Graphs.ipynb

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      "name": "Graphs.ipynb",
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      "name": "python3",
      "display_name": "Python 3"
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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/davidcpage/Imagenette-experiments/blob/master/Graphs.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ek7wWQAzTBgr",
        "colab_type": "text"
      },
      "source": [
        "### Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XWOc9Ny9TAWs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!python -m pip install typeguard\n",
        "!python -m pip install --upgrade pillow fastprogress\n",
        "!python -m pip install git+https://github.com/fastai/fastcore.git\n",
        "!python -m pip install git+https://github.com/fastai/fastai2\n",
        "\n",
        "!python -m pip install --extra-index-url https://developer.download.nvidia.com/compute/redist/cuda/10.0 nvidia-dali"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WTemu5NYhnQ2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "UTILS = 'https://raw.githubusercontent.com/davidcpage/Imagenette-experiments/master/utils.py'\n",
        "!wget $UTILS -O utils.py"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hrKT8LIvuUm8",
        "colab_type": "text"
      },
      "source": [
        "The aim of this notebook is to demonstrate a format for defining (hierarchical) directed graphs. Later we will show how to use this for Pytorch model creation and visualisation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YbRa_zQHGN49",
        "colab_type": "text"
      },
      "source": [
        "### Graphs"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fioSL6kSGQeH",
        "colab_type": "text"
      },
      "source": [
        "Let's define a compact way of representing directed graphs (suitable for describing neural networks) as python dictionaries. Each node has a *name* which should be a string, a *value* which can be anything and an (ordered) list of *inputs* representing incoming edges from other nodes. Inputs are ordered as they typically represent function args. We can alternatively provide a dict of *inputs* to represent named args. Here is our graph format:\n",
        "\n",
        "\n",
        "```\n",
        "Graph := {name: (value, [input])}\n",
        "```\n",
        "\n",
        "or\n",
        "\n",
        "```\n",
        "Graph := {name: (value, {input_name: input}}\n",
        "```\n",
        "\n",
        "Here is an example of such a Graph using both kinds of inputs:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IEvcxnz_W2s_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#define some node values - just strings for now, \n",
        "#we'll use more interesting values later\n",
        "A, B, C, D = 'Aa', 'Bb', 'Cc', 'Dd'\n",
        "\n",
        "graph = {\n",
        "    'a': (A, []),\n",
        "    'b': (B, ['a']),\n",
        "    'c': (C, {'x': 'a', 'y': 'c'}),\n",
        "    'd': (D, ['b'])\n",
        "}"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OpIHhudKHaWE",
        "colab_type": "text"
      },
      "source": [
        "It will be useful to be able to display Graphs. Here is a function that does that:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zb1LrPoaawb-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from utils import *"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "argu0xD1GJDE",
        "colab_type": "code",
        "outputId": "66039955-28af-48b3-ffbe-d2ca68de593e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        }
      },
      "source": [
        "draw = lambda graph, : DotGraph({name: ({'tooltip': str(value)}, inputs) for name, (value, inputs) in graph.items()}, size=10)\n",
        "draw(graph)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f4e45042e10>"
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          },
          "metadata": {
            "tags": []
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          "execution_count": 4
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        "id": "MzQsKyL0IMfp",
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      "source": [
        "The ```draw``` function above is just a thin wrapper around ```DotGraph``` which \n",
        "expects a standard Graph as input - with the constraint that *values* are dicts with fields that Graphviz understands (e.g. 'tooltip'.) If you hover over a node, you should see the *value* displayed as a tooltip. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "povBhoNxL5wS",
        "colab_type": "text"
      },
      "source": [
        "**Colors**\n",
        "\n",
        "Let's make things a bit more interesting by adding some color based on a property of the nodes - in this case the value:"
      ]
    },
    {
      "cell_type": "code",
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        "id": "GVGfs0eFGI0m",
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        }
      },
      "source": [
        "colors = {A: 'blue', B: 'green', C: 'yellow', D: 'green'}\n",
        "draw = lambda graph, max_depth=0, size=None: DotGraph({name: ({'tooltip': str(value), 'fillcolor': colors[str(value)]}, inputs) for name, (value, inputs) in graph.items()}, size=size)\n",
        "draw(graph)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
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              "<utils.DotGraph at 0x7f48121cef60>"
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          "execution_count": 11
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      "source": [
        "Choosing colors by hand is not the best use of our time so here's a helper to do it for us. ColorMap() is just a dictionary which populates itself with colors from a chosen palette when we ask for a missing key. Asking for the same key twice returns the same color which can be useful for coloring nodes consistently by some property (e.g. type.)"
      ]
    },
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          "base_uri": "https://localhost:8080/",
          "height": 176
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      },
      "source": [
        "colors = ColorMap()\n",
        "draw(graph)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48121ea2e8>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N2mDH515LJI6",
        "colab_type": "text"
      },
      "source": [
        "We can inspect a ColorMap like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SPUPfOakJtn-",
        "colab_type": "code",
        "outputId": "43ac14eb-330b-4c93-a05f-b91a5f01d1b7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(colors)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'Aa': '#bebada', 'Bb': '#ffffb3', 'Cc': '#fb8072', 'Dd': '#8dd3c7'}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gR_2h-FFLfUc",
        "colab_type": "text"
      },
      "source": [
        "or like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "91qg4E3wJtlV",
        "colab_type": "code",
        "outputId": "b911c060-b929-46a8-a90a-2a99c3bdc26f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        }
      },
      "source": [
        "colors"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<style>.pill {margin:2px; border-width:1px; border-radius:9px; border-style:solid;display:inline-block; width:100px; height:15px; line-height:15px;}.pill_text {width:90%; margin:auto; font-size:9px; text-align:center; overflow:hidden;}</style><div class=pill style=\"background-color:#bebada\"><div class=pill_text>Aa</div></div><div class=pill style=\"background-color:#ffffb3\"><div class=pill_text>Bb</div></div><div class=pill style=\"background-color:#fb8072\"><div class=pill_text>Cc</div></div><div class=pill style=\"background-color:#8dd3c7\"><div class=pill_text>Dd</div></div>"
            ],
            "text/plain": [
              "{'Aa': '#bebada', 'Bb': '#ffffb3', 'Cc': '#fb8072', 'Dd': '#8dd3c7'}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XVUQO2neUVXp",
        "colab_type": "text"
      },
      "source": [
        "**Default inputs**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H37wzknsPWpm",
        "colab_type": "text"
      },
      "source": [
        "Commonly the graphs that we want to build resemble pipelines with many nodes taking the preceeding node as their only input. We can simplify the specification of such graphs by supplying the preceeding node as the default input if none are provided. (Note that *explicitly* providing an empty list/dict as inputs means that a node has no inputs.)\n",
        "\n",
        "\n",
        "To use this feature we just replace calls to ```graph.items()``` with ```iter_nodes(graph)```. This provides the default inputs and does some other validation such as checking that node names are strings. Here is a new ```draw``` function using ```iter_nodes```:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "On29de9bfDsf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "draw = lambda graph, max_depth=0: DotGraph({name: ({'tooltip': str(value), 'fillcolor': colors[str(value)]}, inputs) for name, (value, inputs) in iter_nodes(graph)})"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UtliwKlrUqn6",
        "colab_type": "text"
      },
      "source": [
        "and a graph with a mixture of explicit and default inputs. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HMXubtjHgUmm",
        "colab_type": "code",
        "outputId": "84f55538-e140-4b0d-8d2a-3a4ed624babf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        }
      },
      "source": [
        "graph2 = {\n",
        "    'a': (A, []),\n",
        "    'b': B,\n",
        "    'd': D, \n",
        "    'c': (C, ['a', 'c']),\n",
        "}\n",
        "draw(graph2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48121e2400>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"242pt\" height=\"116pt\"\n viewBox=\"0.00 0.00 242.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-112 238,-112 238,4 -4,4\"/>\n<!-- a -->\n<g id=\"node1\" class=\"node\">\n<title>a</title>\n<g id=\"a_node1\"><a xlink:title=\"Aa\">\n<path fill=\"#bebada\" stroke=\"#000000\" d=\"M42,-72C42,-72 12,-72 12,-72 6,-72 0,-66 0,-60 0,-60 0,-48 0,-48 0,-42 6,-36 12,-36 12,-36 42,-36 42,-36 48,-36 54,-42 54,-48 54,-48 54,-60 54,-60 54,-66 48,-72 42,-72\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-50.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">a</text>\n</a>\n</g>\n</g>\n<!-- b -->\n<g id=\"node2\" class=\"node\">\n<title>b</title>\n<g id=\"a_node2\"><a xlink:title=\"Bb\">\n<path fill=\"#ffffb3\" stroke=\"#000000\" d=\"M132,-108C132,-108 102,-108 102,-108 96,-108 90,-102 90,-96 90,-96 90,-84 90,-84 90,-78 96,-72 102,-72 102,-72 132,-72 132,-72 138,-72 144,-78 144,-84 144,-84 144,-96 144,-96 144,-102 138,-108 132,-108\"/>\n<text text-anchor=\"middle\" x=\"117\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">b</text>\n</a>\n</g>\n</g>\n<!-- a&#45;&gt;b -->\n<g id=\"edge1\" class=\"edge\">\n<title>a&#45;&gt;b</title>\n<g id=\"a_edge1\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.003,-64.8012C62.2922,-68.1169 71.5569,-71.8228 80.3766,-75.3506\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.1204,-78.6177 89.705,-79.082 81.7201,-72.1184 79.1204,-78.6177\"/>\n</a>\n</g>\n</g>\n<!-- c -->\n<g id=\"node4\" class=\"node\">\n<title>c</title>\n<g id=\"a_node4\"><a xlink:title=\"Cc\">\n<path fill=\"#fb8072\" stroke=\"#000000\" d=\"M132,-36C132,-36 102,-36 102,-36 96,-36 90,-30 90,-24 90,-24 90,-12 90,-12 90,-6 96,0 102,0 102,0 132,0 132,0 138,0 144,-6 144,-12 144,-12 144,-24 144,-24 144,-30 138,-36 132,-36\"/>\n<text text-anchor=\"middle\" x=\"117\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">c</text>\n</a>\n</g>\n</g>\n<!-- a&#45;&gt;c -->\n<g id=\"edge3\" class=\"edge\">\n<title>a&#45;&gt;c</title>\n<g id=\"a_edge3\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.003,-43.1988C62.2922,-39.8831 71.5569,-36.1772 80.3766,-32.6494\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"81.7201,-35.8816 89.705,-28.918 79.1204,-29.3823 81.7201,-35.8816\"/>\n</a>\n</g>\n</g>\n<!-- d -->\n<g id=\"node3\" class=\"node\">\n<title>d</title>\n<g id=\"a_node3\"><a xlink:title=\"Dd\">\n<path fill=\"#8dd3c7\" stroke=\"#000000\" d=\"M222,-108C222,-108 192,-108 192,-108 186,-108 180,-102 180,-96 180,-96 180,-84 180,-84 180,-78 186,-72 192,-72 192,-72 222,-72 222,-72 228,-72 234,-78 234,-84 234,-84 234,-96 234,-96 234,-102 228,-108 222,-108\"/>\n<text text-anchor=\"middle\" x=\"207\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">d</text>\n</a>\n</g>\n</g>\n<!-- b&#45;&gt;d -->\n<g id=\"edge2\" class=\"edge\">\n<title>b&#45;&gt;d</title>\n<g id=\"a_edge2\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M144.003,-90C152.0277,-90 160.9665,-90 169.5309,-90\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"169.7051,-93.5001 179.705,-90 169.705,-86.5001 169.7051,-93.5001\"/>\n</a>\n</g>\n</g>\n<!-- c&#45;&gt;c -->\n<g id=\"edge4\" class=\"edge\">\n<title>c&#45;&gt;c</title>\n<g id=\"a_edge4\"><a xlink:title=\"1\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M100.7183,-36.1527C98.2134,-45.5391 103.6406,-54 117,-54 125.1409,-54 130.3362,-50.8581 132.5861,-46.2796\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"136.0881,-46.3691 133.2817,-36.1527 129.1046,-45.8893 136.0881,-46.3691\"/>\n</a>\n</g>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1mhAjD70N2TK",
        "colab_type": "text"
      },
      "source": [
        "We are free to refer to nodes which don't exist in the graph as inputs. These represent external nodes and don't have a value (so no 'tooltip' or 'fillcolor' in the diagram below.) \n",
        "\n",
        "Since node names are strings, we use the convention that names of external nodes are ints. This helps to make clear which inputs are external and has a further advantage that we shall see below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xQxO1U5FOGgA",
        "colab_type": "code",
        "outputId": "9c445e2a-c949-4b85-b1f9-c7afb650f0a3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        }
      },
      "source": [
        "graph3 = {\n",
        "    'a': (A, [0]),\n",
        "    'b': B,\n",
        "    'd': D, \n",
        "    'c': (C, ['a', 'c']),\n",
        "}\n",
        "draw(graph3)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f481218b5c0>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pXQavij--wzA",
        "colab_type": "text"
      },
      "source": [
        "Note that if we didn't provide explicit inputs for the first node the default is ```[0]``` anyway."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jppjsFmWMA9A",
        "colab_type": "text"
      },
      "source": [
        "**Nested graphs**\n",
        "\n",
        "Sometimes we want to display a graph with nested structure. We can do this by adding path separators '/' in node names:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E-Eg6RqBJtir",
        "colab_type": "code",
        "outputId": "7c53b70d-6ddf-48df-b329-0da1447116c9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        }
      },
      "source": [
        "graph4 = {\n",
        "    'a': A,\n",
        "    'group/b': (B, ['a']),\n",
        "    'c': (C, ['a', 'c']),\n",
        "    'group/d': (D, ['group/b'])\n",
        "}\n",
        "\n",
        "draw(graph4)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f4812187668>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"348pt\" height=\"155pt\"\n viewBox=\"0.00 0.00 348.00 155.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 151)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-151 344,-151 344,4 -4,4\"/>\n<g id=\"clust1\" class=\"cluster\">\n<title>cluster_group</title>\n<path fill=\"#777777\" fill-opacity=\"0.266667\" stroke=\"#000000\" d=\"M184,-64C184,-64 320,-64 320,-64 326,-64 332,-70 332,-76 332,-76 332,-127 332,-127 332,-133 326,-139 320,-139 320,-139 184,-139 184,-139 178,-139 172,-133 172,-127 172,-127 172,-76 172,-76 172,-70 178,-64 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group/b&#45;&gt;group/d -->\n<g id=\"edge5\" class=\"edge\">\n<title>group/b&#45;&gt;group/d</title>\n<g id=\"a_edge5\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M234.003,-90C242.0277,-90 250.9665,-90 259.5309,-90\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"259.7051,-93.5001 269.705,-90 259.705,-86.5001 259.7051,-93.5001\"/>\n</a>\n</g>\n</g>\n<!-- c&#45;&gt;c -->\n<g id=\"edge4\" class=\"edge\">\n<title>c&#45;&gt;c</title>\n<g id=\"a_edge4\"><a xlink:title=\"1\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M190.7183,-36.1527C188.2134,-45.5391 193.6406,-54 207,-54 215.1409,-54 220.3362,-50.8581 222.5861,-46.2796\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"226.0881,-46.3691 223.2817,-36.1527 219.1046,-45.8893 226.0881,-46.3691\"/>\n</a>\n</g>\n</g>\n<!-- 0 -->\n<g id=\"node5\" class=\"node\">\n<title>0</title>\n<path fill=\"#ffffff\" stroke=\"#000000\" d=\"M42,-72C42,-72 12,-72 12,-72 6,-72 0,-66 0,-60 0,-60 0,-48 0,-48 0,-42 6,-36 12,-36 12,-36 42,-36 42,-36 48,-36 54,-42 54,-48 54,-48 54,-60 54,-60 54,-66 48,-72 42,-72\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-50.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">0</text>\n</g>\n<!-- 0&#45;&gt;a -->\n<g id=\"edge1\" class=\"edge\">\n<title>0&#45;&gt;a</title>\n<g id=\"a_edge1\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.003,-54C62.0277,-54 70.9665,-54 79.5309,-54\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.7051,-57.5001 89.705,-54 79.705,-50.5001 79.7051,-57.5001\"/>\n</a>\n</g>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eo7tlyegMvyM",
        "colab_type": "text"
      },
      "source": [
        "We can have multiple levels of nesting and we can still use default inputs:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x7Hu6c-VWbjM",
        "colab_type": "code",
        "outputId": "a500f111-7305-4bfa-ce74-017a402b83a1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        }
      },
      "source": [
        "graph5 = {\n",
        "    'outer_group/a': A,\n",
        "    'outer_group/group/b': B,\n",
        "    'outer_group/group/d': D,\n",
        "    'outer_group/c': (C, ['outer_group/a', 'outer_group/c']),\n",
        "\n",
        "}\n",
        "draw(graph5)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f481214a5f8>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"356pt\" height=\"200pt\"\n viewBox=\"0.00 0.00 356.00 200.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 196)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-196 352,-196 352,4 -4,4\"/>\n<g id=\"clust1\" class=\"cluster\">\n<title>cluster_outer_group</title>\n<path fill=\"#777777\" fill-opacity=\"0.266667\" stroke=\"#000000\" d=\"M94,-8C94,-8 328,-8 328,-8 334,-8 340,-14 340,-20 340,-20 340,-172 340,-172 340,-178 334,-184 328,-184 328,-184 94,-184 94,-184 88,-184 82,-178 82,-172 82,-172 82,-20 82,-20 82,-14 88,-8 94,-8\"/>\n<text 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font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">0</text>\n</g>\n<!-- 0&#45;&gt;outer_group/a -->\n<g id=\"edge1\" class=\"edge\">\n<title>0&#45;&gt;outer_group/a</title>\n<g id=\"a_edge1\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.003,-79C62.0277,-79 70.9665,-79 79.5309,-79\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.7051,-82.5001 89.705,-79 79.705,-75.5001 79.7051,-82.5001\"/>\n</a>\n</g>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S4rcJCODOFgC",
        "colab_type": "text"
      },
      "source": [
        "It's annoying to have to add path prefixes to every node name and input. We want to be able to write this as a hierarchical graph, some of whose node *values* are themselves *graphs*. Let's express the graph above in hierarchical form. First we construct a graph for the nodes in ```group```:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PASaq0i2Xcr9",
        "colab_type": "code",
        "outputId": "f54b9c00-fcdb-43c5-eba1-6d9b3a884c31",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        }
      },
      "source": [
        "group = {'b': B, 'd': D}\n",
        "draw(group)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48120edb00>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"242pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 242.00 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-40 238,-40 238,4 -4,4\"/>\n<!-- b -->\n<g id=\"node1\" class=\"node\">\n<title>b</title>\n<g id=\"a_node1\"><a xlink:title=\"Bb\">\n<path fill=\"#ffffb3\" stroke=\"#000000\" d=\"M132,-36C132,-36 102,-36 102,-36 96,-36 90,-30 90,-24 90,-24 90,-12 90,-12 90,-6 96,0 102,0 102,0 132,0 132,0 138,0 144,-6 144,-12 144,-12 144,-24 144,-24 144,-30 138,-36 132,-36\"/>\n<text text-anchor=\"middle\" x=\"117\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">b</text>\n</a>\n</g>\n</g>\n<!-- d -->\n<g id=\"node2\" class=\"node\">\n<title>d</title>\n<g id=\"a_node2\"><a xlink:title=\"Dd\">\n<path fill=\"#8dd3c7\" stroke=\"#000000\" d=\"M222,-36C222,-36 192,-36 192,-36 186,-36 180,-30 180,-24 180,-24 180,-12 180,-12 180,-6 186,0 192,0 192,0 222,0 222,0 228,0 234,-6 234,-12 234,-12 234,-24 234,-24 234,-30 228,-36 222,-36\"/>\n<text text-anchor=\"middle\" x=\"207\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">d</text>\n</a>\n</g>\n</g>\n<!-- b&#45;&gt;d -->\n<g id=\"edge2\" class=\"edge\">\n<title>b&#45;&gt;d</title>\n<g id=\"a_edge2\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M144.003,-18C152.0277,-18 160.9665,-18 169.5309,-18\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"169.7051,-21.5001 179.705,-18 169.705,-14.5001 169.7051,-21.5001\"/>\n</a>\n</g>\n</g>\n<!-- 0 -->\n<g id=\"node3\" class=\"node\">\n<title>0</title>\n<path fill=\"#ffffff\" stroke=\"#000000\" d=\"M42,-36C42,-36 12,-36 12,-36 6,-36 0,-30 0,-24 0,-24 0,-12 0,-12 0,-6 6,0 12,0 12,0 42,0 42,0 48,0 54,-6 54,-12 54,-12 54,-24 54,-24 54,-30 48,-36 42,-36\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">0</text>\n</g>\n<!-- 0&#45;&gt;b -->\n<g id=\"edge1\" class=\"edge\">\n<title>0&#45;&gt;b</title>\n<g id=\"a_edge1\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.003,-18C62.0277,-18 70.9665,-18 79.5309,-18\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.7051,-21.5001 89.705,-18 79.705,-14.5001 79.7051,-21.5001\"/>\n</a>\n</g>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nw1ttqJy0BGc",
        "colab_type": "text"
      },
      "source": [
        "Next we build a graph representing ```outer_group``` in which the subgraph ```group``` appears as a node value. \n",
        "\n",
        "By providing this node with a dictionary of inputs, keyed by its *external inputs* there is a natural way to bind these onto the inner graph. \n",
        "\n",
        "Here ```group``` has a single external input ```0``` and we want to bind it to the node ```a```:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jEhKZRCPXfDv",
        "colab_type": "code",
        "outputId": "e0811f08-a6fa-4ce2-c35c-ec498dc593e4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        }
      },
      "source": [
        "outer_group = {'a': A, 'group': (group, {0: 'a'}), 'c': (C, ['a', 'c'])}\n",
        "draw(outer_group)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48120ed4a8>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y__Bk3G6A_Y_",
        "colab_type": "text"
      },
      "source": [
        "If our external inputs all are non-negative integers, we can use a list rather than a dict to represent binding of inputs, where the external inputs of the inner graph are now interpreted as indexes in the list instead of keys in a dict:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MhN4oSh_A6yt",
        "colab_type": "code",
        "outputId": "2b8e6590-a660-4c2a-fe9e-69d6d7a6c0fd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        }
      },
      "source": [
        "outer_group = {'a': A, 'group': (group, ['a']), 'c': (C, ['a', 'c'])}\n",
        "draw(outer_group)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48120ed358>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
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      "cell_type": "markdown",
      "metadata": {
        "id": "OiDNHjHBBpw_",
        "colab_type": "text"
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      "source": [
        "The diagram above expresses the hierarchical structure but it's sometimes nice to recover the expanded structure with path separated names. To do this we ```explode``` the graph into a single-level format:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zQSCLMKbCqcg",
        "colab_type": "code",
        "outputId": "5218cedf-364c-404b-c054-4a406c346556",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        }
      },
      "source": [
        "draw(explode(outer_group))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48120ab400>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nIk2DWDg0qG4",
        "colab_type": "text"
      },
      "source": [
        "Now let's define the full graph which has a single node ```outer_group```:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OGWKIrtVWqrx",
        "colab_type": "code",
        "outputId": "6b74f178-460a-4b9d-a1e5-2d7afe05a187",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        }
      },
      "source": [
        "graph6 = {'outer_group': outer_group}\n",
        "draw(graph6)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48120ab6d8>"
            ],
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          },
          "metadata": {
            "tags": []
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          "execution_count": 24
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        "colab_type": "text"
      },
      "source": [
        "We can display the full nested structure by 'exploding' this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TEJYUjaUk8zf",
        "colab_type": "code",
        "outputId": "1fe56fd2-5f55-4a96-b9bd-d5db380338b5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        }
      },
      "source": [
        "draw(explode(graph6))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f4812160240>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N5P3lJhJ2Fdu",
        "colab_type": "text"
      },
      "source": [
        "We can also display intermediate levels of hierarchy by specifiying a ```max_levels``` argument to ```explode```:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "msqSK8XSvLOs",
        "colab_type": "code",
        "outputId": "3b3f3f5a-42d5-447d-bc13-0057d71a4763",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 249
        }
      },
      "source": [
        "draw(explode(graph6, max_levels=1))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48121c8048>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"258pt\" height=\"171pt\"\n viewBox=\"0.00 0.00 258.00 171.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 167)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-167 254,-167 254,4 -4,4\"/>\n<g id=\"clust1\" class=\"cluster\">\n<title>cluster_outer_group</title>\n<path fill=\"#777777\" fill-opacity=\"0.266667\" stroke=\"#000000\" d=\"M94,-8C94,-8 230,-8 230,-8 236,-8 242,-14 242,-20 242,-20 242,-143 242,-143 242,-149 236,-155 230,-155 230,-155 94,-155 94,-155 88,-155 82,-149 82,-143 82,-143 82,-20 82,-20 82,-14 88,-8 94,-8\"/>\n<text text-anchor=\"middle\" x=\"162\" y=\"-139.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">outer_group</text>\n</g>\n<!-- outer_group/a -->\n<g id=\"node1\" class=\"node\">\n<title>outer_group/a</title>\n<g id=\"a_node1\"><a xlink:title=\"Aa\">\n<path fill=\"#bebada\" stroke=\"#000000\" d=\"M132,-79C132,-79 102,-79 102,-79 96,-79 90,-73 90,-67 90,-67 90,-55 90,-55 90,-49 96,-43 102,-43 102,-43 132,-43 132,-43 138,-43 144,-49 144,-55 144,-55 144,-67 144,-67 144,-73 138,-79 132,-79\"/>\n<text text-anchor=\"middle\" x=\"117\" y=\"-57.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">a</text>\n</a>\n</g>\n</g>\n<!-- outer_group/group -->\n<g id=\"node2\" class=\"node\">\n<title>outer_group/group</title>\n<g id=\"a_node2\"><a xlink:title=\"{&#39;b&#39;: &#39;Bb&#39;, &#39;d&#39;: &#39;Dd&#39;}\">\n<path fill=\"#80b1d3\" stroke=\"#000000\" d=\"M222,-52C222,-52 192,-52 192,-52 186,-52 180,-46 180,-40 180,-40 180,-28 180,-28 180,-22 186,-16 192,-16 192,-16 222,-16 222,-16 228,-16 234,-22 234,-28 234,-28 234,-40 234,-40 234,-46 228,-52 222,-52\"/>\n<text text-anchor=\"middle\" x=\"207\" y=\"-30.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">group</text>\n</a>\n</g>\n</g>\n<!-- outer_group/a&#45;&gt;outer_group/group -->\n<g id=\"edge2\" class=\"edge\">\n<title>outer_group/a&#45;&gt;outer_group/group</title>\n<g id=\"a_edge2\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M144.003,-52.8991C152.204,-50.4388 161.3599,-47.692 170.095,-45.0715\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"171.1325,-48.4144 179.705,-42.1885 169.121,-41.7096 171.1325,-48.4144\"/>\n</a>\n</g>\n</g>\n<!-- outer_group/c -->\n<g id=\"node3\" class=\"node\">\n<title>outer_group/c</title>\n<g id=\"a_node3\"><a xlink:title=\"Cc\">\n<path fill=\"#fb8072\" stroke=\"#000000\" d=\"M222,-106C222,-106 192,-106 192,-106 186,-106 180,-100 180,-94 180,-94 180,-82 180,-82 180,-76 186,-70 192,-70 192,-70 222,-70 222,-70 228,-70 234,-76 234,-82 234,-82 234,-94 234,-94 234,-100 228,-106 222,-106\"/>\n<text text-anchor=\"middle\" x=\"207\" y=\"-84.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">c</text>\n</a>\n</g>\n</g>\n<!-- outer_group/a&#45;&gt;outer_group/c -->\n<g id=\"edge3\" class=\"edge\">\n<title>outer_group/a&#45;&gt;outer_group/c</title>\n<g id=\"a_edge3\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M144.003,-69.1009C152.204,-71.5612 161.3599,-74.308 170.095,-76.9285\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"169.121,-80.2904 179.705,-79.8115 171.1325,-73.5856 169.121,-80.2904\"/>\n</a>\n</g>\n</g>\n<!-- outer_group/c&#45;&gt;outer_group/c -->\n<g id=\"edge4\" class=\"edge\">\n<title>outer_group/c&#45;&gt;outer_group/c</title>\n<g id=\"a_edge4\"><a xlink:title=\"1\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M190.7183,-106.1527C188.2134,-115.5391 193.6406,-124 207,-124 215.1409,-124 220.3362,-120.8581 222.5861,-116.2796\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"226.0881,-116.3691 223.2817,-106.1527 219.1046,-115.8893 226.0881,-116.3691\"/>\n</a>\n</g>\n</g>\n<!-- 0 -->\n<g id=\"node4\" class=\"node\">\n<title>0</title>\n<path fill=\"#ffffff\" stroke=\"#000000\" d=\"M42,-79C42,-79 12,-79 12,-79 6,-79 0,-73 0,-67 0,-67 0,-55 0,-55 0,-49 6,-43 12,-43 12,-43 42,-43 42,-43 48,-43 54,-49 54,-55 54,-55 54,-67 54,-67 54,-73 48,-79 42,-79\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-57.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">0</text>\n</g>\n<!-- 0&#45;&gt;outer_group/a -->\n<g id=\"edge1\" class=\"edge\">\n<title>0&#45;&gt;outer_group/a</title>\n<g id=\"a_edge1\"><a xlink:title=\"0\">\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.003,-61C62.0277,-61 70.9665,-61 79.5309,-61\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.7051,-64.5001 89.705,-61 79.705,-57.5001 79.7051,-64.5001\"/>\n</a>\n</g>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_aUqaYBR2WJY",
        "colab_type": "text"
      },
      "source": [
        "Here's a test that exploding in two stages is the same as doing it all at once:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "snJlHh1BvOf2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#test\n",
        "assert explode(explode(graph6, 1), 1) == explode(graph6)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NlxumxfKxlV9",
        "colab_type": "text"
      },
      "source": [
        "Here's a more complicated graph with repeated groups and name clashes:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0YuieA8i9fqU",
        "colab_type": "code",
        "outputId": "6dd063e6-7b0e-4a94-9e17-2e1e82408685",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        }
      },
      "source": [
        "graph7 = {\n",
        "    'outer_group': ({\n",
        "        'b': (A, [0]), \n",
        "        'group':  {'b': (B, [0]), 'd': D},\n",
        "        'group2': ({'b': (B, [0, 1]), 'd': D}, ['group', 'c']),\n",
        "        'group3':  {'b': (B, [0]), 'd': (D, ['b', 0])},\n",
        "        'c': (C, ['b', 'c']),\n",
        "    }, [0])}\n",
        "\n",
        "draw(explode(graph7))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7f48122a43c8>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
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      "source": [
        "draw(explode(graph7, 1))"
      ],
      "execution_count": 0,
      "outputs": [
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zwizPGh3xLxk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#test\n",
        "assert explode(explode(graph7, 1), 1) == explode(graph7)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9FukikcANyh2",
        "colab_type": "text"
      },
      "source": [
        "### Pytorch"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IWPbjJYwu4Fq",
        "colab_type": "text"
      },
      "source": [
        "Let's use the Graph datastructure that we've developed to explore some pytorch models. To start with let's try a ```fastai2.models.xresnet.XResNet``` model without alterations. Since this model is a subclass of ```nn.Sequential```, we already have quite a bit of information about the graph structure which we can use. \n",
        "\n",
        "Let's define a function to convert an ```nn.Sequential``` model into a graph and also a new ```draw``` function which colors nodes by type:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xSA5tA-zEBFe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import fastai2\n",
        "\n",
        "@to_graph.register(nn.Sequential)\n",
        "def f(x):\n",
        "    return {f'node_{k}': v for k,v in x._modules.items()}\n",
        "\n",
        "colors = ColorMap()\n",
        "def draw(network, **kwargs):\n",
        "    return DotGraph({p: ({'fillcolor': colors[type(v).__name__], 'tooltip': str(v)}, inputs) for p, (v, inputs) in iter_nodes(to_graph(network))}, **kwargs)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Md1RkrZkWUQf",
        "colab_type": "text"
      },
      "source": [
        "Now we can try drawing the model:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vJkXZ0x9T_3L",
        "colab_type": "code",
        "outputId": "36a0a21c-3ebe-40b5-f1dd-74aea0401913",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 63
        }
      },
      "source": [
        "model = fastai2.vision.models.xresnet.XResNet(fastai2.layers.SeparableBlock, 1, [2,2,2,2], c_in=3, c_out=10, sa=True)\n",
        "draw(model)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7fb9f8e91e48>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J-nJ9ss0UTzw",
        "colab_type": "code",
        "outputId": "86f52fcc-a1ad-4fd0-9623-b530929912ce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        }
      },
      "source": [
        "draw(explode(model))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6cPTQGsYVSbJ",
        "colab_type": "text"
      },
      "source": [
        "Not a bad start! The node names could do with a bit of work. Here is one possible way to improve things by naming according to type and position in the layer. Also if a sequential model is defined by an (Ordered)Dict then we ought to keep the names passed in:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nXKwY-n8Ua0K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "short_names_ = {\n",
        "    nn.Conv2d: 'Conv',\n",
        "    nn.BatchNorm2d: 'Norm',\n",
        "    nn.ReLU: 'Actn',\n",
        "    nn.AdaptiveAvgPool2d: 'Avgpool',\n",
        "    nn.AvgPool2d: 'Avgpool',\n",
        "    nn.MaxPool2d: 'Maxpool',\n",
        "    fastai2.layers.SimpleSelfAttention: 'SA',\n",
        "    nn.Identity: 'Id',\n",
        "}\n",
        "\n",
        "def short_name(typ):\n",
        "    return short_names_.get(typ, typ.__name__)\n",
        "\n",
        "@to_graph.register(nn.Sequential)\n",
        "def f(x):\n",
        "    if all([(str(i) == k) for i,k in enumerate(x._modules.keys())]):\n",
        "        mods = {f'{short_name(type(v))}_{k}': v for k,v in x._modules.items()}\n",
        "    else:\n",
        "        mods = x._modules\n",
        "    return mods"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E-bIsp5LWvV9",
        "colab_type": "code",
        "outputId": "bd85f34b-e4d9-4afa-bea9-2d1e2976a078",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "draw(model)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7fb9f8dd2ba8>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dKuJdsNHWvvC",
        "colab_type": "code",
        "outputId": "d8796541-c9bc-4bcb-fcee-c1bfbf8ad2f1",
        "colab": {
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          "height": 79
        }
      },
      "source": [
        "draw(explode(model))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<utils.DotGraph at 0x7fb9f8caf2e8>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FFmrij4qWzBG",
        "colab_type": "text"
      },
      "source": [
        "Better! \n",
        "\n",
        "The next problem is a deeper one. When we try to ```explode``` the process stops at nodes which are not ```nn.Sequential``` (since these are the only type of node we know how to convert into graphs.)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zk436x9iXoUn",
        "colab_type": "text"
      },
      "source": [
        "Lets add a new combinator, the ```SplitMerge``` layer:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i9n9amDmWx4k",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Mul(nn.Module):\n",
        "    def forward(self, x, y): return x * y\n",
        "\n",
        "class Add(nn.Module):\n",
        "    def forward(self, x, y): return x + y\n",
        "\n",
        "class SplitMerge(nn.Module):\n",
        "    def __init__(self, branches, merge=Add, post=None):\n",
        "        super().__init__()\n",
        "        if isinstance(branches, list):\n",
        "            branches = {f'branch{i}': branch for i, branch in enumerate(branches)}\n",
        "        for name, branch in branches.items():\n",
        "            self.add_module(name, branch)\n",
        "        self.branches = branches\n",
        "        self.merge, self.post = merge(), post\n",
        "\n",
        "    def forward(self, x):\n",
        "        branch_outputs = [branch(x) for branch in self.branches.values()]\n",
        "        x = self.merge(*branch_outputs)\n",
        "        if self.post is not None:\n",
        "            x = self.post(x)\n",
        "        return x\n",
        "\n",
        "@to_graph.register(SplitMerge)\n",
        "def f(self):\n",
        "    graph = union({'in': nn.Identity()}, {k: (v, ['in']) for k,v in self.branches.items()})\n",
        "    graph[short_name(type(self.merge))] = (self.merge, list(self.branches.keys()))\n",
        "    if self.post:\n",
        "        graph[short_name(type(self.post))] = self.post\n",
        "    return graph"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NRtqiGR5YWrx",
        "colab_type": "text"
      },
      "source": [
        "Now let's redefine ```SEModule``` and ```ResBlock``` as ```SplitMerge``` layers (below we just do a minimal conversion from the existing layers but it should be clear how to write these directly)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iNx9-yZ3YJgm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class SEModule(SplitMerge):\n",
        "    def __init__(self, orig):\n",
        "        layers = orig.layers\n",
        "        branches = {'squeeze': nn.Sequential(*layers[:-1]), 'id': nn.Sequential()}\n",
        "        super().__init__(branches, merge=Mul)    \n",
        "\n",
        "class ResBlock(SplitMerge):\n",
        "    def __init__(self, *args, **kwargs):\n",
        "        orig = fastai2.layers.ResBlock(*args, **kwargs)\n",
        "        convpath = nn.Sequential(*[SEModule(x) if isinstance(x, fastai2.layers.SequentialEx) else x for x in orig.convpath._modules.values()])\n",
        "        super().__init__({'conv_path': convpath, 'id_path': orig.idpath}, post=orig.act)\n",
        "\n",
        "def SeparableBlock(expansion, ni, nf, reduction=16, stride=1, base_width=4, **kwargs):\n",
        "    return ResBlock(expansion, ni, nf, stride=stride, reduction=reduction, nh2=nf*2, dw=True, **kwargs)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZPbg-xhEYJih",
        "colab_type": "code",
        "outputId": "1d2e7bc0-a69e-4d70-8d5b-0c77fa07c5c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "model = fastai2.vision.models.xresnet.XResNet(SeparableBlock, 1, [2,2,2,2], c_in=3, c_out=10, sa=True)\n",
        "draw(model)"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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          "metadata": {
            "tags": []
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          "execution_count": 46
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    },
    {
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      "metadata": {
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        "colab_type": "code",
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      "source": [
        "draw(explode(model))"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1MOKkjaPdwT6",
        "colab_type": "text"
      },
      "source": [
        "It's fun to explore different levels of the hierarchy by apecifying the ```max_levels``` argument to ```explode```:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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      "source": [
        "draw(explode(model,max_levels=2))"
      ],
      "execution_count": 48,
      "outputs": [
        {
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          "data": {
            "text/plain": [
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BUmT9e426rsf",
        "colab_type": "text"
      },
      "source": [
        "We can define an ```nn.Module``` which can handle arbitrary an (well-formed) graph:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vVkHWk6iXkdM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Network(nn.Module):\n",
        "    colors = ColorMap()\n",
        "    def __init__(self, graph, cache_activations=False):\n",
        "        self._graph = to_graph(graph)\n",
        "        super().__init__()\n",
        "        self.cache_activations = cache_activations\n",
        "        for path, (val, _) in iter_nodes(self._graph): \n",
        "            setattr(self, path.replace('/', '__'), val)\n",
        "    \n",
        "    def __setattr__(self, name, value):\n",
        "        super().__setattr__(name, value)\n",
        "        path = name.replace('__', '/')\n",
        "        if path in self._graph:\n",
        "            old_val = self._graph[path]\n",
        "            if isinstance(old_val, tuple):\n",
        "                _, inputs = old_val\n",
        "                self._graph[path] = (value, inputs)\n",
        "            else:\n",
        "                self._graph[path] = value\n",
        "\n",
        "    def forward(self, *args):\n",
        "        prev = args[0]\n",
        "        outputs = self.cache = dict(enumerate(args))\n",
        "        for k, (node, inputs) in iter_nodes(self._graph):\n",
        "            if k not in outputs: \n",
        "                prev = outputs[k] = node(*[outputs[x] for x in inputs])\n",
        "        if not self.cache_activations: self.cache = None\n",
        "        return prev\n",
        "\n",
        "    def draw(self, **kwargs):\n",
        "        return DotGraph({p: ({'fillcolor': self.colors[type(v).__name__], 'tooltip': str(v)}, inputs) for p, (v, inputs) in iter_nodes(to_graph(self))}, **kwargs)\n",
        "\n",
        "    def explode(self, max_levels=-1):\n",
        "        convert = lambda x: to_graph(x) if isinstance(x, Network) else x\n",
        "        return Network(explode(self, max_levels, convert=convert))\n",
        "\n",
        "\n",
        "@to_graph.register(Network)\n",
        "def f(x): return x.graph"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cEtARl_deSvf",
        "colab_type": "text"
      },
      "source": [
        "We can now check that the fully exploded model (which makes a perfectly good ```Network``` in itself) computes the same forward pass as the original model:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "81tkZT7KeEIf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "m = model.cuda()\n",
        "m2 = Network(explode(m))\n",
        "inputs = torch.randn(64,3,128,128).cuda()\n",
        "assert torch.sum(torch.abs(m(inputs) - m2(inputs))).item() == 0.0"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "4doNutNzflti"
      },
      "source": [
        "Note that if we set ```.cache_activations``` to true on the exploded model, we can retrieve all the intermediate activation values:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C-MEASDDeEFF",
        "colab_type": "code",
        "outputId": "f6daecc7-023e-4518-d60b-897924c11278",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "m2.cache_activations = True\n",
        "m2(inputs)\n",
        "list(m2.cache.keys())"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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              " 'Sequential_5/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_1/Conv_0',\n",
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              " 'Sequential_5/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Norm_1',\n",
              " 'Sequential_5/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Actn_2',\n",
              " 'Sequential_5/ResBlock_1/conv_path/Sequential_0/ConvLayer_1/Conv_0',\n",
              " 'Sequential_5/ResBlock_1/conv_path/Sequential_0/ConvLayer_1/Norm_1',\n",
              " 'Sequential_5/ResBlock_1/conv_path/SEModule_1/in',\n",
              " 'Sequential_5/ResBlock_1/conv_path/SEModule_1/squeeze/Avgpool_0',\n",
              " 'Sequential_5/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_1/Conv_0',\n",
              " 'Sequential_5/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_1/Actn_1',\n",
              " 'Sequential_5/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_2/Conv_0',\n",
              " 'Sequential_5/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_2/Sigmoid_1',\n",
              " 'Sequential_5/ResBlock_1/conv_path/SEModule_1/Mul',\n",
              " 'Sequential_5/ResBlock_1/Add',\n",
              " 'Sequential_5/ResBlock_1/Actn',\n",
              " 'Sequential_6/ResBlock_0/in',\n",
              " 'Sequential_6/ResBlock_0/conv_path/Sequential_0/ConvLayer_0/Conv_0',\n",
              " 'Sequential_6/ResBlock_0/conv_path/Sequential_0/ConvLayer_0/Norm_1',\n",
              " 'Sequential_6/ResBlock_0/conv_path/Sequential_0/ConvLayer_0/Actn_2',\n",
              " 'Sequential_6/ResBlock_0/conv_path/Sequential_0/ConvLayer_1/Conv_0',\n",
              " 'Sequential_6/ResBlock_0/conv_path/Sequential_0/ConvLayer_1/Norm_1',\n",
              " 'Sequential_6/ResBlock_0/conv_path/SEModule_1/in',\n",
              " 'Sequential_6/ResBlock_0/conv_path/SEModule_1/squeeze/Avgpool_0',\n",
              " 'Sequential_6/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_1/Conv_0',\n",
              " 'Sequential_6/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_1/Actn_1',\n",
              " 'Sequential_6/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_2/Conv_0',\n",
              " 'Sequential_6/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_2/Sigmoid_1',\n",
              " 'Sequential_6/ResBlock_0/conv_path/SEModule_1/Mul',\n",
              " 'Sequential_6/ResBlock_0/id_path/Avgpool_0',\n",
              " 'Sequential_6/ResBlock_0/id_path/ConvLayer_1/Conv_0',\n",
              " 'Sequential_6/ResBlock_0/id_path/ConvLayer_1/Norm_1',\n",
              " 'Sequential_6/ResBlock_0/Add',\n",
              " 'Sequential_6/ResBlock_0/Actn',\n",
              " 'Sequential_6/ResBlock_1/in',\n",
              " 'Sequential_6/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Conv_0',\n",
              " 'Sequential_6/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Norm_1',\n",
              " 'Sequential_6/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Actn_2',\n",
              " 'Sequential_6/ResBlock_1/conv_path/Sequential_0/ConvLayer_1/Conv_0',\n",
              " 'Sequential_6/ResBlock_1/conv_path/Sequential_0/ConvLayer_1/Norm_1',\n",
              " 'Sequential_6/ResBlock_1/conv_path/SEModule_1/in',\n",
              " 'Sequential_6/ResBlock_1/conv_path/SEModule_1/squeeze/Avgpool_0',\n",
              " 'Sequential_6/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_1/Conv_0',\n",
              " 'Sequential_6/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_1/Actn_1',\n",
              " 'Sequential_6/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_2/Conv_0',\n",
              " 'Sequential_6/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_2/Sigmoid_1',\n",
              " 'Sequential_6/ResBlock_1/conv_path/SEModule_1/Mul',\n",
              " 'Sequential_6/ResBlock_1/Add',\n",
              " 'Sequential_6/ResBlock_1/Actn',\n",
              " 'Sequential_7/ResBlock_0/in',\n",
              " 'Sequential_7/ResBlock_0/conv_path/Sequential_0/ConvLayer_0/Conv_0',\n",
              " 'Sequential_7/ResBlock_0/conv_path/Sequential_0/ConvLayer_0/Norm_1',\n",
              " 'Sequential_7/ResBlock_0/conv_path/Sequential_0/ConvLayer_0/Actn_2',\n",
              " 'Sequential_7/ResBlock_0/conv_path/Sequential_0/ConvLayer_1/Conv_0',\n",
              " 'Sequential_7/ResBlock_0/conv_path/Sequential_0/ConvLayer_1/Norm_1',\n",
              " 'Sequential_7/ResBlock_0/conv_path/SEModule_1/in',\n",
              " 'Sequential_7/ResBlock_0/conv_path/SEModule_1/squeeze/Avgpool_0',\n",
              " 'Sequential_7/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_1/Conv_0',\n",
              " 'Sequential_7/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_1/Actn_1',\n",
              " 'Sequential_7/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_2/Conv_0',\n",
              " 'Sequential_7/ResBlock_0/conv_path/SEModule_1/squeeze/ConvLayer_2/Sigmoid_1',\n",
              " 'Sequential_7/ResBlock_0/conv_path/SEModule_1/Mul',\n",
              " 'Sequential_7/ResBlock_0/id_path/Avgpool_0',\n",
              " 'Sequential_7/ResBlock_0/id_path/ConvLayer_1/Conv_0',\n",
              " 'Sequential_7/ResBlock_0/id_path/ConvLayer_1/Norm_1',\n",
              " 'Sequential_7/ResBlock_0/Add',\n",
              " 'Sequential_7/ResBlock_0/Actn',\n",
              " 'Sequential_7/ResBlock_1/in',\n",
              " 'Sequential_7/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Conv_0',\n",
              " 'Sequential_7/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Norm_1',\n",
              " 'Sequential_7/ResBlock_1/conv_path/Sequential_0/ConvLayer_0/Actn_2',\n",
              " 'Sequential_7/ResBlock_1/conv_path/Sequential_0/ConvLayer_1/Conv_0',\n",
              " 'Sequential_7/ResBlock_1/conv_path/Sequential_0/ConvLayer_1/Norm_1',\n",
              " 'Sequential_7/ResBlock_1/conv_path/SEModule_1/in',\n",
              " 'Sequential_7/ResBlock_1/conv_path/SEModule_1/squeeze/Avgpool_0',\n",
              " 'Sequential_7/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_1/Conv_0',\n",
              " 'Sequential_7/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_1/Actn_1',\n",
              " 'Sequential_7/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_2/Conv_0',\n",
              " 'Sequential_7/ResBlock_1/conv_path/SEModule_1/squeeze/ConvLayer_2/Sigmoid_1',\n",
              " 'Sequential_7/ResBlock_1/conv_path/SEModule_1/Mul',\n",
              " 'Sequential_7/ResBlock_1/Add',\n",
              " 'Sequential_7/ResBlock_1/Actn',\n",
              " 'Avgpool_8',\n",
              " 'Flatten_9',\n",
              " 'Dropout_10',\n",
              " 'Linear_11']"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_o7gUKYlgFdj",
        "colab_type": "code",
        "outputId": "842d7a5b-7efe-4a22-fc2c-0d9bf4dd4254",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "source": [
        "m2.cache['Sequential_7/ResBlock_1/conv_path/Sequential_0/ConvLayer_1/Conv_0'][0][0]"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.3368, -0.1468,  0.4092, -0.5297],\n",
              "        [ 0.6140,  0.4266,  1.7334,  0.3539],\n",
              "        [ 0.0969, -0.9980,  0.6533, -0.0225],\n",
              "        [ 0.7459,  1.0654,  0.7076, -0.7231]], device='cuda:0',\n",
              "       grad_fn=<SelectBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MZCMVPnffsj6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}