“The Dynamics of Intelligence Explosions” by Toby_Ord

Toby Ord Abstract AI is increasingly being used to help with AI R&D. Under certain conditions this feedback loop might be able to produce an intelligence explosion, with rapidly escalating AI capabilities. I explore the mathematics of the most explosive possibilities, with an eye to understanding what drives the dynamics. I show that singular growth (towards a vertical asymptote) is harder to achieve than would be expected from recent economics-inspired modelling, and that there is an important but neglected class of growth rates that are faster than exponential but don't lead to a vertical asymptote. I draw out the generation time (the time to go around the feedback loop) as a neglected parameter that plays a pivotal role in determining the behaviour of any intelligence explosion — one cannot have singular growth unless the generation time rapidly approaches zero. Keywords: recursive self-improvement, RSI, intelligence explosion, explosive growth, finite time singularity, generation time. Preview of Figure 1. A vertical asymptote requires the gradient (rise over run) to approach infinity within a finite time. Decreasing the run is key. It cannot be achieved with a fixed feedback generation time (centre) no matter how quickly the improvements grow [...] --- Outline: (00:12) Abstract (01:50) The Possibility of an Intelligence Explosion (06:40) Modelling RSI through Differential Equations (13:52) A Note on Singularities (16:36) Generalising the Standard Differential Equation for RSI (24:11) Feedback loops & discrete timesteps (42:14) Intelligence Measures (52:46) Going Finite (01:01:05) Conclusions (01:06:26) Appendix: Table of Rates of Growth (01:07:04) References The original text contained 16 footnotes which were omitted from this narration. --- First published: August 28th, 2026 Source: https://www.lesswrong.com/posts/o7QwBAYqpbvBL6SRH/the-dynamics-of-intelligence-explosions --- Narrated by TYPE III AUDIO. --- Images from the article: Apple Podcasts and Spotify do not show images in the episode description. Try Pocket Casts, or another podcast app.