Gaussian Adaptation - The Evolution in The Brain

The Evolution in The Brain

In the brain the evolution of DNA-messages is supposed to be replaced by an evolution of signal patterns and the phenotypic landscape is replaced by a mental landscape, the complexity of which will hardly be second to the former. The metaphor with the mental landscape is based on the assumption that certain signal patterns give rise to a better well-being or performance. For instance, the control of a group of muscles leads to a better pronunciation of a word or performance of a piece of music.

In this simple model it is assumed that the brain consists of interconnected components that may add, multiply and delay signal values.

• A nerve cell kernel may add signal values,
• a synapse may multiply with a constant and
• An axon may delay values.

This is a basis of the theory of digital filters and neural networks consisting of components that may add, multiply and delay signalvalues and also of many brain models, Levine 1991.

In the figure below the brain stem is supposed to deliver Gaussian distributed signal patterns. This may be possible since certain neurons fire at random (Kandel et al.). The stem also constitutes a disordered structure surrounded by more ordered shells (Bergström, 1969), and according to the central limit theorem the sum of signals from many neurons may be Gaussian distributed. The triangular boxes represent synapses and the boxes with the + sign are cell kernels.

In the cortex signals are supposed to be tested for feasibility. When a signal is accepted the contact areas in the synapses are updated according to the formulas below in agreement with the Hebbian theory. The figure shows a 2-dimensional computer simulation of Gaussian adaptation according to the last formula in the preceding section.

m and W are updated according to:

m₁ = 0.9 m₁ + 0.1 x1; m₂ = 0.9 m₂ + 0.1 x₂;

w₁₁ = 0.9 w₁₁ + 0.1 y₁g₁; w₁₂ = 0.9 w₁₂ + 0.1 y₁g₂;

w₂₁ = 0.9 w₂₁ + 0.1 y₂g₁; w₂₂ = 0.9 w₂₂ + 0.1 y₂g₂;

As can be seen this is very much like a small brain ruled by the theory of Hebbian learning (Kjellström, 1996, 1999 and 2002).