Graph of Softplus Function

The softplus function can be used to define the $$\beta$$ or $$\sigma$$ parameter of a normal distribution because its output range is from 0 to $$\infty$$. It is defined mathematically as $$\zeta(x) = \log(1 + e^x)$$.

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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) 

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Softplus Function

The logistic sigmoid function can be used to define the $$\phi$$ parameter of a Bernoulli distribution because its output range is between 0 and 1. It is defined mathematically as $$\sigma(x) = \frac{1}{1+e^{-x}}$$.

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