McCulloch-Pitts Cell

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Diagram of a McCulloch-Pitts cell according to Minsky
Simulation of AND, OR and NOT gates using McCulloch-Pitts cells

A McCulloch-Pitts cell or McCulloch-Pitts neuron is a model of neurons proposed by Warren McCulloch and Walter Pitts in 1943 . Both wanted to design a simplified model of real processes in neural structures in order to clarify whether the brain can really calculate the Turing-calculable functions.

The McCulloch-Pitts neuron model is the simplest neuron model in neuroinformatics . Artificial neural networks made from McCulloch-Pitts cells can only use binary signals. Each individual neuron can only produce a 1 or 0 as output. Inhibitory signals can be processed in the same way as biological neural networks. Every McCulloch-Pitts cell has any real number as a threshold .

A McCulloch-Pitts cell with exciting input lines to which the signals are applied and inhibiting input lines to which the signals are applied calculates the following: If one of the signals is 1, the neuron outputs a 0. Otherwise the input signals are added up and compared with the threshold . If the sum of the excitations is greater than or equal , the neuron returns 1, otherwise it returns 0.

That is, McCulloch-Pitts cells can be inactivated by a single inhibitory lead. There is also an analogous behavior in some biological neurons.

A directed graph of such McCulloch-Pitts gates is called a McCulloch-Pitts network. If the graph does not contain any cycles , the network is called forward; if it contains cycles, it is called recursive . By McCulloch-Pitts networks both have And- , Oder and NOT gate simulate. So they form a complete basis of Boolean algebra . As an electronic component, the McCulloch-Pitts neuron is much more powerful than a simple and or or gate. With it as a component, very efficient electrical circuits can be implemented , i.e. with less consumption of components and cables than with conventional gates. For this reason, McCulloch-Pitts cells are still used and researched in electrical engineering today, known as threshold value elements.

literature

  • Warren McCulloch and Walter Pitts: A logical calculus of the ideas immanent in nervous activity . In: Bulletin of Mathematical Biophysics , Vol. 5 (1943), pp. 115-133, ISSN  0007-4985