softplusfunktio

The softplus function is a smooth approximation of the rectified linear unit (ReLU) function. It is defined mathematically as f(x) = ln(1 + e^x). The softplus function is always positive and differentiable, which can be advantageous in certain machine learning applications compared to the non-differentiable ReLU. Its derivative is the sigmoid function, g(x) = e^x / (1 + e^x) = 1 / (1 + e^-x). As x approaches infinity, softplus approaches x, and as x approaches negative infinity, softplus approaches 0. This behavior is similar to ReLU, which outputs 0 for negative inputs and the input itself for positive inputs. The softplus function is often used in neural networks as an activation function, particularly in scenarios where a smooth, non-negative output is desired. It can also be employed in models requiring continuous outputs, such as in the context of variational autoencoders. While it shares similarities with ReLU, its smooth nature can sometimes lead to different optimization dynamics and potentially better gradient flow.