The Softplus Activation Function, often denoted as , is a smooth and differentiable approximation of the ReLU (Rectified Linear Unit) activation function. It aims to address the issue of "dying ReLU," a problem where ReLU units can output zero for any input and never recover.

The Softplus function takes an input and applies the natural logarithm to the result of 1 plus the exponentiation of x. This ensures that the output is always positive. As x becomes large, the function approaches a linear trend, similar to ReLU, making it an alternative for addressing the "dying ReLU" problem.


  • The function is smooth and differentiable, which makes it suitable for gradient-based optimization methods used in training neural networks.
  • It is non-monotonic, meaning it doesn't strictly increase or decrease, providing unique properties compared to simple linear or monotonic activation functions.


  • The Softplus function is predominantly used in Artificial Neural Networks (ANN) as an activation function, particularly in hidden layers, where it helps introduce non-linearity while avoiding the Vanishing Gradient problem.
  • The Softplus function can be advantageous when the smoothness of the derivative is desired, and the model's non-linearity should be maintained within specific input ranges.