Fθ's model of the world.
Probably nothing like this can work, but I now feel like there are two live proposals for capturing the optimistic minimal circuits intuition---the one in this current comment, and in this other comment. I still feel like the aggressive speed penalization is doing something, and I feel like probably we can either find a working proposal in that space or else come up with some clearer counterexample.
Recently I've been thinking about ML systems that generalize poorly (copying human errors) because of either re-using predictive models of humans or using human inference procedures to map between world models.
My initial focus was on preventing re-using predictive models of humans. But I'm feeling increasingly like there is going to be a single solution to the two problems, and that the world-model mismatch problem is a good domain to develop the kind of algorithm we need. I want to say a bit about why.
I'm currently thinking about dealing with world model mismatches by learning a correspondence between models using something other than a simplicity prior / training a neural network to answering questions. Intuitively we want to do something more like "lining up" the two models and seeing what parts correspond to which others. We have a lot of conditions/criteria for such alignments, so we don't necessarily have to just stick with simplicity. This comment fleshes out one possible approach a little bit.
If this approach succeeds, then it also directly applicable to avoiding re-using human models---we want to be lining up the internal computation of our model with concepts like "There is a cat in the room" rather than just asking the model to predict whether there is a cat however it wants (which it may do by copying a human labeler). And on the flip side, I think that the "re-using human models" problem is a good constraint to have in mind when thinking about ways to do this correspondence. (Roughly speaking, because something like computational speed or "locality" seems like a really central constraint for matching up world models, and doing that approach naively can greatly exacerbate the problems with copying the training process.)
So for now I think it makes sense for me to focus on whether learning this correspondence is actually plausible. If that succeeds then I can step back and see how that changes my overall view of the landscape (I think it might be quite a significant change), and if it fails then I hope to at least know a bit more about the world model mismatch problem.
I think the best analogy in existing practice is probably doing interpretability work---mapping up the AI's model to my model is kind of like looking at neurons and trying to make sense of what they are computing (or looking for neurons that compute something). And giving up on a "simplicity prior" is very natural when doing interpretability, instead using other considerations to determine whether a correspondence is good. It still seems kind of plausible that in retrospect my current work will look like it was trying to get a solid theoretical picture on what interpretability should do (including in the regime where the correspondence is quite complex, and when the goal is a much more complete level of understanding). I swing back and forth on how strong the analogy to interpretability seems / whether or not this is how it will look in retrospect. (But at any rate, my research methodology feels like a very different approach to similar questions.)
Here's a slightly more formal algorithm along these lines:
Reviewing how this behaves in each of the bad cases from the parent:
There are a lot of problems and missing details in this proposal:
Overall I'm becoming significantly more optimistic that something like this will work (though still less likely than not). Trying to step back and see the big picture, it seems like there are three key active ingredients:
My next step would probably be looking at cases where these high-level ingredients aren't sufficient (e.g. are there cases where "generate obs then do inference in the human model" is actually cheaper?). If they look pretty good, then I'll spend some more time trying to fill in the details in a more plausible way.