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Diversity is supposed to create better groups and societies but sometimes fails. It is explained why the power of diversity may not create better groups in the current diversity prediction theory. Diversity may hurt civic life and introduce distrust. This is because the current diversity prediction theory is based on real numbers that ignore individual abilities. Its diversity prediction theory maximizes performance with infinite population size. Contrary to this, collective intelligence or swarm intelligence is not maximized by infinite population size, but by population size. The extended diversity prediction theory using the complex number allows us to express individual abilities or qualities. The diversity of complex numbers always produces better groups and societies. The wisdom of crowds, collective intelligence, swarm intelligence or nature-inspired intelligence is implemented in the current machine learning or artificial intelligence, called Random Forest. The problem of the current diversity prediction theory is detailed in this paper. • Diversity is supposed to create better groups and societies but sometimes fails. • Diversity in real numbers ignores individual abilities. • Diversity of population size plays a key role in collective intelligence. • Diversity in complex numbers allows us to express individual abilities. • Diversity in complex numbers always produces better groups and societies. [ABSTRACT FROM AUTHOR]

Abstract: Most of local minima caused by the hierarchical structure can be resolved by extending the real-valued neural network to complex numbers. It was proved in 2000 that a critical point of the real-valued neural network with hidden neurons always gives many critical points of the real-valued neural network with hidden neurons. These critical points consist of many lines in the parameter space which could be local minima or saddle points. Local minima cause plateaus which have a strong negative influence on learning. However, most of the critical points of complex-valued neural network are saddle points unlike those of the real-valued neural network. This is a prominent property of the complex-valued neural network. [Copyright &y& Elsevier]