Sigmoid Neurons: Working Principles

Sigmoid Neurons: Working Principles

• Sigmoid neurons are a type of artificial neuron that uses a sigmoid function as its activation function.
• The sigmoid function maps any input value to a value between 0 and 1.
• This range allows the neuron to output probabilities.
• The sigmoid function typically takes the weighted sum of inputs and a bias term as input.
• The resulting value is then fed to the sigmoid function to produce the output.

Input to Sigmoid Neuron

• Inputs are typically numerical values.
• These values represent features or signals relevant to the task the neuron is performing.
• Multiple inputs can be combined using weights to determine the overall influence of each input.
• Inputs are processed by applying weights to them individually (weighted summation).

Weights

• Each input has an associated weight.
• These weights modulate the influence of each input on the neuron's output.
• Weights are learned during the training process of a neural network.
• Higher weights indicate a higher importance or influence of the corresponding input.

Bias

• A bias term is added to the weighted sum of inputs.
• It creates a threshold effect.
• Biases allow the neuron to adjust the output range without entirely changing the weights themselves.

Weighted Sum

• The weighted sum of inputs represents the neuron's activation level.
• It's calculated by multiplying each input by its respective weight and then adding up these products.
• The bias is added to this weighted sum.
• This sum forms the input to the sigmoid activation function.

Activation Function (Sigmoid)

• The purpose of the sigmoid function is to map any input value to a value between 0 and 1 (probabilities).
• A sigmoid function is a differentiable function which continuously maps data from the real line to the range [0,1].

Output

• The output of the sigmoid neuron is a single value between 0 and 1.
• This value is interpreted as a probability output representing the activation level of the neuron or the probability of a specific class.

Simplified Model of Sigmoid Neuron Operation

• The neuron receives input values (x₁, x₂, ..., x_n).
• Each input is multiplied by a corresponding weight (w₁, w₂, ..., w_n).
• The weighted inputs are summed together.
• A bias term (b) is added to the sum.
• The resulting sum is passed through the sigmoid function.
• The output of the sigmoid function (σ(z)) is the output of the neuron.

z = w₁x₁ + w₂x₂ + ... + w_nx_n + b

a = σ(z)

Importance of Sigmoid Activation Function

• The sigmoid function is critical in neural networks.
• It's used as an activation function to introduce non-linearity into the network.
• Without non-linear activation the network is just a set of linear transformations.

Limitations of Sigmoid Neurons

• The vanishing gradient problem.
• Sigmoid activation function outputs in the range [0, 1], causing values to get compressed during training.

Explore the fundamentals of sigmoid neurons, which utilize the sigmoid function as their activation mechanism. Understand how inputs are weighted and combined to enable the neuron to output probabilities between 0 and 1. This quiz will test your knowledge on the functioning and importance of these artificial neurons in neural networks.