I created these notes for use when I facilitate AI safety courses. I'm sharing these notes early because this issue is topical and I suspect it is better to make an imperfect version available early rather than a much more polished version available later. Please note: some of this content was taken from Additional Course Context . I decided recently that the content on take-off speeds really belonged in the same document as the content on RSI, so I'll be releasing an new version of Additional Course Context at some point (to avoid spamming LW, it'll probably be Substack only ; none of my work is paywalled). Some of the other content was taken from Notes on “We’re in Triage Mode for AI Safety”. This Miles' article has been removed from the governance course, so I was looking for a new home for this content. I wanted to include it in a document that was intended to be shared in all the courses I facilitate.

Whilst there isn’t a strict definition of fast vs. slow takeoff, possibly the most influential definition comes from Paul Christiano (2018):

There will be a complete 4 year interval in which world output doubles, before the first 1 year interval in which world output doubles. (Similarly, we’ll see an 8 year doubling before a 2 year doubling, etc.)

At risk of oversimplifying, Paul argues that we should prima facie expect a slow takeoff because someone will generally figure out how to produce a “slightly worse” version of AI before someone figures out how to build the better version (he claims this is supported by the historical record of technological development overall).

Yudkowsky disagrees (2021), criticising the intuition that “design precursors with 95% of the technology should at least have 10% of the impact. He writes: "An awful lot of my model of deployment lag is adoption lag and regulatory lag and bureaucratic sclerosis across companies and countries” and “My mainline view is that growth stays at 5%/year and then everybody falls over dead in 3 seconds and the world gets transformed into paperclips"

How should we characterise progress up until now?

If Hanson or Christiano or Karnofsky etc etc believed this was what a "slow takeoff" looked like, they failed to convey that to their reassured, cheerful audience.

If you thought this was what fast takeoff looked like, you also failed to convey that.

For reference, Eliezer previously defined a fast as meaning, “a timescale of weeks or hours rather than years or decades”.

Forethought defines an additional scenario . For example, imagine if AI dramatically accelerates algorithm progress for a while, but then this plateaus whilst we figure out how to make robots that can automate the construction of chip fabs.

(Diagram note: the types of intelligence explosion will be explained in the next section)

In contrast, Arvind Narayanan (of AI as a Normal Technology ) argues any RSI we do achieve will be narrow (that is jagged): ie. progress on verifiable tasks will continue “for a few more years” or even accelerate whilst progress on unverifiable tasks more or less remains “frustratingly hard”.

Richard Ngo also expects jaggedness to persist, as opposed to everything “going vertical”. Why? Because of a poorly understood “divergence” between “measured capabilities” and “real-world impacts” (nonetheless he asserts “things are going to look much weirder than almost anyone expects”):

Whilst this is arguably less relevant these days, take-off speed is distinct from timelines. Take-off speeds are about how fast an intelligence explosion occurs if/when it happens whilst timelines are about when a particular milestone is achieved. Both slow-takeoff/short-timelines and fast-takeoff/long-timelines are conceptually possible.

Forethought examines three kinds of feedback loops :

Building on top of this, Forethought defines three kinds of intelligence explosion:

The reason why each type of intelligence explosion includes the previous factors is that they’ve ordered the factors by expected lead-time. If an intelligence explosion is possible, fast takeoff vs. slow takeoff likely depends heavily on what kinds of intelligence explosion would be sufficiently powerful to trigger it. For example, a fast takeoff is much more likely where a software-only explosion is possible, however, if you need to automate the full-stack, then there’d be a much stronger argument for a slow takeoff.

Tim Urban argues that, “it’s most intuitive for us to think linearly , when we should be thinking exponentially ”

This forms a key crux: Can we project exponential trends into the future on the basis of induction (ie. the future being like the past) or is this foolish given that exponentials must end at some point? Development of most technologies has occurred as a series of s-curves (ie. sigmoids) which would support the latter view.

In contrast, Astralcodex points out that simply knowing that something is a sigmoid doesn’t tell you where you are on the curve (a hilarious graph from the World Energy Organisation shows them repeatedly, incorrectly predicting that exponential progress in terms of solar power will finish):

He also has a graph showing where researchers incorrectly predicted that the METR time horizons would cap out just as the curve zoomed upward):

Connor Leahry writes : “There are only two times to react to an exponential: Too early, or too late.” In many case this is true. However, early on it may be hard to know if it is an exponential or not. Unfortunately, in many cases we’ll just have to make such decisions under uncertainty.

We’ll begin by considering two tables from DeepMind’s AGI to ASI which lays out potential bottlenecks and fundamental limitations of AI:

Toby Ord has argued that many people have failed to realise the implications of the shift from pre-training scaling to RL and inference-time scaling. A 100x increase in pre-training is equivalent to a 1,000x increase in inference or a 1,000,000x scale up of RL . He suggests that this effect has been masked since these factors hadn’t been scaled, but he suggests this is set to change with models already utilising significant inference-time compute and RL assigned a significant proportion of training compute (he has written a whole series on AI scaling ).

Toby emphasises that METR wasn’t confidently able to rule out a one-time jump rather than an increase in slope. He performed a quick analysis using Opus which suggested that 1.4x is a better estimate of the new slope gradient than METR’s 1.9x.

Seb Krier shared graphs (generated with Claude) indicating that a linear increase in AECI requires an exponential increase in spending.

Tom Davidson points out that this might be viable because linear increases in ECI provide (in his view) exponential increases in productivity. Thus the outputs scale in the inputs.

AI as a normal technology argues that diffusion cycles provide a bottleneck. Specifically, in their model, it takes time for model capabilities to flow through to product changes and then for people to use them. This produces the data that we need for the next round of capabilities improvements and the dependency on data from deployment limits the speed of potential feedback loops:

Next we’ll consider Ramez Naam’s Where’s the “Intelligence Explosion”? which pushes back against the notion that we’ll encounter RSI any time soon. He argues that the current AI feedback loop is only 10-20% of the strength required. He interprets OpenAI internal automation data as showing the real world AI research is much harder than other benchmarks show. He further notes that Anthropic predicted a 40× speed up in researcher productivity would be required to double their rate of progress due to other bottlenecks.

This was published 27th Sep 2026, ie. before METR’s independent report on AI acceleration. It’ll be interesting to see his response:

https://x.com/ramez/status/2118472046812213577

We’ll begin by naively projecting these trends forward:

Ajeya Cotra writes : If we take it at face value that AI is now nearly doubling the rate of AI capabilities progress and assume acceleration from AI is smooth, this naively implies that we would reach extreme superintelligence within a year

The dumbest possible way to model the intelligence explosion says you get there in about a year. But this seems to line up with more sophisticated models (like from the AI Futures Project).

So what might it look like if this model turn out to be accurate, or at least, “accurate enough”? Tim Urban argues that we have a distorted view of intelligence because are perceptions are very human centric (and, as such, stretch out the human range):

Conversely Steve Newman offers the following frame : what if AI is moving fast, but the “distance” to travel is longer than most people think, since we often only become aware of the limitations of models over time?:

(Of course, it is possible that both could be true at the same time)

We’ll now go to the more sophisticated analysis from the AI Futures project that Ben Todd was referring to, starting with their general model. They predict that an intelligence explosion would have three separate stages:

They define the following milestones (see the diagram above for estimated speed-up) where the operationalisations all imagine that we “drop” the AI into the present day:

Next we’ll examine what their model predicted take-off to look like if we decided to allow the companies to race to ASI (what they call “Plan D”). This model was developed before the most recent results (published July 10 2026):