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McCulloch–Pitts neuron

nounAlso: MCP neuron, McCulloch–Pitts model, threshold logic unit

In plain wordsThe first mathematical model of a brain cell as a simple on–off switch: it fires if enough of its inputs are on and no blocking input is. Networks of them can carry out logic.

  1. A binary threshold unit proposed by Warren McCullochWarren McCulloch, prop. n.: An American brain scientist who, with Walter Pitts, wrote the 1943 paper that first described nerve cells as simple logic units, the seed of today's artificial neural networks. and Walter PittsWalter Pitts, prop. n.: A largely self-taught American logician who, at about 20 and without a degree, co-invented with Warren McCulloch a simple logical model of a brain cell, the starting point of neural networks. in 1943 as an idealized neuron. Its inputs are all-or-none signals, each wired as either excitatory or inhibitory, and time advances in discrete steps. At each step a single active inhibitory input silences the unit outright; failing that, the unit fires (outputs 1) exactly when the count of active excitatory inputs is at or above a fixed threshold. With suitable thresholds and wiring, single units implement AND, OR and NOT, so networks of them can compute any Boolean function, and networks with loops behave like finite automata, as Stephen Kleene later formalized. The model does not learn: connections and thresholds are set by hand. Adding real-valued adjustable weights and a learning rule produced the perceptronperceptron, n.: One of the first learning machines: a single artificial neuron that sorts inputs into two groups by drawing a straight dividing line, nudging its weights whenever it guesses wrong., and the unit is the ancestor of the artificial neuronartificial neuron, n.: The basic building block of a neural network: a tiny calculator that multiplies each incoming number by a weight, adds them up, and passes the total through a simple function to decide its output. used in every modern neural networkneural network, n.: A kind of computer program that learns a task from examples by tuning thousands to billions of connections between simple number-crunching units, an arrangement loosely inspired by nerve cells in the brain..

    With a threshold of two and two excitatory inputs, a McCulloch–Pitts neuron computes AND.

y={1if ∑ixi≥θ and no inhibitory input is active0otherwisey = \begin{cases} 1 & \text{if } \sum_i x_i \ge \theta \text{ and no inhibitory input is active} \\ 0 & \text{otherwise} \end{cases}

Origin

Introduced in 'A Logical Calculus of the Ideas Immanent in Nervous Activity' in the Bulletin of Mathematical Biophysics (1943) by the neurophysiologist Warren McCulloch and the young, largely self-taught logician Walter Pitts. The paper influenced John von Neumann's 1945 EDVAC report, which described computer components as idealized neurons, and the founders of cyberneticscybernetics, n.: The study of how animals, machines and organizations steer themselves using feedback: sensing the result of an action and correcting course. It was both a parent and an early rival of AI..

Related

See also
  • perceptronperceptron, n.: One of the first learning machines: a single artificial neuron that sorts inputs into two groups by drawing a straight dividing line, nudging its weights whenever it guesses wrong.
  • artificial neuronartificial neuron, n.: The basic building block of a neural network: a tiny calculator that multiplies each incoming number by a weight, adds them up, and passes the total through a simple function to decide its output.
  • neural networkneural network, n.: A kind of computer program that learns a task from examples by tuning thousands to billions of connections between simple number-crunching units, an arrangement loosely inspired by nerve cells in the brain.
  • cyberneticscybernetics, n.: The study of how animals, machines and organizations steer themselves using feedback: sensing the result of an action and correcting course. It was both a parent and an early rival of AI.
  • Hebbian learningHebbian learning, n.: The idea that a connection between two brain cells grows stronger when they are active at the same time — the principle behind the slogan 'cells that fire together wire together'.
  • connectionismconnectionism, n.: The view that minds and intelligent machines are best built from huge networks of simple, neuron-like units whose connection strengths are learned, rather than from explicit rules and symbols.
Contrast with
  • perceptronperceptron, n.: One of the first learning machines: a single artificial neuron that sorts inputs into two groups by drawing a straight dividing line, nudging its weights whenever it guesses wrong.

Sources

  1. McCulloch, W. S. & Pitts, W. (1943). A Logical Calculus of the Ideas Immanent in Nervous Activity. Bulletin of Mathematical Biophysics 5, 115–133.

Mentioned in

artificial neuronartificial neuron, n.: The basic building block of a neural network: a tiny calculator that multiplies each incoming number by a weight, adds them up, and passes the total through a simple function to decide its output., neural networkneural network, n.: A kind of computer program that learns a task from examples by tuning thousands to billions of connections between simple number-crunching units, an arrangement loosely inspired by nerve cells in the brain., connectionismconnectionism, n.: The view that minds and intelligent machines are best built from huge networks of simple, neuron-like units whose connection strengths are learned, rather than from explicit rules and symbols., cyberneticscybernetics, n.: The study of how animals, machines and organizations steer themselves using feedback: sensing the result of an action and correcting course. It was both a parent and an early rival of AI., Hebbian learningHebbian learning, n.: The idea that a connection between two brain cells grows stronger when they are active at the same time — the principle behind the slogan 'cells that fire together wire together'., Warren McCullochWarren McCulloch, prop. n.: An American brain scientist who, with Walter Pitts, wrote the 1943 paper that first described nerve cells as simple logic units, the seed of today's artificial neural networks., Walter PittsWalter Pitts, prop. n.: A largely self-taught American logician who, at about 20 and without a degree, co-invented with Warren McCulloch a simple logical model of a brain cell, the starting point of neural networks.