Spontaneous Origin of Topological Complexity in Self-Organizing Neural Networks

Attention is drawn to the possibility that self-organizing biological neural networks could spontaneously acquire the capability to carry out sophisticated computations. In particular it is shown that the effective action governing the formation of synaptic connections in models of networks of feature detectors that encorporate Kohonen-like self-organization can spontaneously lead to structures that are topologically nontrivial in both a 2-dimensional and 4-dimensional sense. It is suggested that the appearance of biological neural structures with a nontrivial 4-dimensional topology is the fundamental organizational principle underlying the emergence of advanced cognitive capabilities.