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.
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.