An is a mathematical model of a biological neuron used as the basic unit of an artificial neural network.

Context: Core definition: Artificial neuron as a computational unit

The neuron computes a with bias before applying a nonlinearity.

Context: Bias and weighted summation

The standard neuron output has the form y_k = φ(∑_{j=0}^m w_kj x_j), where φ is the .

Context: Activation function role

Adding a bias term to the weighted sum causes which shifts the effective decision boundary.

Context: Cause→effect: bias shifts the decision boundary

Bias can be implemented by setting x0=+1 and using weight w0=b, so the neuron computes u=∑ w_j x_j before applying φ. This means bias is represented as an extra input with weight .

Context: Bias implementation: x0=+1 and w0=b

A outputs 1 when its input meets or exceeds a threshold and outputs 0 otherwise.

Context: Step/threshold activation

Using a sigmoid activation in deep multilayer networks causes backpropagated gradients to , making optimization difficult.

Context: Cause→effect: sigmoid leads to vanishing gradients

A is defined as f(x)=max(0,x), producing the positive part of its input.

Context: Rectifier/ReLU definition

Using a rectifier (ReLU) activation causes training of deeper networks to become and more effective.

Context: Cause→effect: ReLU improves deep training

An MCP neuron is a restricted, synchronous, discrete-time threshold model with binary quiet/firing outputs. Its update rule is based on a threshold.

Context: McCulloch–Pitts neuron dynamics

MCP neurons can represent linearly separable boolean functions such as AND/OR/NOR, but they cannot compute .

Context: Expressivity limits: MCP cannot compute XOR

McCulloch–Pitts (MCP) neuron dynamics and threshold logic enable simulation power: any finite state machine can be simulated by an MCP neural network, and with an infinite tape, MCP networks can simulate any .

Context: Simulation power: FSM and Turing machines

In the biological mapping, dendrites correspond to input weighting, the soma performs , and the axon fires when threshold is reached.

Context: Biological neuron components and signal flow

Biological axon firing discrete pulses when soma potential reaches threshold causes pulse rate to be translated into continuous-valued signaling for simulations. This effect is produced by higher firing frequency increasing the rate at which neighboring cells receive .

Context: Cause→effect: axon firing frequency and signaling

Do not confuse a neuron’s activation function with a linear system’s transfer function. The text warns that the should not be mistaken for a transfer function.

Context: Common confusion: activation function vs transfer function