TikZ: Diagram of a perceptron

Question

I'm trying to create a TikZ based version of the following diagram (taken from here), but I don't know how to approach it.

It doesn't need to look exactly like the original, but the basic idea should be preserved. It would especially be great if the paths from X_n to the sum function were straight lines without a "bend" like in the original. That makes a matrix layout difficult to use.

The definition of the output function can be left away.

Could someone point me to an approach that will work in this case, or even create a tikz texample?

---

Update: I ended up combining the approaches by @m0nhawk and @Toscho and came up with this:

Sourcecode is here: https://github.com/dbrgn/blog/blob/master/content/images/2013/3/26/perceptron.tex

Answer 1

Here is the simple reconstruction. Issues:

• Left of equations, can easily be added with node.
• Make inputs and weights with \foreach.
• Increase the Activation function to be more like the original one.
• Improve TikZ styles.

Code:

\documentclass[tikz]{standalone}
\usepackage{tikz}
    \usetikzlibrary{positioning}

\tikzset{basic/.style={draw,fill=blue!20,text width=1em,text badly centered}}
\tikzset{input/.style={basic,circle}}
\tikzset{weights/.style={basic,rectangle}}
\tikzset{functions/.style={basic,circle,fill=blue!10}}

\begin{document}
    \begin{tikzpicture}
        \node[functions] (center) {};
        \node[below of=center,font=\scriptsize,text width=4em] {Activation function};
        \draw[thick] (0.5em,0.5em) -- (0,0.5em) -- (0,-0.5em) -- (-0.5em,-0.5em);
        \draw (0em,0.75em) -- (0em,-0.75em);
        \draw (0.75em,0em) -- (-0.75em,0em);
        \node[right of=center] (right) {};
            \path[draw,->] (center) -- (right);
        \node[functions,left=3em of center] (left) {$\sum$};
            \path[draw,->] (left) -- (center);
        \node[weights,left=3em of left] (2) {$w_2$} -- (2) node[input,left of=2] (l2) {$x_2$};
            \path[draw,->] (l2) -- (2);
            \path[draw,->] (2) -- (left);
        \node[below of=2] (dots) {$\vdots$} -- (dots) node[left of=dots] (ldots) {$\vdots$};
        \node[weights,below of=dots] (n) {$w_n$} -- (n) node[input,left of=n] (ln) {$x_n$};
            \path[draw,->] (ln) -- (n);
            \path[draw,->] (n) -- (left);
        \node[weights,above of=2] (1) {$w_1$} -- (1) node[input,left of=1] (l1) {$x_1$};
            \path[draw,->] (l1) -- (1);
            \path[draw,->] (1) -- (left);
        \node[weights,above of=1] (0) {$w_0$} -- (0) node[input,left of=0] (l0) {$1$};
            \path[draw,->] (l0) -- (0);
            \path[draw,->] (0) -- (left);
        \node[below of=ln,font=\scriptsize] {inputs};
        \node[below of=n,font=\scriptsize] {weights};
    \end{tikzpicture}
\end{document}

Picture:

Answer 2

Here a shorter code without positioning, so you can scale the picture.

\documentclass[tikz]{article}
\usepackage{tikz}

\tikzset{basic/.style={draw,fill=blue!50!green!20,
                       text badly centered,minimum width=3em}}
\tikzset{input/.style={basic,circle}}
\tikzset{weights/.style={basic,rectangle,minimum width=2em}}
\tikzset{functions/.style={basic,circle,fill=blue!50!green!20}}
\newcommand{\addsymbol}{\draw[thick] (0.5em,0.5em) -- (0,0.5em) -- 
                        (0,-0.5em) --  (-0.5em,-0.5em)
                        (0em,0.75em) -- (0em,-0.75em)
                        (0.75em,0em) -- (-0.75em,0em);}

\begin{document}
    \begin{tikzpicture}[scale=1.2]
    \foreach \h [count=\hi ] in {$x_n$,$x_2$,$x_1$,$1$}{%
          \node[input] (f\hi) at (0,\hi*2cm-5 cm) {\h};
        }
    \node[functions] (sum) at (4,0) {$\sum$};
    \foreach \h [count=\hi ] in {$w_n$,$w_2$,$w_1$,$w_0$}{%
          \path (f\hi) -- node[weights] (w\hi) {\h} (sum);
          \draw[->] (f\hi) -- (w\hi);
          \draw[->] (w\hi) -- (sum);
        }        
    \node[functions] (step) at (7,0) {};
       \begin{scope}[xshift=7cm,scale=.75]
         \addsymbol
       \end{scope}
    \draw[->] (sum) -- (step);
    \draw[->] (step) -- ++(1,0);
    % Labels
    \node[above=1cm]  at (f4) {inputs};
    \node[above=1cm] at (w4) {weights};
    \end{tikzpicture}
\end{document}

Answer 3

With PSTricks but not completed...

\documentclass[preview,border=12pt]{standalone}
\usepackage{pst-node}
\usepackage{amsmath}
\psset
{
    rowsep=4mm,
    colsep=8mm,
    mnodesize=10mm,
    mnode=r,
}
\newcommand{\C}[1]{[mnode=circle,fillstyle=solid,fillcolor=blue!20]$#1$}
\newcommand{\R}[1]{[mnode=r]\psframebox[fillstyle=solid,fillcolor=blue!20]{\parbox{4mm}{\strut\centering$#1$}}}
\def\Symbol{%
\psset{unit=3mm}
\pspicture(-1,-1)(1,1)
    \psset{linewidth=0.4pt}
    \psline(-1,0)(1,0)
    \psline(0,-1)(0,1)
    \psline[linewidth=2\pslinewidth](-0.75,-0.5)(0,-0.5)(0,0.5)(0.75,0.5)
\endpspicture
}
\begin{document}
\offinterlineskip
\begin{psmatrix}
    \C{1}           & \R{w_0}\\
    \C{x_1}         & \R{w_1}\\
    \C{x_2}         & \R{w_2}       & \C{\Sigma}    & [mnode=circle,fillstyle=solid,fillcolor=blue!20,name=symbol]\Symbol   &   [mnode=p]\\
    \vdots          & \vdots\\
    \C{x_n}         & \R{w_n}\\
    \text{inputs}   & \text{weights}
    \psset{arrows=->}
    \ncline{1,1}{1,2}
        \ncline{2,1}{2,2}
            \ncline{3,1}{3,2}
                \ncline{5,1}{5,2}
    \ncdiagg{1,2}{3,3}
        \ncdiagg{2,2}{3,3}
            \ncdiagg{3,2}{3,3}
                \ncdiagg{5,2}{3,3}
    \ncline{3,3}{3,4}
    \ncline{3,4}{3,5}
\end{psmatrix}
\end{document}

Answer 4

If I understand you correctly, you want the nodes w_n to lie on straight lines from the nodes x_n to the node ∑. Then you can do

\usetikzlibrary{calc}
[…]
\node[…](w1) at ($(x1)!0.5!(sum)$) {\(w_n\)};
[…]

or

[…]
\path(x1)--node[…](w1){\(w_n\)}(sum);
[…]

Answer 5

I modified the solution of @Naphat to make it match the OP requested solution:

\documentclass[tikz]{article}
\usepackage{tikz}

\tikzset{basic/.style={draw,fill=none,
                       text badly centered,minimum width=3em}}
\tikzset{input/.style={basic,circle,minimum width=3.5em}}
\tikzset{weights/.style={basic,rectangle,minimum width=2em}}
\tikzset{functions/.style={basic,circle, minimum width=4em}}
\newcommand{\addaxes}{\draw (0em,1em) -- (0em,-1em)
                            (-1em,0em) -- (1em,0em);}
\newcommand{\relu}{\draw[line width=1.5pt] (-1em,0) -- (0,0)
                                (0,0) -- (0.75em,0.75em);}
\newcommand{\stepfunc}{\draw[line width=1.5pt] (0.65em,0.65em) -- (0,0.65em) 
                                    -- (0,-0.65em) -- (-0.65em,-0.65em);}

\begin{document}
    \begin{tikzpicture}[scale=1.2]
    % Draw input nodes
    \foreach \h [count=\hi ] in {$x_2$,$x_1$,$1$}{%
        \node[input] (f\hi) at (0,\hi*1.5cm-1.5 cm) {\h};
      }
    % Dot dot dot ... x_n
    \node[below=0.62cm] (idots) at (f1) {\vdots};
    \node[input, below=0.62cm] (last_input) at (idots) {$x_n$};
    % Draw summation node
    \node[functions] (sum) at (4,0) {\Huge$\sum$};
    % Draw edges from input nodes to summation node
    \foreach \h [count=\hi ] in {$w_2$,$w_1$,$w_0$}{%
          \path (f\hi) -- node[weights] (w\hi) {\h} (sum);
          \draw[->] (f\hi) -- (w\hi);
          \draw[->] (w\hi) -- (sum);
        }
    % Dot dot dot ... w_n
    \node[below=0.05cm] (wdots) at (w1) {\vdots};
    \node[weights, below=0.45cm] (last_weight) at (wdots) {$w_n$};
    % Add edges for last node and last weight etc
    \path[draw,->] (last_input) -- (last_weight);
    \path[draw,->] (last_weight) -- (sum);
    % Draw node for activation function
    \node[functions] (activation) at (7,0) {};
    % Place activation function in its node
    \begin{scope}[xshift=7cm,scale=1.25]
        \addaxes
        % flexible selection of activation function
        % \relu
        \stepfunc
    \end{scope}
    % Connect sum to activation function
    \draw[->] (sum) -- (activation) node (sum_eq) [midway, below=2cm, scale=1.2] {$\sum\limits_{i=0}^n w_ix_i$} node (sum_activation_midway) [midway, below] {};
    \path[draw,->] (sum_eq) -- (sum_activation_midway);
    \draw[->] (activation) -- ++(3,0) node (perceptron_output) [below=0.2cm, scale=1.2] {$output = \begin{cases}1 & \text{if }\ \sum\limits_{i=0}^n w_ix_i > 0,\\-1 & \text{otherwise}\end{cases}$};
    % Labels
    \node[above=1cm]  at (f3) {Inputs};
    \node[above=1cm] at (w3) {Weights};
    \node[above=1.5cm] at (activation) {Activation Function};
    \end{tikzpicture}
\end{document}

Answer 6

I am aware this is an old post, but I'll share what I did in case in becomes useful for others. I liked @m0nhawk's design (with \vdots) and @Alain Matthes' code, so I combined them. I also changed the activation to ReLU, but the code step function is still avilable.

It should be noted that I broke the size "scalability" from @Alain Matthes' code. Instead I use \resizebox to resize the figure.

\documentclass[tikz]{article}
\usepackage{tikz}

\tikzset{basic/.style={draw,fill=none,
                       text badly centered,minimum width=3em}}
\tikzset{input/.style={basic,circle,minimum width=3.5em}}
\tikzset{weights/.style={basic,rectangle,minimum width=2em}}
\tikzset{functions/.style={basic,circle, minimum width=4em}}
\newcommand{\addaxes}{\draw (0em,1em) -- (0em,-1em)
                            (-1em,0em) -- (1em,0em);}
\newcommand{\relu}{\draw[line width=1.5pt] (-1em,0) -- (0,0)
                                (0,0) -- (0.75em,0.75em);}
\newcommand{\stepfunc}{\draw[line width=1.5pt] (0.65em,0.65em) -- (0,0.65em) 
                                    -- (0,-0.65em) -- (-0.65em,-0.65em);}

\begin{document}
    \begin{tikzpicture}[scale=1.2]
    % Draw input nodes
    \foreach \h [count=\hi ] in {$x_2$,$x_1$,$x_0=1$}{%
          \node[input] (f\hi) at (0,\hi*1.25cm-1.5 cm) {\h};
        }
    % Dot dot dot ... x_n
    \node[below=0.62cm] (idots) at (f1) {\vdots};
    \node[input, below=0.62cm] (last_input) at (idots) {$x_n$};
    % Draw summation node
    \node[functions] (sum) at (4,0) {\Huge$\sum$};
    \node[below=0.69cm] at (sum) {$\sum_{i=0}^n w_ix_i$};
    % Draw edges from input nodes to summation node
    \foreach \h [count=\hi ] in {$w_2$,$w_1$,$w_0$}{%
          \path (f\hi) -- node[weights] (w\hi) {\h} (sum);
          \draw[->] (f\hi) -- (w\hi);
          \draw[->] (w\hi) -- (sum);
        }
    % Dot dot dot ... w_n
    \node[below=0.05cm] (wdots) at (w1) {\vdots};
    \node[weights, below=0.45cm] (last_weight) at (wdots) {$w_n$};
    % Add edges for last node and last weight etc
    \path[draw,->] (last_input) -- (last_weight);
    \path[draw,->] (last_weight) -- (sum);
    % Draw node for activation function
    \node[functions] (activation) at (7,0) {};
    % Place activation function in its node
    \begin{scope}[xshift=7cm,scale=1.25]
        \addaxes
        % flexible selection of activation function
        \relu
        % \stepfunc
    \end{scope}
    % Connect sum to relu
    \draw[->] (sum) -- (activation);
    \draw[->] (activation) -- ++(1,0);
    % Labels
    \node[above=1cm]  at (f3) {inputs};
    \node[above=1cm] at (w3) {weights};
    \node[above=1cm] at (activation) {activation function};
    \end{tikzpicture}
\end{document}