# Sigmoid Neuron The sigmoid [[Neuron]] is often used in neural networks due to its ability to model non-linear relationships. The sigmoid function, which is the activation function for this type of neuron, is defined as: $ \sigma(x) = \frac{1}{1 + e^{-x}} $ This function outputs a value between 0 and 1, making it particularly useful for binary classification tasks. The derivative of the sigmoid function, which is necessary for backpropagation during training, is given by: $ \sigma'(x) = \sigma(x) \cdot (1 - \sigma(x)) $ The chain rule is used to compute the gradient during backpropagation, and the weight update rule in gradient descent is defined as: $ \Delta w = -\eta \nabla_\mathbf{w} \epsilon = -\eta \sum_{i=1}^{m} \nabla_\mathbf{w} \epsilon^{(i)} $ where $\eta$ is the learning rate, $\epsilon$ is the error function, and $m$ is the number of training examples. This allows the network to learn by adjusting the weights to minimize the error, thereby improving its predictive performance over time. --- ## References - [[Deep learning - Anna Bosch Rué Jordi Casas Roma Toni Lozano Bagén]]