I’m glad you are thinking about this. I am very optimistic about AI alignment research along these lines. However, I’m inclined to think that the strong form of the natural abstraction hypothesis is pretty much false. Different languages and different cultures, and even different academic fields within a single culture (or different researchers within a single academic field), come up with different abstractions. See for example lsusr’s posts on the color blue or the flexibility of abstract concepts. (The Whorf hypothesis might also be worth looking into.)
This is despite humans having pretty much identical cognitive architectures (assuming that we can create a de novo AGI with a cognitive architecture as similar to a human brain as human brains are to each other seems unrealistic). Perhaps you could argue that some human-generated abstractions are “natural” and others aren’t, but that leaves the problem of ensuring that the human operating our AI is making use of the correct, “natural” abstractions in their own thinking. (Some ancient cultures lacked a concept of the number 0. From our perspective, and that of a superintelligent AGI, 0 is a ‘natural’ abstraction. But there could be ways in which the superintelligent AGI invents ‘natural’ abstraction that we haven’t yet invented, such that we are living in a “pre-0 culture” with respect to this abstraction, and this would cause an ontological mismatch between us and our AGI.)
But I’m still optimistic about the overall research direction. One reason is if your dataset contains human-generated artifacts, e.g. pictures with captions written in English, then many unsupervised learning methods will naturally be incentivized to learn English-language abstractions to minimize reconstruction error. (For example, if we’re using self-supervised learning, our system will be incentivized to correctly predict the English-language caption beneath an image, which essentially requires the system to understand the picture in terms of English-language abstractions. This incentive would also arise for the more structured supervised learning task of image captioning, but the results might not be as robust.)
This is the natural abstraction hypothesis in action: across the sciences, we find that low-dimensional summaries of high-dimensional systems suffice for broad classes of “far-away” predictions, like the speed of a sled.
Social sciences are a notable exception here. And I think social sciences (or even humanities) may be the best model for alignment—‘human values’ and ‘corrigibility’ seem related to the subject matter of these fields.
Anyway, I had a few other comments on the rest of what you wrote, but I realized what they all boiled down to was me having a different set of abstractions in this domain than the ones you presented. So as an object lesson in how people can have different abstractions (heh), I’ll describe my abstractions (as they relate to the topic of abstractions) and then explain how they relate to some of the things you wrote.
I’m thinking in terms of minimizing some sort of loss function that looks vaguely like
reconstruction_error + other_stuff
where reconstruction_error is a measure of how well we’re able to recreate observed data after running it through our abstractions, and other_stuff is the part that is supposed to induce our representations to be “useful” rather than just “predictive”. You keep talking about conditional independence as the be-all-end-all of abstraction, but from my perspective, it is an interesting (potentially novel!) option for the other_stuff term in the loss function. The same way dropout was once an interesting and novel other_stuff which helped supervised learning generalize better (making neural nets “useful” rather than just “predictive” on their training set).
The most conventional choice for other_stuff would probably be some measure of the complexity of the abstraction. E.g. a clustering algorithm’s complexity can be controlled through the number of centroids, or an autoencoder’s complexity can be controlled through the number of latent dimensions. Marcus Hutter seems to be as enamored with compression as you are with conditional independence, to the point where he created the Hutter Prize, which offers half a million dollars to the person who can best compress a 1GB file of Wikipedia text.
Another option for other_stuff would be denoising, as we discussed here.
You speak of an experiment to “run a reasonably-detailed low-level simulation of something realistic; see if info-at-a-distance is low-dimensional”. My guess is if the other_stuff in your loss function consists only of conditional independence things, your representation won’t be particularly low-dimensional—your representation will see no reason to avoid the use of 100 practically-redundant dimensions when one would do the job just as well.
Similarly, you speak of “a system which provably learns all learnable abstractions”, but I’m not exactly sure what this would look like, seeing as how for pretty much any abstraction, I expect you can add a bit of junk code that marginally decreases the reconstruction error by overfitting some aspect of your training set. Or even junk code that never gets run / other functional equivalences.
The right question in my mind is how much info at a distance you can get for how many additional dimensions. There will probably be some number of dimensions N such that giving your system more than N dimensions to play with for its representation will bring diminishing returns. However, that doesn’t mean the returns will go to 0, e.g. even after you have enough dimensions to implement the ideal gas law, you can probably gain a bit more predictive power by checking for wind currents in your box. See the elbow method (though, the existence of elbows isn’t guaranteed a priori).
(I also think that an algorithm to “provably learn all learnable abstractions”, if practical, is a hop and a skip away from a superintelligent AGI. Much of the work of science is learning the correct abstractions from data, and this algorithm sounds a lot like an uberscientist.)
Anyway, in terms of investigating convergence, I’d encourage you to think about the inductive biases induced by both your loss function and also your learning algorithm. (We already know that learning algorithms can have different inductive biases than humans, e.g. it seems that the input-output surfaces for deep neural nets aren’t as biased towards smoothness as human perceptual systems, and this allows for adversarial perturbations.) You might end up proving a theorem which has required preconditions related to the loss function and/or the algorithm’s inductive bias.
Another riff on this bit:
This is the natural abstraction hypothesis in action: across the sciences, we find that low-dimensional summaries of high-dimensional systems suffice for broad classes of “far-away” predictions, like the speed of a sled.
Maybe we could differentiate between the ‘useful abstraction hypothesis’, and the stronger ‘unique abstraction hypothesis’. This statement supports the ‘useful abstraction hypothesis’, but the ‘unique abstraction hypothesis’ is the one where alignment becomes way easier because we and our AGI are using the same abstractions. (Even though I’m only a believer in the useful abstraction hypothesis, I’m still optimistic because I tend to think we can have our AGI cast a net wide enough to capture enough useful abstractions that ours are in their somewhere, and this number will be manageable enough to find the right abstractions from within that net—or something vaguely like that.) In terms of science, the ‘unique abstraction hypothesis’ doesn’t just say scientific theories can be useful, it also says there is only one ‘natural’ scientific theory for any given phenomenon, and the existence of competing scientific schools sorta seems to disprove this.
Anyway, the aspect of your project that I’m most optimistic about is this one:
This raises another algorithmic problem: how do we efficiently check whether a cognitive system has learned particular abstractions? Again, this doesn’t need to be fully general or arbitrarily precise. It just needs to be general enough to use as a tool for the next step.
Since I don’t believe in the “unique abstraction hypothesis”, checking whether a given abstraction corresponds to a human one seems important to me. The problem seems tractable, and a method that’s abstract enough to work across a variety of different learning algorithms/architectures (including stuff that might get invented in the future) could be really useful.
I’m glad you are thinking about this. I am very optimistic about AI alignment research along these lines. However, I’m inclined to think that the strong form of the natural abstraction hypothesis is pretty much false. Different languages and different cultures, and even different academic fields within a single culture (or different researchers within a single academic field), come up with different abstractions. See for example lsusr’s posts on the color blue or the flexibility of abstract concepts. (The Whorf hypothesis might also be worth looking into.)
This is despite humans having pretty much identical cognitive architectures (assuming that we can create a de novo AGI with a cognitive architecture as similar to a human brain as human brains are to each other seems unrealistic). Perhaps you could argue that some human-generated abstractions are “natural” and others aren’t, but that leaves the problem of ensuring that the human operating our AI is making use of the correct, “natural” abstractions in their own thinking. (Some ancient cultures lacked a concept of the number 0. From our perspective, and that of a superintelligent AGI, 0 is a ‘natural’ abstraction. But there could be ways in which the superintelligent AGI invents ‘natural’ abstraction that we haven’t yet invented, such that we are living in a “pre-0 culture” with respect to this abstraction, and this would cause an ontological mismatch between us and our AGI.)
But I’m still optimistic about the overall research direction. One reason is if your dataset contains human-generated artifacts, e.g. pictures with captions written in English, then many unsupervised learning methods will naturally be incentivized to learn English-language abstractions to minimize reconstruction error. (For example, if we’re using self-supervised learning, our system will be incentivized to correctly predict the English-language caption beneath an image, which essentially requires the system to understand the picture in terms of English-language abstractions. This incentive would also arise for the more structured supervised learning task of image captioning, but the results might not be as robust.)
Social sciences are a notable exception here. And I think social sciences (or even humanities) may be the best model for alignment—‘human values’ and ‘corrigibility’ seem related to the subject matter of these fields.
Anyway, I had a few other comments on the rest of what you wrote, but I realized what they all boiled down to was me having a different set of abstractions in this domain than the ones you presented. So as an object lesson in how people can have different abstractions (heh), I’ll describe my abstractions (as they relate to the topic of abstractions) and then explain how they relate to some of the things you wrote.
I’m thinking in terms of minimizing some sort of loss function that looks vaguely like
reconstruction_error + other_stuffwhere
reconstruction_erroris a measure of how well we’re able to recreate observed data after running it through our abstractions, andother_stuffis the part that is supposed to induce our representations to be “useful” rather than just “predictive”. You keep talking about conditional independence as the be-all-end-all of abstraction, but from my perspective, it is an interesting (potentially novel!) option for theother_stuffterm in the loss function. The same way dropout was once an interesting and novelother_stuffwhich helped supervised learning generalize better (making neural nets “useful” rather than just “predictive” on their training set).The most conventional choice for
other_stuffwould probably be some measure of the complexity of the abstraction. E.g. a clustering algorithm’s complexity can be controlled through the number of centroids, or an autoencoder’s complexity can be controlled through the number of latent dimensions. Marcus Hutter seems to be as enamored with compression as you are with conditional independence, to the point where he created the Hutter Prize, which offers half a million dollars to the person who can best compress a 1GB file of Wikipedia text.Another option for
other_stuffwould be denoising, as we discussed here.You speak of an experiment to “run a reasonably-detailed low-level simulation of something realistic; see if info-at-a-distance is low-dimensional”. My guess is if the
other_stuffin your loss function consists only of conditional independence things, your representation won’t be particularly low-dimensional—your representation will see no reason to avoid the use of 100 practically-redundant dimensions when one would do the job just as well.Similarly, you speak of “a system which provably learns all learnable abstractions”, but I’m not exactly sure what this would look like, seeing as how for pretty much any abstraction, I expect you can add a bit of junk code that marginally decreases the reconstruction error by overfitting some aspect of your training set. Or even junk code that never gets run / other functional equivalences.
The right question in my mind is how much info at a distance you can get for how many additional dimensions. There will probably be some number of dimensions N such that giving your system more than N dimensions to play with for its representation will bring diminishing returns. However, that doesn’t mean the returns will go to 0, e.g. even after you have enough dimensions to implement the ideal gas law, you can probably gain a bit more predictive power by checking for wind currents in your box. See the elbow method (though, the existence of elbows isn’t guaranteed a priori).
(I also think that an algorithm to “provably learn all learnable abstractions”, if practical, is a hop and a skip away from a superintelligent AGI. Much of the work of science is learning the correct abstractions from data, and this algorithm sounds a lot like an uberscientist.)
Anyway, in terms of investigating convergence, I’d encourage you to think about the inductive biases induced by both your loss function and also your learning algorithm. (We already know that learning algorithms can have different inductive biases than humans, e.g. it seems that the input-output surfaces for deep neural nets aren’t as biased towards smoothness as human perceptual systems, and this allows for adversarial perturbations.) You might end up proving a theorem which has required preconditions related to the loss function and/or the algorithm’s inductive bias.
Another riff on this bit:
Maybe we could differentiate between the ‘useful abstraction hypothesis’, and the stronger ‘unique abstraction hypothesis’. This statement supports the ‘useful abstraction hypothesis’, but the ‘unique abstraction hypothesis’ is the one where alignment becomes way easier because we and our AGI are using the same abstractions. (Even though I’m only a believer in the useful abstraction hypothesis, I’m still optimistic because I tend to think we can have our AGI cast a net wide enough to capture enough useful abstractions that ours are in their somewhere, and this number will be manageable enough to find the right abstractions from within that net—or something vaguely like that.) In terms of science, the ‘unique abstraction hypothesis’ doesn’t just say scientific theories can be useful, it also says there is only one ‘natural’ scientific theory for any given phenomenon, and the existence of competing scientific schools sorta seems to disprove this.
Anyway, the aspect of your project that I’m most optimistic about is this one:
Since I don’t believe in the “unique abstraction hypothesis”, checking whether a given abstraction corresponds to a human one seems important to me. The problem seems tractable, and a method that’s abstract enough to work across a variety of different learning algorithms/architectures (including stuff that might get invented in the future) could be really useful.