Graph of Softplus Function

Softplus function defines $\beta$ or $\sigma$ of normal distribution since they have a range from 0 to $\infty.

$\zeta(x) = log(1+e^x)$


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There are some functions used while describing probability distribution in deep learning models they are
- Logistic Sigmoid
- Softplus Function


Properties of Common Functions

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

Sigmoid function defines the $\phi$ parameter of Bernoulli distribution. Sigmoid function can depict any real value in the range between 0 and 1.

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


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