In fact the above is conservative in assuming one compute doubling yields just one labor doubling. You get that by running more copies. But you’ll train smarter models
If one compute doubling yields two labor doublings (holding software constant) then, rerunning the above analysis:
One compute doubling → two labor doublings (constant software) → in equilibrium, 6 labor doublings drive 4 software doublings (r=0.7)
today one compute doubling is associated with one (or fewer) labor doublings. In the new equ it’s associated with 6
How much faster would ai progress be compared to today?
Suppose that today labor and compute due exp are equally important and produce progress via cobb Douglas. Suppose they grow at equal rates
Then with full automation and r=0.7, labor is growing 6x faster than before. And overall ai progress is 3.5x faster
tldr: Under a simple model and reasonable assumptions, if we automate AI R&D and compute growth stays constant then the pace of AI software progress is 3-5X faster. This means the pace of overall AI progress would be 2-3X faster.
Assume AI software R&D is Cobb Douglas:
g_S = L^alpha E^beta S^-1/r
L = cognitive labour
E = experimental compute
r governs ideas getting harder to find as you ramp up both cognitive labour and experimental compute. (Note I’ve often confusingly defined r as the returns when you just ramp up cognitive labour—really I should call that r_cog = r * alpha.)
In this system, before automating away humans, it turns out that:
if L grows exponentially at g_L then (holding E fixed) g_S = g_L * alpha * r
if E grows exponentially at g_E then (holding L fixed) g_S = g_E * beta * r
When you automate AI R&D, L = S. In this situation, it turns out that:
if L grows exponentially at g_L (eg due to exogenously increasing compute), then: g_S = g_L * alpha * r / (1 - alpha * r)
And if r * alpha > 1 we get a software-only intelligence explosion!
if E grows exponentially at g_E (eg due to exogenously increasing compute), S grows at: g_S = g_E * beta * r / (1 - alpha * r)
In other words, even absent an SIE, automating AI R&D boosts the standard growth rates by a factor of 1 / (1 - alpha * r) due to the fizzling feedback loop of “better software → better AI researchers → better software”.
This model allows us to ballpark how much faster overall AI progress would be in a regime with full automation but no SIE.
That regime causes two changes:
g_L gets faster. Firstly, compute growth is somewhat faster than the growth of human AI researchers. Secondly, L is superlinear in compute bc you can run faster and smarter models with more compute.
All growth rates are boosted by a factor of 1 / (1 - alpha * r). Ryan used an estimate of r_cog = r * alpha = 0.7. So this is a boost by a factor of 1 / (1 − 0.7) = ~3.
Concretely, let’s make the following assumptions:
g_L = g_E today (conservatively assume compute and human researchers have grown at the same pace)
alpha = beta = 0.5
r = 1.4 (so that we recover Ryan’s r * alpha = 0.7)
After automating AI R&D, L grows twice as fast as compute: g_L = 2 * g_E
Then today the total pace of software progress is :
g_S = progress due to growing labour + progress due to growing compute
= g_E * alpha * r + g_E * beta * r
= g_E * r
And after AI R&D automation g_L is 2X faster and everything gets boosted by a factor of 3. The pace of software progress is:
g_S = progress due to growing labour + progress due to growing compute
= (2 * g_E * alpha * r + g_E * beta * r)*3
= 4.5 * g_E * r
So that’s 4.5x faster software progress, holding the rate of compute growth constant! If software and compute contribute equally to AI progress, that’s a bit under 3x faster total AI progress.
I think not too surprising, given we’re using an r*alpha value close to 1.
If we used r*alpha =0.5, our boost factor shrinks to 2 and we’d get 3x faster software progress and 2x faster total AI progress.
In fact the above is conservative in assuming one compute doubling yields just one labor doubling. You get that by running more copies. But you’ll train smarter models
If one compute doubling yields two labor doublings (holding software constant) then, rerunning the above analysis:
One compute doubling → two labor doublings (constant software) → in equilibrium, 6 labor doublings drive 4 software doublings (r=0.7)
today one compute doubling is associated with one (or fewer) labor doublings. In the new equ it’s associated with 6
How much faster would ai progress be compared to today?
Suppose that today labor and compute due exp are equally important and produce progress via cobb Douglas. Suppose they grow at equal rates
Then with full automation and r=0.7, labor is growing 6x faster than before. And overall ai progress is 3.5x faster
Of course, compute may be growing more slowly
I thought about this a bit more.
tldr: Under a simple model and reasonable assumptions, if we automate AI R&D and compute growth stays constant then the pace of AI software progress is 3-5X faster. This means the pace of overall AI progress would be 2-3X faster.
Assume AI software R&D is Cobb Douglas:
g_S = L^alpha E^beta S^-1/r
L = cognitive labour
E = experimental compute
r governs ideas getting harder to find as you ramp up both cognitive labour and experimental compute. (Note I’ve often confusingly defined r as the returns when you just ramp up cognitive labour—really I should call that r_cog = r * alpha.)
In this system, before automating away humans, it turns out that:
if L grows exponentially at g_L then (holding E fixed) g_S = g_L * alpha * r
if E grows exponentially at g_E then (holding L fixed) g_S = g_E * beta * r
When you automate AI R&D, L = S. In this situation, it turns out that:
if L grows exponentially at g_L (eg due to exogenously increasing compute), then:
g_S = g_L * alpha * r / (1 - alpha * r)
And if r * alpha > 1 we get a software-only intelligence explosion!
if E grows exponentially at g_E (eg due to exogenously increasing compute), S grows at:
g_S = g_E * beta * r / (1 - alpha * r)
In other words, even absent an SIE, automating AI R&D boosts the standard growth rates by a factor of 1 / (1 - alpha * r) due to the fizzling feedback loop of “better software → better AI researchers → better software”.
This model allows us to ballpark how much faster overall AI progress would be in a regime with full automation but no SIE.
That regime causes two changes:
g_L gets faster. Firstly, compute growth is somewhat faster than the growth of human AI researchers. Secondly, L is superlinear in compute bc you can run faster and smarter models with more compute.
All growth rates are boosted by a factor of 1 / (1 - alpha * r). Ryan used an estimate of r_cog = r * alpha = 0.7. So this is a boost by a factor of 1 / (1 − 0.7) = ~3.
Concretely, let’s make the following assumptions:
g_L = g_E today (conservatively assume compute and human researchers have grown at the same pace)
alpha = beta = 0.5
r = 1.4 (so that we recover Ryan’s r * alpha = 0.7)
After automating AI R&D, L grows twice as fast as compute: g_L = 2 * g_E
Then today the total pace of software progress is :
g_S = progress due to growing labour + progress due to growing compute
= g_E * alpha * r + g_E * beta * r
= g_E * r
And after AI R&D automation g_L is 2X faster and everything gets boosted by a factor of 3. The pace of software progress is:
g_S = progress due to growing labour + progress due to growing compute
= (2 * g_E * alpha * r + g_E * beta * r)*3
= 4.5 * g_E * r
So that’s 4.5x faster software progress, holding the rate of compute growth constant! If software and compute contribute equally to AI progress, that’s a bit under 3x faster total AI progress.
I think not too surprising, given we’re using an r*alpha value close to 1.
If we used r*alpha =0.5, our boost factor shrinks to 2 and we’d get 3x faster software progress and 2x faster total AI progress.