Hypothetically, if the Bio Anchors paper had claimed that strict brute-force evolution would take 1060 ops instead of 1043, what about your argument would actually change? It seems to me that none of it would, to any meaningful degree.
If there are 20 vs 40 orders of magnitude between “here” and “upper limit,” then you end up with ~5% vs ~2.5% on the typical order of magnitude. A factor of 2 in probability seems like a large change, though I’m not sure what you mean by “to any meaningful degree.”
It looks like the plausible ML extrapolations span much of the range from here to 1040. If we were in a different world where the upper bound was much larger, it would be more plausible for someone to think that the ML-based estimates are too low.
If you’re dividing your probability from algorithms derived from evolutionary brute force uniformly between now and then, then I would consider that a meaningful degree. But that doesn’t seem like an argument being made by Bio Anchors or defended here, nor do I believe that’s a legitimate thing you can do. Would you apply this argument to other arbitrary algorithms? Like if there’s a known method of calculating X with Y times more computation, then in general there’s a 50% chance that there’s a method derived from that method for calculating X with √Y times more computation?
I think I endorse the general schema. Namely: if I believe that we can achieve X with 1043 flops but not 1023 flops (holding everything else constant), then I think that gives a prima facie reason to guess a 50% chance that we could achieve it with 1033 flops.
(This isn’t fully general, like if you told me that we could achieve something with 22100 flops but not 2210 I’d be more inclined to guess a median of 2250 than 2299.)
I’m surprised to see this bullet being bitten. I can easily think of trivial examples against the claim, where we know the minimum complexity of simple things versus their naïve implementations, but I’m not sure what arguments there are for it. It sounds pretty wild to me honestly, I have no intuition algorithmic complexity works anything like that.
If you think the probability derived from the upper limit set by evolutionary brute force should be spread out uniformly over the next 20 orders of magnitude, then I assume you think that if we bought 4 orders of magnitude today, there is a 20% chance that a method derived from evolutionary brute force will give us AGI? Whereas I would put that probability much lower, since brute force evolution is not nearly powerful enough at those scales.
I would say there is a meaningful probability that a method not derived from evolutionary brute force, particularly scaled up neural networks, will give us AGI at that point with only minimal fiddling. However that general class of techniques does not observe the evolutionary brute force upper bound. It is entirely coherent to say that as you push neural network size, their improvements flatten out and never reach AGI. The chance that a 1016 parameter model unlocks AGI given a 1011 parameter model doesn’t is much larger than the chance that a 1031 parameter model unlocks AGI given a 1026 parameter model doesn’t. So it’s not clear how you could expect neural networks to observe the upper bound for an unrelated algorithm, and so it’s unclear why their probability distribution would be affected by where exactly that upper bound lands.
I’m also unclear whether you consider this a general rule of thumb for probabilities in general, or something specific to algorithms. Would you for instance say that if there was a weak proof that we could travel interstellar with Y times better fuel energy density, then there’s a 50% chance that there’s a method derived from that method for interstellar travel with just √Y times better energy density?
I’m surprised to see this bullet being bitten. I can easily think of trivial examples against the claim, where we know the minimum complexity of simple things versus their naïve implementations, but I’m not sure what arguments there are for it. It sounds pretty wild to me honestly, I have no intuition algorithmic complexity works anything like that.
I don’t know what you mean by an “example against the claim.” I certainly agree that there is often other evidence that will improve your bet. Perhaps this is a disagreement about the term “prima facie”?
Learning that there is a very slow algorithm for a problem is often a very important indicator that a problem is solvable, and savings like 1040 to 1030 seem routine (and often have very strong similarities between the algorithms). And very often the running time of one algorithm is indeed a useful indicator for the running time of a very different approach. It’s possible we are thinking about different domains here, I’m mostly thinking of traditional algorithms (like graph problems, approximation algorithms, CSPs, etc.) scaled to input sizes where the computation cost is in this regime. Though it seems like the same is also true for ML (though I have much less data there and moreover all the examples are radically less crisp).
The chance that a 1016 parameter model unlocks AGI given a 1011 parameter model doesn’t is much larger than the chance that a 1031 parameter model unlocks AGI given a 1026 parameter model doesn’t.
This seems wrong but maybe for reasons unrelated to the matter at hand. (In general an unknown number is much more likely to lie between 1011 and 1016 than between 1026 and 1031, just as an unknown number is more likely to lie between 11 and 16 than between 26 and 31.)
I’m also unclear whether you consider this a general rule of thumb for probabilities in general, or something specific to algorithms. Would you for instance say that if there was a weak proof that we could travel interstellar with Y times better fuel energy density, then there’s a 50% chance that there’s a method derived from that method for interstellar travel with just √Y times better energy density?
I think it’s a good rule of thumb for estimating numbers in general. If you know a number is between A and B (and nothing else), where A and B are on the order of 1020, then a log-uniform distribution between A and B is a reasonable prima facie guess.
This holds whether the number is “The best you can do on the task using method X” or “The best you can do on the task using any method we can discover in 100 years” or “The best we could do on this task with a week and some duct tape” or “The mass of a random object in the universe.”
If you think the probability derived from the upper limit set by evolutionary brute force should be spread out uniformly over the next 20 orders of magnitude, then I assume you think that if we bought 4 orders of magnitude today, there is a 20% chance that a method derived from evolutionary brute force will give us AGI? Whereas I would put that probability much lower, since brute force evolution is not nearly powerful enough at those scales.
I don’t know what “derived from evolutionary brute force” means (I don’t think anyone has said those words anywhere in this thread other than you?)
But in terms of P(AGI), I think that “20% for next 4 orders of magnitude” is a fine prima facie estimate if you bring in this single consideration and nothing else. Of course I don’t think anyone would ever do that, but frankly I still think “20% for the next 4 orders of magnitude” is still better than most communities’ estimates.
If there are 20 vs 40 orders of magnitude between “here” and “upper limit,” then you end up with ~5% vs ~2.5% on the typical order of magnitude. A factor of 2 in probability seems like a large change, though I’m not sure what you mean by “to any meaningful degree.”
It looks like the plausible ML extrapolations span much of the range from here to 1040. If we were in a different world where the upper bound was much larger, it would be more plausible for someone to think that the ML-based estimates are too low.
If you’re dividing your probability from algorithms derived from evolutionary brute force uniformly between now and then, then I would consider that a meaningful degree. But that doesn’t seem like an argument being made by Bio Anchors or defended here, nor do I believe that’s a legitimate thing you can do. Would you apply this argument to other arbitrary algorithms? Like if there’s a known method of calculating X with Y times more computation, then in general there’s a 50% chance that there’s a method derived from that method for calculating X with √Y times more computation?
I think I endorse the general schema. Namely: if I believe that we can achieve X with 1043 flops but not 1023 flops (holding everything else constant), then I think that gives a prima facie reason to guess a 50% chance that we could achieve it with 1033 flops.
(This isn’t fully general, like if you told me that we could achieve something with 22100 flops but not 2210 I’d be more inclined to guess a median of 2250 than 2299.)
I’m surprised to see this bullet being bitten. I can easily think of trivial examples against the claim, where we know the minimum complexity of simple things versus their naïve implementations, but I’m not sure what arguments there are for it. It sounds pretty wild to me honestly, I have no intuition algorithmic complexity works anything like that.
If you think the probability derived from the upper limit set by evolutionary brute force should be spread out uniformly over the next 20 orders of magnitude, then I assume you think that if we bought 4 orders of magnitude today, there is a 20% chance that a method derived from evolutionary brute force will give us AGI? Whereas I would put that probability much lower, since brute force evolution is not nearly powerful enough at those scales.
I would say there is a meaningful probability that a method not derived from evolutionary brute force, particularly scaled up neural networks, will give us AGI at that point with only minimal fiddling. However that general class of techniques does not observe the evolutionary brute force upper bound. It is entirely coherent to say that as you push neural network size, their improvements flatten out and never reach AGI. The chance that a 1016 parameter model unlocks AGI given a 1011 parameter model doesn’t is much larger than the chance that a 1031 parameter model unlocks AGI given a 1026 parameter model doesn’t. So it’s not clear how you could expect neural networks to observe the upper bound for an unrelated algorithm, and so it’s unclear why their probability distribution would be affected by where exactly that upper bound lands.
I’m also unclear whether you consider this a general rule of thumb for probabilities in general, or something specific to algorithms. Would you for instance say that if there was a weak proof that we could travel interstellar with Y times better fuel energy density, then there’s a 50% chance that there’s a method derived from that method for interstellar travel with just √Y times better energy density?
I don’t know what you mean by an “example against the claim.” I certainly agree that there is often other evidence that will improve your bet. Perhaps this is a disagreement about the term “prima facie”?
Learning that there is a very slow algorithm for a problem is often a very important indicator that a problem is solvable, and savings like 1040 to 1030 seem routine (and often have very strong similarities between the algorithms). And very often the running time of one algorithm is indeed a useful indicator for the running time of a very different approach. It’s possible we are thinking about different domains here, I’m mostly thinking of traditional algorithms (like graph problems, approximation algorithms, CSPs, etc.) scaled to input sizes where the computation cost is in this regime. Though it seems like the same is also true for ML (though I have much less data there and moreover all the examples are radically less crisp).
This seems wrong but maybe for reasons unrelated to the matter at hand. (In general an unknown number is much more likely to lie between 1011 and 1016 than between 1026 and 1031, just as an unknown number is more likely to lie between 11 and 16 than between 26 and 31.)
I think it’s a good rule of thumb for estimating numbers in general. If you know a number is between A and B (and nothing else), where A and B are on the order of 1020, then a log-uniform distribution between A and B is a reasonable prima facie guess.
This holds whether the number is “The best you can do on the task using method X” or “The best you can do on the task using any method we can discover in 100 years” or “The best we could do on this task with a week and some duct tape” or “The mass of a random object in the universe.”
I don’t know what “derived from evolutionary brute force” means (I don’t think anyone has said those words anywhere in this thread other than you?)
But in terms of P(AGI), I think that “20% for next 4 orders of magnitude” is a fine prima facie estimate if you bring in this single consideration and nothing else. Of course I don’t think anyone would ever do that, but frankly I still think “20% for the next 4 orders of magnitude” is still better than most communities’ estimates.