Definition
McCulloch–Pitts Model
The McCulloch–Pitts model, introduced by Warren McCulloch and Walter Pitts in A Logical Calculus of the Ideas Immanent in Nervous Activity (1943), is a mathematical model of a neuron as a Boolean logic unit.
Each neuron receives binary inputs. Excitatory inputs contribute to a sum; a single active inhibitory input forces the output to . If the sum of excitatory inputs reaches a fixed threshold and no inhibitory input is active, the neuron fires — output . Otherwise, output .
Every McCulloch–Pitts neuron computes a propositional logic function of its inputs. Networks of such neurons can express arbitrary Boolean circuits, modelling the brain itself as a logical machine.
Computational Power
Simple networks of McCulloch–Pitts neurons can perform Boolean operations — AND, OR, NOT — by choosing appropriate thresholds and inhibitory connections. Since any Boolean function can be composed from these primitives, networks of McCulloch–Pitts neurons can express arbitrary Boolean circuits.
Networks with loops can store state across time steps. A neuron whose output feeds back to its own input can persist a value, implementing a rudimentary form of memory. This echoes an earlier proposal by Lawrence Kubie (1930) that closed loops in the central nervous system explain memory.
McCulloch and Pitts further claimed that their nets, if provided with a tape, are equivalent to a Turing machine — i.e., Turing Completeness. They did not, however, provide a formal proof.
Limitations
The model provides no learning mechanism. Connections are fixed at construction; weights cannot be modified by experience. This is the central gap between the McCulloch–Pitts neuron and later artificial neural networks, which add plastic weights and turn the logical unit into a connectionist machine.