Research

AI labs are increasingly using AI itself to accelerate AI research, creating a feedback loop that could lead to an intelligence explosion. We develop a general semi-endogenous growth model with an innovation network, where research and automation in one sector increase the productivity of research in other sectors, and derive a clean analytical condition under which growth becomes superexponential (``explosive''). We find that automating research can offset diminishing returns to ideas by activating two reinforcing channels: a technological feedback loop across research sectors, and an economic feedback loop in which higher output finances further research. Growth becomes explosive if the combined strength of technological and economic feedback loops overcomes diminishing returns. In a simple simulation calibrated to trends in AI progress, fully automating software research and modest (5%) automation in other sectors generates a singularity within six years. Bottlenecks do not overturn the result if task automation advances sufficiently fast.

In this note I consider an economy with two factor inputs, one growing exponentially and one growing hyperbolically. I derive the conditions under which aggregate output is growing super exponentially vs subexponentially. In the case where the slow growing factor is in fact fixed, I get a closed form solution for the date at which the growth regime changes from super to subexponential.

This note derives conditions under which an endogenous automation frontier eliminates task bottlenecks in a CES task-based model, despite complementarities across tasks. An expanding AI task share can offset the drag from unbalanced factor growth, and the key condition admits a clean form: automation scales without bottlenecks so long as the slope of the AI productivity gradient is less than the elasticity of substitution between AI and labor.