  We describe innovation in terms of a generalized branching process. Each new
invention pairs with any existing one to produce a number of offspring, which
is Poisson distributed with mean p. Existing inventions die with probability
p/\tau at each generation. In contrast to mean field results, no phase
transition occurs; the chance for survival is finite for all p > 0. For \tau =
\infty, surviving processes exhibit a bottleneck before exploding
super-exponentially - a growth consistent with a law of accelerating returns.
This behavior persists for finite \tau. We analyze, in detail, the asymptotic
behavior as p \to 0.
