\begin{tikzpicture}
    \pic[] at (0,0) { nn={3}{2,5,5,2}{0.15cm}{0.02cm} };

    \node also [neuron label={\only<1|handout:0>{\#}}] (l1-1);
    \node also [neuron label={\only<1|handout:0>{\#}}] (l1-2);

    \node also [neuron label={\only<2|handout:0>{\#}}] (l2-1);
    \node also [neuron label={\only<2|handout:0>{\#}}] (l2-2);
    \node also [neuron label={\only<2|handout:0>{\#}}] (l2-3);
    \node also [neuron label={\only<2|handout:0>{\#}}] (l2-4);
    \node also [neuron label={\only<2|handout:0>{\#}}] (l2-5);

    \node also [neuron label={\only<3|handout:0>{\#}}] (l3-1);
    \node also [neuron label={\only<3|handout:0>{\#}}] (l3-2);
    \node also [neuron label={\only<3|handout:0>{\#}}] (l3-3);
    \node also [neuron label={\only<3|handout:0>{\#}}] (l3-4);
    \node also [neuron label={\only<3|handout:0>{\#}}] (l3-5);

    \node also [neuron label={\only<4-|handout:0>{\#}}] (l4-1);
    \node also [neuron label={\only<4-|handout:0>{\#}}] (l4-2);
\end{tikzpicture}