Recursive Criticality of AI Self-Improvement

arXiv cs.AISeptember 2, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2609.00137v1 Announce Type: new Abstract: AI is increasingly used in the R\&D process that produces future AI systems. We study the conditions under which this feedback becomes self-amplifying. Our model describes how the rate of AI capability growth depends on baseline research productivity, recursive feedback, and the increasing difficulty of research progress. We derive a recursive reproduction number, $\mathcal{R}_{\mathrm{AI}}$, that determines whether improvements are amplified or damped across development cycles. This quantity compares the strength of feedback with the rate at which further progress becomes more difficult. When $\mathcal{R}_{\mathrm{AI}}>1$, the effects of impro

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