How can I equally space the row height in this table?

Question

Source and author: https://tex.stackexchange.com/a/431218/237848

The output looks like this:

Source Code:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{table}[h]
\centering
\begin{tabular}{llll}
    \hline
    \multicolumn{1}{l}{Name} & \multicolumn{1}{l}{Function} & \multicolumn{1}{l}{Derivative} & \multicolumn{1}{l}{Figure} \\ 
    \hline
    Sigmoid & $\sigma(x)=\frac{1}{1+e^{-x}}$ & $f'(x)=f(x)(1-f(x))^2$  &  
    \begin{tikzpicture}[baseline={(0,0.2)}]
     \draw (-1,0) -- (1,0);
     \draw (0,0) -- (0,1);
     \draw plot[domain=-1:1,variable=\x] ({\x},{1/(1+exp(-4*\x))});
    \end{tikzpicture}\\
    \\
    tanh & $\sigma(x)=\frac{e^x-e^{-x}}{e^z+e^{-z}} $ & $f'(x)=1-f(x)^2$   
    &  \begin{tikzpicture}[baseline={(0,0)}]
     \draw (-1,0) -- (1,0);
     \draw (0,-1) -- (0,1);
     \draw plot[domain=-1:1,variable=\x] ({\x},{tanh(4*\x)});
    \end{tikzpicture} \\
    ReLU & $f(x) =\begin{cases}
    0 & ~\text{if}~ x<0 \\ 
    x & ~\text{if}~x \geq 0.
    \end{cases}$ & $f'(x)=\begin{cases}
    0 & ~\text{if}~ x<0 \\ 
    x & ~\text{if}~1 \geq 0.
    \end{cases} $ & 
    \begin{tikzpicture}[baseline={(0,0.5)}]
     \draw (-1,0) -- (1,0);
     \draw (0,0) -- (0,1);
     \draw plot[domain=-1:1,variable=\x] ({\x},{ifthenelse(\x<0,0,\x)});
    \end{tikzpicture}\\
    Softmax & $f(x)=\frac{e^x}{\sum_i e^x}$ & $f'(x)=\frac{e^x}{\sum_i e^x} - \frac{(e^x)^2}{(\sum_i e^x)^2}$ &                            
\end{tabular}
\caption{Non-linear activation functions.}
\label{tab:activationfct}
\end{table}
\end{document}

What code will you recommend me to add to OP's code above, so that the four rows are of equal height, excluding the very first row that has Name, Function, etc.?

Thank you for your time and help.

Answer 1

Admitteldy, not all rows are of equal height, but at least the spacing around the tikzpictures in the last column is improved with the help of the cellspace package. I also made sure, all equations are typeset using \displaystyle in order to avoid font size changes. In order to make sure, the table fits into the textwidth, I used tabular* and in order to vertically center the plots with the text in the first column, I slightly changed the baseline=... option in all tikzpicture environments.

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{booktabs}
\usepackage{caption}
\usepackage[column=0]{cellspace}
\setlength{\cellspacetoplimit}{\tabcolsep}
\setlength{\cellspacebottomlimit}{\cellspacetoplimit}
\newlength{\mylength}       
\settoheight{\mylength}{R}
\begin{document}
\begin{table}[h]
\centering
\setlength{\tabcolsep}{0pt}
\caption{Non-linear activation functions.}
\label{tab:activationfct}
\begin{tabular*}{\linewidth}{@{\extracolsep{\fill}}0l *{2}{>{$\displaystyle}0l<{$}} 0l}
    \toprule
    \multicolumn{1}{@{}l}{Name} & \multicolumn{1}{l}{Function} & \multicolumn{1}{l}{Derivative} & \multicolumn{1}{l}{Figure} \\ 
    \midrule
    Sigmoid 
      & \sigma(x)=\frac{1}{1+e^{-x}} 
      & f'(x)=f(x)(1-f(x))^2  
      &  \begin{tikzpicture}[baseline={([yshift=-0.5\mylength]current bounding box.center)}]
           \draw (-1,0) -- (1,0);
           \draw (0,0) -- (0,1);
           \draw plot[domain=-1:1,variable=\x] ({\x},{1/(1+exp(-4*\x))});
         \end{tikzpicture}\\
    tanh 
      & \sigma(x)=\frac{e^x-e^{-x}}{e^z+e^{-z}} 
      & f'(x)=1-f(x)^2   
      &  \begin{tikzpicture}[baseline={([yshift=-0.5\mylength]current bounding box.center)}]
           \draw (-1,0) -- (1,0);
           \draw (0,-1) -- (0,1);
           \draw plot[domain=-1:1,variable=\x] ({\x},{tanh(4*\x)});
         \end{tikzpicture} \\
    ReLU 
      & f(x) =\begin{cases}
          0 & ~\text{if}~ x<0 \\ 
          x & ~\text{if}~x \geq 0.
        \end{cases} 
      & f'(x)=\begin{cases}
          0 & ~\text{if}~ x<0 \\ 
          x & ~\text{if}~1 \geq 0.
        \end{cases} 
    & \begin{tikzpicture}[baseline={([yshift=-0.5\mylength]current bounding box.center)}]
         \draw (-1,0) -- (1,0);
         \draw (0,0) -- (0,1);
         \draw plot[domain=-1:1,variable=\x] ({\x},{ifthenelse(\x<0,0,\x)});
      \end{tikzpicture}\\
    Softmax 
      & f(x)=\frac{e^x}{\sum_i e^x} 
      & f'(x)=\frac{e^x}{\sum_i e^x} - \frac{(e^x)^2}{(\sum_i e^x)^2}\\
  \bottomrule                           
\end{tabular*}
\end{table}
\end{document}