Hence, the honest-imitation hypothesis is heavily penalized compared to hypotheses that are in themselves agents which are more “epistemically sophisticated” than the outer loop of the AI.
In a deep learning context, the latter hypothesis seems much more heavily favored when using a simplicity prior (since gradient descent is simple to specify) than a speed prior (since gradient descent takes a lot of computation). So as long as the compute costs of inference remain smaller than the compute costs of training, a speed prior seems more appropriate for evaluating how easily hypotheses can become more epistemically sophisticated than the outer loop.
Not quite sure what you’re saying here. Is the claim that speed penalties would help shift the balance against mesa-optimizers? This kind of solutions are worth looking into, but I’m not too optimistic about them atm. First, the mesa-optimizer probably won’t add a lot of overhead compared to the considerable complexity of emulating a brain. In particular, it need not work by anything like our own ML algorithms. So, if it’s possible to rule out mesa-optimizers like this, it would require a rather extreme penalty. Second, there are limits on how much you can shape the prior while still having feasible learning. And I suspect that such an extreme speed penalty would not cut it. Third, depending on the setup, an extreme speed penalty might harm generalization[1]. But we definitely need to understand it more rigorously.
The most appealing version is Christiano’s “minimal circuits”, but that only works for inputs of fixed size. It’s not so clear what’s the variable-input-size (“transformer”) version of that.
No, I wasn’t advocating adding a speed penalty, I was just pointing at a reason to think that a speed prior would give a more accurate answer to the question of “which is favored” than the bounded simplicity prior you’re assuming:
Suppose that your imitator works by something akin to Bayesian inference with some sort of bounded simplicity prior (I think it’s true of transformers)
But now I realise that I don’t understand why you think this is true of transformers. Could you explain? It seems to me that there are many very simple hypotheses which take a long time to calculate, and which transformers therefore can’t be representing.
The word “bounded” in “bounded simplicity prior” referred to bounded computational resources. A “bounded simplicity prior” is a prior which involves either a “hard” (i.e. some hypotheses are excluded) or a “soft” (i.e. some hypotheses are down-weighted) bound on computational resources (or both), and also inductive bias towards simplicity (specifically it should probably behave as ~ 2^{-description complexity}). For a concrete example, see the prior I described here (w/o any claim to originality).
This seems like a good thing to keep in mind, but also sounds too pessimistic about the ability of gradient descent to find inference algorithms that update more efficiently than gradient descent.
I do expect this to happen. The question is merely: what’s the best predictor of how hard it is to find inference algorithms more efficient effective than gradient descent? Is it whether those inference algorithms are more complex than gradient descent? Or is it whether those inference algorithms run for longer than gradient descent? Since gradient descent is very simple but takes a long time to run, my bet is the latter: there are many simple ways to convert compute to optimisation, but few compute-cheap ways to convert additional complexity to optimization.
Faster than gradient descent is not a selective pressure, at least if we’re considering typical ML training procedures. What is a selective pressure is regularization, which functions much more like a complexity prior than a speed prior.
So (again sticking to modern day ML as an example, if you have something else in mind that would be interesting) of course there will be a cutoff in terms of speed, excluding all algorithms that don’t fit into the neural net. But among algorithms that fit into the NN, the penalty on their speed will be entirely explainable as a consequence of regularization that e.g. favors circuits that depend on fewer parameters, and would therefore be faster after some optimization steps.
If examples of successful parameters were sparse and tended to just barely fit into the NN, then this speed cutoff will be very important. But in the present day we see that good parameters tend to be pretty thick on the ground, and you can fairly smoothly move around in parameter space to make different tradeoffs.
In a deep learning context, the latter hypothesis seems much more heavily favored when using a simplicity prior (since gradient descent is simple to specify) than a speed prior (since gradient descent takes a lot of computation). So as long as the compute costs of inference remain smaller than the compute costs of training, a speed prior seems more appropriate for evaluating how easily hypotheses can become more epistemically sophisticated than the outer loop.
Not quite sure what you’re saying here. Is the claim that speed penalties would help shift the balance against mesa-optimizers? This kind of solutions are worth looking into, but I’m not too optimistic about them atm. First, the mesa-optimizer probably won’t add a lot of overhead compared to the considerable complexity of emulating a brain. In particular, it need not work by anything like our own ML algorithms. So, if it’s possible to rule out mesa-optimizers like this, it would require a rather extreme penalty. Second, there are limits on how much you can shape the prior while still having feasible learning. And I suspect that such an extreme speed penalty would not cut it. Third, depending on the setup, an extreme speed penalty might harm generalization[1]. But we definitely need to understand it more rigorously.
The most appealing version is Christiano’s “minimal circuits”, but that only works for inputs of fixed size. It’s not so clear what’s the variable-input-size (“transformer”) version of that.
No, I wasn’t advocating adding a speed penalty, I was just pointing at a reason to think that a speed prior would give a more accurate answer to the question of “which is favored” than the bounded simplicity prior you’re assuming:
But now I realise that I don’t understand why you think this is true of transformers. Could you explain? It seems to me that there are many very simple hypotheses which take a long time to calculate, and which transformers therefore can’t be representing.
The word “bounded” in “bounded simplicity prior” referred to bounded computational resources. A “bounded simplicity prior” is a prior which involves either a “hard” (i.e. some hypotheses are excluded) or a “soft” (i.e. some hypotheses are down-weighted) bound on computational resources (or both), and also inductive bias towards simplicity (specifically it should probably behave as ~ 2^{-description complexity}). For a concrete example, see the prior I described here (w/o any claim to originality).
Ah, I see. That makes sense now!
This seems like a good thing to keep in mind, but also sounds too pessimistic about the ability of gradient descent to find inference algorithms that update more efficiently than gradient descent.
I do expect this to happen. The question is merely: what’s the best predictor of how hard it is to find inference algorithms more
efficienteffective than gradient descent? Is it whether those inference algorithms are more complex than gradient descent? Or is it whether those inference algorithms run for longer than gradient descent? Since gradient descent is very simple but takes a long time to run, my bet is the latter: there are many simple ways to convert compute to optimisation, but few compute-cheap ways to convert additional complexity to optimization.Faster than gradient descent is not a selective pressure, at least if we’re considering typical ML training procedures. What is a selective pressure is regularization, which functions much more like a complexity prior than a speed prior.
So (again sticking to modern day ML as an example, if you have something else in mind that would be interesting) of course there will be a cutoff in terms of speed, excluding all algorithms that don’t fit into the neural net. But among algorithms that fit into the NN, the penalty on their speed will be entirely explainable as a consequence of regularization that e.g. favors circuits that depend on fewer parameters, and would therefore be faster after some optimization steps.
If examples of successful parameters were sparse and tended to just barely fit into the NN, then this speed cutoff will be very important. But in the present day we see that good parameters tend to be pretty thick on the ground, and you can fairly smoothly move around in parameter space to make different tradeoffs.