Problem

The hyperbolic tangent is another commonly used activation function in neural networks. The function is given by $$\begin{align} \textrm{tanh}(x) = \frac{e^{x}-e^{-x}}{e^x + e^{-x}} \end{align}$$ Show that the $\textrm{tanh}$ function is related to the sigmoid function by $$\begin{align} \textrm{tanh}(x) = 2\sigma(2x) - 1. \end{align}$$

Solution

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