Recursive self-improvement (RSI) is the loop in which an AI system improves the process that produces it (its code, its architecture, its training) and, having become more capable, improves it further still. It is the mechanism assumed behind FOOM and the singularity; its classic statement is Good's: an ultraintelligent machine could design even better machines (Good, 1966, p. 33).
Yudkowsky (2008) illustrated it with Fermi's pile of 1942. With a neutron multiplication factor of 0.9994 the reaction dies out; at 1.0006 it sustains itself and grows. If each improvement triggers, on average, slightly more than one further improvement, a tiny difference separates stagnation from explosion. Omohundro added that almost any goal-directed agent would have reasons to improve itself, because doing so serves almost any goal (Omohundro, 2008) (see instrumental convergence). Logicians get a more elegant version: Schmidhuber's (2003) "Gödel machine" rewrites its own code only once it finds a proof that the rewrite is useful, which moves the problem onto the limits of self-reference.
In the era of language models, the concrete version would no longer be a program editing its source code, but models that write the code, generate the data and evaluate the experiments used to train their successors. That is why automating AI research is, for some, the roadmap and, for others, the red line. The song places it at the end of a genealogy that starts with masked language modeling: "To recursive self-upgrade" (osmarks, n.d.).
Skeptics point out that real loops have friction: diminishing returns, data running out, experiments that cost compute and physical time. The chain-reaction metaphor presupposes that "intelligence" multiplies like neutrons, and that is precisely what is in dispute.