adding colour and text inside a node of a neural network

I have the following structure of the neural network, But I would like to modify it and colour all input nodes as black and write f(x) inside the hidden nodes. Kindly guide me on how to attain it.

to something like this

 usetikzlibrary{positioning}
    tikzset{%
      every neuron/.style={
        circle,
        draw,
        minimum size=1cm
      },
      neuron missing/.style={
        draw=none, 
        scale=4,
        text height=0.333cm,
        execute at begin node=color{black}$vdots$
      },
    }
    
    begin{tikzpicture}[x=1.3cm, y=1.3cm, >=stealth]
    
    foreach m/l [count=y] in {1,2,3,missing,4}
      node [every neuron/.try, neuron m/.try] (input-m) at (0,2.5-y) {};
    
    foreach m [count=y] in {1,missing,2}
      node [every neuron/.try, neuron m/.try ] (hidden-m) at (2,2-y*1.25) {};
    
    
    foreach m [count=y] in {1,2,missing,3}
      node [every neuron/.try, neuron m/.try ] (output-m) at (4,2.0-y) {};
    
    foreach l [count=i] in {1,2,3,j}
      draw [<-] (input-i) -- ++(-1,0)
        node [above, midway] {$I_l_f$};
    
    foreach l [count=i] in {1,k}
      node [above] at (hidden-i.north) {$H_l_f$};
    
    
    foreach l [count=i] in {1,2,l}
      draw [->] (output-i) -- ++(1,0)
        node [above, midway] {$O_l_f$};
        
    foreach i in {1,...,4}
      foreach j in {1,...,2}
        draw [->] (input-i) -- (hidden-j);
    
    foreach i in {1,...,2}
      foreach j in {1,...,3}
        draw [->] (hidden-i) -- (output-j);
    
    foreach l [count=x from 0] in {Input, Hidden, Output}
      node [align=center, above] at (x*2,2) {l  layer};
    
    end{tikzpicture}

documentclass{article}
usepackage{tikz}

usetikzlibrary{positioning}
begin{document}


tikzset{%
    every neuron/.style={
        circle,
        draw,
        minimum size=1cm
    },
    neuron missing/.style={
        draw=none, fill=none,%<-----------------new
        scale=4,
        text height=0.333cm,
        execute at begin node=color{black}$vdots$
    },
}

begin{tikzpicture}[x=1.3cm, y=1.3cm, >=stealth]
    
    foreach m/l [count=y] in {1,2,3,missing,4}
    node [fill=black!20, every neuron/.try, neuron m/.try, ] (input-m) at (0,2.5-y) {};%<-----fill=
    
    foreach m [count=y] in {1,missing,2}
    node [every neuron/.try, neuron m/.try ] (hidden-m) at (2,2-y*1.25) {};
    
    
    foreach m [count=y] in {1,2,missing,3}
    node [every neuron/.try, neuron m/.try ] (output-m) at (4,2.0-y) {};
    
    foreach l [count=i] in {1,2,3,j}
    draw [<-] (input-i) -- ++(-1,0)
    node [above, midway] {$I$};
    
    foreach l [count=i] in {1,k}
    node [above] at (hidden-i.north) {$H$};
    
    
    foreach l [count=i] in {1,2,l}
    draw [->] (output-i) -- ++(1,0)
    node [above, midway] {$O$};
    
    foreach i in {1,...,4}
    foreach j in {1,...,2}
    draw [->] (input-i) -- (hidden-j);
    
    foreach i in {1,...,2}
    foreach j in {1,...,3}
    draw [->] (hidden-i) -- (output-j);
    
    foreach l [count=x from 0] in {Input, Hidden, Output}
    node [align=center, above] at (x*2,2) {l  layer};
    node (nx1) at (hidden-1) {$mathbf{f_x}$};%<---------------new
    node (nx2) at (hidden-2) {$mathbf{f_x}$};%<---------------new
end{tikzpicture}
end{document}