40 lines
898 B
Markdown
40 lines
898 B
Markdown
---
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id:
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aliases: []
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tags:
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- authorship/original
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- destiny/permanent
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- status/incomplete
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- topic/math
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- type/encyclopedia-entry
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title: Sigmoid Functions
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dg-publish: true
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---
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# Sigmoid Functions
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![[sigmoid-function-example.excalidraw]]
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$f'(x)$ is a **sigmoid** function.
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A sigmoid function compresses a function with infinite range to (0,1)
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This is preferable to a floor-ceiling piece-wise function
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since it remains differentiable.
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## Formula
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$$
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\sigma(x) = \frac{1}{1 + e^{-x}}
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$$
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```tikz
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\begin{document}
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\begin{tikzpicture}[domain=-5:5]
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\draw[->] (-5.2,0) -- (5.2,0) node[right] {$x$}; % x axis
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\draw[->] (0,-5.2) -- (0,5.2) node[above] {$y$}; % y axis
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\draw[color=red] plot (\x,\x) node[right] {$f(x) = x$};
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\draw[color=orange] plot (\x,{1/(1+exp(-\x))}) node[right] {$\sigma(x) = \frac{1}{1 + e^{-x}}$};
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\end{tikzpicture}
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\end{document}
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```
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