How to make node relative order fixed in graphviz?

Question

I'm trying to draw a neural network in graphviz. Here is what my picture currently looks like:

As you can see, the order of the labels of the nodes don't appear correctly. For instance, I want $a_0^(2)$ sticks to the top of layer 2 and I want to arrange the rest of nodes in the same layer with numerical increasing order (i.e $a_1^(2)$, $a_2^(2)$, ...)

How can I do this? Much thanks!

Here is my code:

digraph G {
    rankdir=LR;
    splines=line;
    nodesep=".05";
    edge [comment="Wildcard node added automatic in EG."];
    node [label=""];
    subgraph cluster_0 {
        color=white;
        label="layer 1 (input layer)";
        edge [comment="Wildcard node added automatic in EG."];
        node [color=chartreuse, 
              style=filled, 
              shape=circle];
        x0 [color=yellow, 
            fillcolor=yellow, 
            label=<x<sub>0</sub>>];
        x1 [fillcolor=chartreuse, 
            label=<x<sub>1</sub>>];
        x2 [fillcolor=chartreuse, 
            label=<x<sub>2</sub>>];
        x3 [fillcolor=chartreuse, 
            label=<x<sub>3</sub>>];
    }

    subgraph cluster_1 {
        color=white;
        label="layer 2 (hidden layer)";
        edge [comment="Wildcard node added automatic in EG."];
        node [color=dodgerblue, 
              style=filled, 
              shape=circle];
        a02 [color=yellow, 
             label=<a<sub>0</sub><sup>(2)</sup>>, 
             pos="0,0", 
             fillcolor=yellow];
        a12 [label=<a<sub>1</sub><sup>(2)</sup>>, 
             pos="0,-1", 
             fillcolor=dodgerblue];
        a22 [label=<a<sub>2</sub><sup>(2)</sup>>, 
             pos="0,-2", 
             fillcolor=dodgerblue];
        a32 [label=<a<sub>3</sub><sup>(2)</sup>>, 
             pos="0,-3", 
             fillcolor=dodgerblue];
        a42 [label=<a<sub>4</sub><sup>(2)</sup>>, 
             pos="0,-4", 
             fillcolor=dodgerblue];
        a52 [label=<a<sub>5</sub><sup>(2)</sup>>, 
             pos="0,-5", 
             fillcolor=dodgerblue];
    }

    subgraph cluster_2 {
        color=white;
        label="layer 3 (hidden layer)";
        edge [comment="Wildcard node added automatic in EG."];
        node [color=dodgerblue, 
              style=filled, 
              shape=circle];
        a03 [color=yellow, 
             fillcolor=yellow, 
             label=<a<sub>0</sub><sup>(3)</sup>>];
        a13 [fillcolor=dodgerblue, 
             label=<a<sub>1</sub><sup>(3)</sup>>];
        a23 [fillcolor=dodgerblue, 
             label=<a<sub>2</sub><sup>(3)</sup>>];
        a33 [fillcolor=dodgerblue, 
             label=<a<sub>3</sub><sup>(3)</sup>>];
        a43 [fillcolor=dodgerblue, 
             label=<a<sub>4</sub><sup>(3)</sup>>];
        a53 [fillcolor=dodgerblue, 
             label=<a<sub>5</sub><sup>(3)</sup>>];
    }

    subgraph cluster_3 {
        color=white;
        label="layer 4 (output layer)";
        edge [comment="Wildcard node added automatic in EG."];
        node [color=coral1, 
              style=filled, 
              shape=circle];
        O1 [fillcolor=coral1, 
            label=<a<sub>1</sub><sup>(4)</sup>>];
        O2 [fillcolor=coral1, 
            label=<a<sub>2</sub><sup>(4)</sup>>];
        O3 [fillcolor=coral1, 
            label=<a<sub>3</sub><sup>(4)</sup>>];
        O4 [fillcolor=coral1, 
            label=<a<sub>4</sub><sup>(4)</sup>>];
    }

    x0 -> a12;
    x0 -> a22;
    x0 -> a32;
    x0 -> a42;
    x0 -> a52;
    x1 -> a12;
    x1 -> a22;
    x1 -> a32;
    x1 -> a42;
    x1 -> a52;
    x2 -> a12;
    x2 -> a22;
    x2 -> a32;
    x2 -> a42;
    x2 -> a52;
    x3 -> a12;
    x3 -> a22;
    x3 -> a32;
    x3 -> a42;
    x3 -> a52;
    a02 -> a13;
    a02 -> a23;
    a02 -> a33;
    a02 -> a43;
    a02 -> a53;
    a12 -> a13;
    a12 -> a23;
    a12 -> a33;
    a12 -> a43;
    a12 -> a53;
    a22 -> a13;
    a22 -> a23;
    a22 -> a33;
    a22 -> a43;
    a22 -> a53;
    a32 -> a13;
    a32 -> a23;
    a32 -> a33;
    a32 -> a43;
    a32 -> a53;
    a42 -> a13;
    a42 -> a23;
    a42 -> a33;
    a42 -> a43;
    a42 -> a53;
    a52 -> a13;
    a52 -> a23;
    a52 -> a33;
    a52 -> a43;
    a52 -> a53;
    a03 -> O1;
    a13 -> O1;
    a23 -> O1;
    a33 -> O1;
    a43 -> O1;
    a53 -> O1;
    a03 -> O2;
    a13 -> O2;
    a23 -> O2;
    a33 -> O2;
    a43 -> O2;
    a53 -> O2;
    a03 -> O3;
    a13 -> O3;
    a23 -> O3;
    a33 -> O3;
    a43 -> O3;
    a53 -> O3;
    a03 -> O4;
    a13 -> O4;
    a23 -> O4;
    a33 -> O4;
    a43 -> O4;
    a53 -> O4;
}

Answer 1

I don't think changing the labels is a good solution.

If the ordering of the nodes within each layer is important, I suggest adding invisible edges within each layer, forcing the order of the nodes.

Something like this:

digraph G {
    rankdir = LR;
    splines=false;
    edge[style=invis];
    ranksep= 1.4;
    {
        rank=same;
        x0->x1->x2->x3;
    }
    {
        rank=same;
        a0->a1->a2->a3->a4;
    }
    {
        rank=same;
        b0->b1->b2->b3->b4;
    }
    {
        rank=same;
        c0->c1->c2->c3;
    }

    edge[style=solid, tailport=e, headport=w];
    {x0; x1; x2; x3} -> {a0;a1;a2;a3;a4};
    {a0;a1;a2;a3;a4} -> {b0;b1;b2;b3;b4};
    {b0;b1;b2;b3;b4} -> {c0,c1,c2,c3};
}

Answer 2

So, I use some dirty tricks to get the following picture:

1. I connect all the nodes together with the following code like the following:

   x0 -> a02 [style=invisible, dir=none];

2. I relabel the nodes text according to each nodes position displayed in the picture (this is the really dirty one)

So, my complete code is available at here.

Please let me know if there is any better solution to this issue.