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Recursive Criticality of AI Self-Improvement
摘要
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 improvements compound across development cycles, placing the system in a self-amplifying regime. When $\mathcal{R}_{\mathrm{AI}}<1$, 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. Higher baseline research productivity can accelerate progress without changing whether the system is self-amplifying, but the duration of the development cycle becomes a limiting timescale for amplification. Increasing research difficulty can end a period of self-amplification. Extending the model to multiple research actors shows that improveme