# The Dynamics of Intelligence Explosions

arXiv: https://arxiv.org/abs/2608.14426 · HTML: https://mlsanity.com/paper/2608.14426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 34 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 4 of 4)

- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Measuring AI Ability to Complete Long Software Tasks](https://mlsanity.com/paper/2503.14499/) (2025)
- [AI capabilities can be significantly improved without expensive retraining](https://mlsanity.com/paper/2312.07413/) (2023)
- [Measuring AI R&D Automation](https://mlsanity.com/paper/2603.03992/) (2026)

## Built on by (most cited first, 1 of 1)

- [The Singularity Has a Distribution: Exact Timing Laws and Detection Limits for a Stochastic Intelligence Explosion](https://mlsanity.com/paper/2610.18445/) (2026)

## Abstract (arXiv)

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.