The compiler example is very limited in explaining the concept, as it is only single-step and by definition, the Seed AI algorithm should be infinitely recursive.
A limited example is that program language compilers are frequently used to compile themselves. As compilers become more optimized, they can be re-compile themselves so that it can be faster at compiling.
Despite this, they cannot then produce faster code and so this can only provide a very limited one step self-improvement.
If you want to know anything more, I would suggest having a look at the organizations that are doing active research in this field.
Consolidated Robotics does the AI (under the name of Consolidated), yet they were bought out by Halliburton in 2005.
In 2005, the privately held Consolidated was earned by energy conglomerate Halliburton for an estimated price of $25 billion US. The company continues to operate under the name Consolidated, though as a wholly-owned and operated division of Halliburton.
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