Threshold Crossings as Tail Events for Catastrophic AI Risk

We analyse circumstances in which bifurcation-driven jumps in AI systems are associated with emergent heavy-tailed outcome distributions. By analysing how a control parameter's random fluctuations near a catastrophic threshold generate extreme outcomes, we demonstrate in what circumstances the probability of a sudden, large-scale, transition aligns closely with the tail probability of the resulting damage distribution. Our results contribute to research in monitoring, mitigation and control of AI systems when seeking to manage potentially catastrophic AI risk.