Episode Details

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 [...]

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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.

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First published:
August 28th, 2026

Source:
https://www.lesswrong.com/posts/o7QwBAYqpbvBL6SRH/the-dynamics-of-intelligence-explosions

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Narrated by TYPE III AUDIO.

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Images from the article:

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