Recursive Criticality of AI Self-Improvement

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 making further research progress. We derive a recursive reproduction number, RAI, that determines whether incremental improvements are amplified or damped across development cycles. This quantity compares the strength of recursive feedback with the rate at which further progress becomes more difficult. When RAI > 1, the effects of incremental improvements compound across development cycles, placing the system in a self-amplifying regime. When RAI < 1, their effects weaken across cycles. The transition depends on the structure of the AI R&D feedback loop and need not occur at any particular level of model capability. A system can therefore enter a self-amplifying regime before acceleration becomes visible, while rapid progress can also occur without self-amplification. In the minimal model, higher baseline research productivity can accelerate progress without changing whether the system is self-amplifying.

Introduction. Recursive AI self-improvement (RSI) is usually understood as a positive feedback loop in AI capabilities. AI research agents are beginning to perform work that lies inside the process used to build future AI systems. They write and debug code, propose experiments, analyse results, reproduce papers, operate software tools, and increasingly sustain technical work over longer horizons [1–5]. RSI is therefore better viewed as a property of an AI–R&D system than of an isolated, fully autonomous agent. The system may include human researchers, laboratories, compute infrastructure, evaluation procedures and organizations that integrate and deploy successor models. This paper asks three questions. Under what conditions does AI assistance to AI R&D cross from ordinary acceleration into a self-amplifying regime? How do feedback delay and a hardening research progress determine whether that regime produces a small transient displacement or significantly compressed transition to artificial general intelligence (AGI) and artificial super intelligence (ASI)?

Discussion / Conclusion. Recursive self-improvement is best understood as a dynamical property of an AI-enabled R&D system. In our model, the transition to self-amplifying improvement occurs when realized recursive gain exceeds the local hardening of the research frontier, so that RAI = χ/aσ > 1. Incremental improvements then amplify across successive development cycles. This transition is determined by the structure of the development process and need not coincide with a particular capability threshold such as AGI. Crossing RAI = 1 is a local condition for amplification and does not by itself imply indefinite acceleration or unbounded capability growth. The framework separates the onset, speed, and persistence of recursive amplification.RAI = 1 determines whether incremental gains amplify, while development-cycle delay constrains how rapidly that amplification unfolds.