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 organization of feature detectors in neural networks which incorporate Kohonen-like self-organization can spontaneously lead to structures that are topologically non-trivial in both a twoand a four-dimensional sense. It is suggested that the appearance of biological neural structures with a non-trivial four-dimensional topology is the fundamental organizational development underlying the advanced cognitive capabilities of the mammalian brain.