# Sigmoid Neuron

A Sigmoid Neuron is an artificial neuron that uses a Logistic Sigmoid Activation Function.

• AKA: Sigmoidal Neuron, Logistic Neuron, Log-Sigmoid Neuron, Sigmoid Neural Unit.
• Context:
• It can be mathematically described as

$\displaystyle{ y_j=\sigma(z_j)=1/(1+e^{-z_j})\quad \text{with} \quad z_j=\sum_{i=0}^nw_{ji}x_i+b \quad \text{for}\quad j=0,\cdots, p }$

where $\displaystyle{ x_i }$ are the Neural Network Input vector, $\displaystyle{ y_j }$ are the Neural Network Output vector, $\displaystyle{ w_{ji} }$ is the Neural Network Weights and $\displaystyle{ b }$ is the Bias Neuron.

• Example(s):
• Let's consider a sigmoid neuron with 3 inputs $\displaystyle{ \{x_1,x_2,x_3\} }$, 3 neural network weight values $\displaystyle{ \{w_1,w_2,w_3\} }$ and bias value $\displaystyle{ b }$. The output is given by $\displaystyle{ y=1/(1+e-z) }$ with $\displaystyle{ z=w_1*x_1+w_2*x_2+w_3*x_3 + b }$.
• Let's consider a sigmoid neuron with 3 inputs $\displaystyle{ X=\{0.5699, 0.1250, 0.5925\} }$, 3 neural network weight values $\displaystyle{ W=\{0.2217, 0.5029, 0.1168\} }$ and bias value $\displaystyle{ b=0.02 }$. The output is $\displaystyle{ y=1/(1+e^{-0.2780})=0.5691 }$ as $\displaystyle{ z=0.221*0.56997+0.5029*0.1250+0.1168*0.5925 + 0.02=0.2780 }$.
• Counter-Example(s):
• See: Artificial Neural Network, Perceptron.