The ______________ function is often used as an activation function in the output layer of a binary classification problem.

The sigmoid function is often used as an activation function in the output layer of a binary classification problem. The sigmoid function maps any input value to a value between 0 and 1, making it suitable for representing probabilities. When used in the output layer of a binary classification neural network, the sigmoid function allows the model to output a probability that can be interpreted as the likelihood of one class versus another (usually 1 versus 0).

The mathematical representation of the sigmoid function is given by:

$\sigma(x) = \frac{1}{1 + e^{-x}}$

where $x$ is the input to the function. Because the output of the sigmoid falls within the range (0, 1), it can be effectively used to determine class membership in binary classification tasks.