Sigmoid Function
Calculate the sigmoid function (Sigmoid Function) sa(x).
The sigmoid function is used in neural networks as an activation function, among other applications.
| \( \normalsize Sigmoid\ function\ \varsigma_{\alpha}(x)\\ \varsigma_{\alpha}(x) = \large \frac{1}{1+e^{-\alpha x}} = \large \frac {\tanh(\alpha x /2) + 1}{2}\\ \normalsize \varsigma '_{\alpha}(x) = \alpha \varsigma_{\alpha}(x) \{ 1 - \varsigma_{\alpha}(x) \} \\ \normalsize \varsigma ''_{\alpha}(x) = \alpha^{2} \varsigma_{\alpha}(x) \{ 1- \varsigma_{\alpha}(x) \} \{ 1 - 2 \varsigma_{\alpha}(x) \} \\ \) |
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