An "intelligence explosion" is what happens if a machine intelligence has fast, consistent returns on investing work into improving its own cognitive powers, over an extended period. This would most stereotypically happen because it became able to optimize its own cognitive software, but could also apply in the case of "invested cognitive power in seizing all the computing power on the Internet" or "invested cognitive power in cracking the protein folding problem and then built nanocomputers".
A strong version of this idea suggests that once the positive feedback starts to play a role, it will lead to a very dramatic leap in capability very quickly. This is known as a “hard takeoff.” In this scenario, technological progress drops into the characteristic timescale of transistors rather than human neurons, and the ascent rapidly surges upward and creates superintelligence (a mind orders of magnitude more powerful than a human's) before it hits physical limits. A hard takeoff is distinguished from a "soft takeoff" only by the speed with which said limits are reached.
Philosopher David Chalmers published a significant analysis of the Singularity, focusing on intelligence explosions, in Journal of Consciousness Studies. His analysis of how they could occur defends the likelihood of an intelligence explosion. He performed a very careful analysis of the main premises and arguments for the existence of the a singularity from an intelligence explosion. According to him, the main argument is:"
—————-
He also discusses the nature of general intelligence, and possible obstacles to a singularity. A good deal of discussion is given to the dangers of an intelligence explosion, and Chalmers concludes that we must negotiate it very carefully by building the correct values into the initial AIs.
Luke Muehlhauser and Anna Salamon argue in Intelligence Explosion: Evidence and Import in detail that there is a substantial chance of an intelligence explosion within 100 years, and extremely critical in determining the future. They trace the implications of many types of upcoming technologies, and point out the feedback loops present in them. This leads them to deduce that an above-human level AI will almost certainly lead to an intelligence explosion. They conclude with recommendations for bringing about a safe intelligence explosion.
The following is a common example of a possible path for an AI to bring about an intelligence explosion. First, the AI is smart enough to conclude that inventing molecular nanotechnology will be of greatest benefit to it. Its first act of recursive self-improvement is to gain access to other computers over the internet. This extra computational ability increases the depth and breadth of its search processes. It then uses gained knowledge of material physics and a distributed computing program to invent the first general assembler nanomachine. Then it uses some manufacturing technology, accessible from the internet, to build and deploy the nanotech. It programs the nanotech to turn a large section of bedrock into a supercomputer. This is its second act of recursive self-improvement, only possible because of the first. Then it could use this enormous computing power to consider hundreds of alternative decision algorithms, better computing structures and so on. After this, this AI would go from a near to human level intelligence to a superintelligence, providing a dramatic and abruptly increase in capability.