Easily. Simply define the efficiency metric to favor speed and accuracy in mail sorting, high speed trading, predicting movie box office revenue, or chess playing and you're done.
If you define efficiency as the number of days required to write a textbook without any feedback from faculty or students divided by the number of pages, then the answering becomes difficult. The tipping point when silicon is expected to outperform carbon for that task is unpredictable. It could be one month, one year, one decade, one century, one millennium, or never.
There remain many other such tasks.
Yes, it is possible that an invention of homo sapiens will later become the dominant life form on Earth, but there is no mathematically terse proof that such must occur.
A scenario that would interfere is if Russia and the U.S. were to engage in a full nuclear exchange and render the Earth inhabitable before any teams achieves in computers whatever criteria we choose for measuring efficiency.
If what some are calling general intelligence 1 occurs in computers and, as some within that group are claiming without proof, a runaway process ensues, then the computers themselves would presumably be able to improve their own efficiency.
this is not clearly defined, there are two answers.
The answer is, "Yes," for the examples of artificial network successes listed above. Research how they were already done and use the same tools.
The answer is, "No," for the creating from scratch and with limited feedback and starting information any of these.
- A university curriculum that prepares students to perform in a wide variety of jobs
- A design for a solar research laboratory
- A generator to produce content for a political satire column
- A design for a robot brain that, when placed in a robot, competes with a human successfully in arbitrary environments with arbitrary goals
There is insufficient theory as of this writing to construct tools to support these extents of general creativity. Human's can do the first three but not the fourth as of yet.
Note on the Term "General Intelligence"
General intelligence is a poorly defined term in spite of the number of words devoted to the topic. There also exists significant variation in these poor definitions.
Most authors define it as what can be characterized as adaptability to a wide array of conditions similar to that of the human beings, when human beings are placed in harsh environments, ones where adaptability is required for social or physical survival. (The performance of comfortable humans is not a very meaningful criteria to be met.)