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A slow takeoff is where AI capabilities improve gradually, giving us plenty of time to adapt. In a moderate takeoff we might see accelerating progress, but we still won’t be caught off guard by a dramatic change. Whereas, in a fast or hard takeoff AI would go from being not very generally competent to sufficiently superhuman to control the future too fast for humans to course correct if something goes wrong.
The article Distinguishing definitions of takeoff goes into more detail on this.