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The McCulloch-Pitts Neuron

The McCulloch-Pitts Neuron. Characteristics. The activation of a McCulloch Pitts neuron is binary. Neurons are connected by directed weighted paths. A connection path is excitatory if the weight on the path is positive else its inhibitory.

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The McCulloch-Pitts Neuron

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  1. The McCulloch-Pitts Neuron

  2. Characteristics • The activation of a McCulloch Pitts neuron is binary. • Neurons are connected by directed weighted paths. • A connection path is excitatory if the weight on the path is positive else its inhibitory. • All excitatory connections to a neuron have the same weights. • Each neuron has a fixed threshold: • f(n) = 1 if n >= θ 0 if n < θ • The threshold is set so that inhibition is absolute. The McCulloch-Pitts Neuron

  3. A McCulloch-Pitts Neuron The McCulloch-Pitts Neuron

  4. Examples • Train a McCulloch-Pitts neural network to perform the OR function. • Train a McCulloch-Pitts neural network to perform the AND function. • Train a McCulloch-Pitts neural network to perform the AND NOT function. • Train a McCulloch-Pitts neural network to perform the XOR function. The McCulloch-Pitts Neuron

  5. Linear Separability • A single layer neural network can only learn linear separable problems. • Multilayer nets using a linear activation function have the same problem. • In linear separable problems the region where y is positive, i.e. the neuron fires, is separated from the region where y is negative, i.e where the neuron does not fire, by the line : The McCulloch-Pitts Neuron

  6. Graph for the AND Function The AND function is linearly separable The McCulloch-Pitts Neuron

  7. Graph for the OR Function The OR function is linearly separable The McCulloch-Pitts Neuron

  8. Graphic for the XOR Function The XOR function is not linearly separable The McCulloch-Pitts Neuron

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