I think I get it, thanks! (What follows is my understanding, please correct if wrong!) The idea is something like: A falling leaf is not a computer, it can’t be repurposed to perform many different useful computations. But a neuron is; depending on the weights of its synapses it can be an and gate, an or gate, or various more complicated things. And this paper in the OP is evidence that the range of more complicated useful computations it can do is quite large, which is reason to think that in maybe in the relevant sense a lot of the brain’s skills have to involve fancy calculations within neurons. (Just because they do doesn’t mean they have to, but if neurons are general-purpose computers capable of doing lots of computations, that seems like evidence compared to if neurons were more like falling leaves)
I still haven’t read the paper—does the experiment distinguish between the “it’s a tiny computer” hypothesis vs. the “it’s like a falling leaf—hard to simulate, but not in an interesting way” hypothesis?
Ya, this is what I’m thinking, although have to is also a matter of scaling, e.g. a larger brain could accomplish the same with less powerful neurons. There’s also probably a lot of waste in the human brain, even just among the structures most important for reasoning (although the same could end up being true or an AGI/TAI we try to build; we might need a lot of waste before we can prune or make smaller student networks, etc.).
On falling leaves, the authors were just simulating the input and output behaviour of the neurons, not the physics/chemistry/biology (I’m not sure if that’s what you had in mind), but based on the discussion on this post, the 1000x could be very misleading and could mostly go away as you scale to try to simulate a larger biological network, or you could have a similar cost in trying to simulate an artificial neural network with a biological one. They didn’t check for these possibilities (so it could still be in some sense like simulating falling leaves).
Still, 1000x seems high to me for biological neurons not being any more powerful than artificial neurons, although this is pretty much just gut intuition, and I can’t really explain why. Based on the conversations here (with you and others), I think 10x is a reasonable guess.
What I meant by the falling leaf thing: If we wanted to accurately simulate where a leaf would land when dropped from a certain height and angle, it would require a ton of complex computation. But (one can imagine) it’s not necessary for us to do this; for any practical purpose we can just simplify it to a random distribution centered directly below the leaf with variance v.
Similarly (perhaps) if we want to accurately simulate the input-output behavior of a neuron, maybe we need 8 layers of artificial neurons. But maybe in practice if we just simplified it to “It sums up the strength of all the neurons that fired at it in the last period, and then fires with probability p, where p is an s-curve function of the strength sum...” maybe that would work fine for practical purposes—NOT for purpose of accurately reproducing the human brain’s behavior, but for purposes of building an approximately brain-sized artificial neural net that is able to learn and excel at the same tasks.
My original point no. 1 was basically that I don’t see how the experiment conducted in this paper is much evidence against the “simplified model would work fine for practical purposes” hypothesis.
Ya, that’s fair. If this is the case, I might say that the biological neurons don’t have additional useful degrees of freedom for the same number of inputs, and the paper didn’t explicitly test for this either way, although, imo, what they did test is weak Bayesian evidence for biological neurons having more useful degrees of freedom, since if they could be simulated with few artificial neurons, we could pretty much rule out that hypothesis. Maybe this evidence is too weak to update much on, though, especially if you had a prior that simulating biological neurons would be pretty hard even if they had no additional useful degrees of freedom.
Now I think we are on the same page. Nice! I agree that this is weak bayesian evidence for the reason you mention; if the experiment had discovered that one artificial neuron could adequately simulate one biological neuron, that would basically put an upper bound on things for purposes of the bio anchors framework (cutting off approximately the top half of Ajeya’s distribution over required size of artificial neural net). Instead they found that you need thousands. But (I would say) this is only weak evidence because prior to hearing about this experiment I would have predicted that it would be difficult to accurately simulate a neuron, just as it’s difficult to accurately simulate a falling leaf. Pretty much everything that happens in biology is complicated and hard to simulate.
I think I get it, thanks! (What follows is my understanding, please correct if wrong!) The idea is something like: A falling leaf is not a computer, it can’t be repurposed to perform many different useful computations. But a neuron is; depending on the weights of its synapses it can be an and gate, an or gate, or various more complicated things. And this paper in the OP is evidence that the range of more complicated useful computations it can do is quite large, which is reason to think that in maybe in the relevant sense a lot of the brain’s skills have to involve fancy calculations within neurons. (Just because they do doesn’t mean they have to, but if neurons are general-purpose computers capable of doing lots of computations, that seems like evidence compared to if neurons were more like falling leaves)
I still haven’t read the paper—does the experiment distinguish between the “it’s a tiny computer” hypothesis vs. the “it’s like a falling leaf—hard to simulate, but not in an interesting way” hypothesis?
Ya, this is what I’m thinking, although have to is also a matter of scaling, e.g. a larger brain could accomplish the same with less powerful neurons. There’s also probably a lot of waste in the human brain, even just among the structures most important for reasoning (although the same could end up being true or an AGI/TAI we try to build; we might need a lot of waste before we can prune or make smaller student networks, etc.).
On falling leaves, the authors were just simulating the input and output behaviour of the neurons, not the physics/chemistry/biology (I’m not sure if that’s what you had in mind), but based on the discussion on this post, the 1000x could be very misleading and could mostly go away as you scale to try to simulate a larger biological network, or you could have a similar cost in trying to simulate an artificial neural network with a biological one. They didn’t check for these possibilities (so it could still be in some sense like simulating falling leaves).
Still, 1000x seems high to me for biological neurons not being any more powerful than artificial neurons, although this is pretty much just gut intuition, and I can’t really explain why. Based on the conversations here (with you and others), I think 10x is a reasonable guess.
What I meant by the falling leaf thing:
If we wanted to accurately simulate where a leaf would land when dropped from a certain height and angle, it would require a ton of complex computation. But (one can imagine) it’s not necessary for us to do this; for any practical purpose we can just simplify it to a random distribution centered directly below the leaf with variance v.
Similarly (perhaps) if we want to accurately simulate the input-output behavior of a neuron, maybe we need 8 layers of artificial neurons. But maybe in practice if we just simplified it to “It sums up the strength of all the neurons that fired at it in the last period, and then fires with probability p, where p is an s-curve function of the strength sum...” maybe that would work fine for practical purposes—NOT for purpose of accurately reproducing the human brain’s behavior, but for purposes of building an approximately brain-sized artificial neural net that is able to learn and excel at the same tasks.
My original point no. 1 was basically that I don’t see how the experiment conducted in this paper is much evidence against the “simplified model would work fine for practical purposes” hypothesis.
Ya, that’s fair. If this is the case, I might say that the biological neurons don’t have additional useful degrees of freedom for the same number of inputs, and the paper didn’t explicitly test for this either way, although, imo, what they did test is weak Bayesian evidence for biological neurons having more useful degrees of freedom, since if they could be simulated with few artificial neurons, we could pretty much rule out that hypothesis. Maybe this evidence is too weak to update much on, though, especially if you had a prior that simulating biological neurons would be pretty hard even if they had no additional useful degrees of freedom.
Now I think we are on the same page. Nice! I agree that this is weak bayesian evidence for the reason you mention; if the experiment had discovered that one artificial neuron could adequately simulate one biological neuron, that would basically put an upper bound on things for purposes of the bio anchors framework (cutting off approximately the top half of Ajeya’s distribution over required size of artificial neural net). Instead they found that you need thousands. But (I would say) this is only weak evidence because prior to hearing about this experiment I would have predicted that it would be difficult to accurately simulate a neuron, just as it’s difficult to accurately simulate a falling leaf. Pretty much everything that happens in biology is complicated and hard to simulate.