NTT123/1resnet.ipynb

## 1resnet.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "1ResNet.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/gist/NTT123/0c7d5ac377e5394d12479d0576605fc4/1resnet.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "Bqs_wMwrfgxG",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# ResNet with one-neuron hidden layers is a Universal Approximator\n"
      ]
    },
    {
      "metadata": {
        "id": "xXXfD5BqXciM",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Method"
      ]
    },
    {
      "metadata": {
        "id": "ihcUbzrqOwPN",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "This note implements the experiment from a [paper](https://arxiv.org/abs/1806.10909) which shows that it is enough to use an unbounded stack of  residual blocks with ReLU units to approximate any function!\n",
        "\n",
        "Let $f(\\cdot)$ be a nonlinear function. A residual block is:\n",
        "$$\n",
        "F(x) = f(Wx + b) + x\n",
        "$$"
      ]
    },
    {
      "metadata": {
        "id": "yzZY1ikQgxvu",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "We implement a deep neural network with the basic block shown in Figure 1."
      ]
    },
    {
      "metadata": {
        "id": "yZEu8V7dgKsQ",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "<img width=\"542\" align=\"middle\"  src=\"data:image/png;base64,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\" style=\"max-width: 100px;\">"
      ]
    },
    {
      "metadata": {
        "id": "B8Bip6wPyi_o",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "We build a deep neural network of 2d input as follows:"
      ]
    },
    {
      "metadata": {
        "id": "_DWtUn7ByZPy",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "<img  width=\"542\"  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\" style=\"max-width: 100px;\">"
      ]
    },
    {
      "metadata": {
        "id": "tSOAnHzpXf2J",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Experiment"
      ]
    },
    {
      "metadata": {
        "id": "25r9JCz8zg_i",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "We  generate a dataset of $(x_i, y_i)$ as follows:\n",
        "\n",
        "$$\n",
        "y_i =\\begin{cases}\n",
        "1 & \\text{if }~~ \\|x_i \\| \\leq 1, \\\\\n",
        "-1 & \\text{if }~~ 2 \\leq \\| x_i\\| \\leq 3\n",
        "\\end{cases}\n",
        "$$"
      ]
    },
    {
      "metadata": {
        "id": "3eBcNSeazJev",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        },
        "outputId": "0cfbdcb0-1556-4bb2-ee4e-7bb8c1cadaf3"
      },
      "cell_type": "code",
      "source": [
        "#@title Generated dataset\n",
        "\n",
        "# Install pytorch 0.4.0\n",
        "#\n",
        "from os import path\n",
        "from wheel.pep425tags import get_abbr_impl, get_impl_ver, get_abi_tag\n",
        "platform = '{}{}-{}'.format(get_abbr_impl(), get_impl_ver(), get_abi_tag())\n",
        "\n",
        "accelerator = 'cu80' if path.exists('/opt/bin/nvidia-smi') else 'cpu'\n",
        "\n",
        "!pip install -q http://download.pytorch.org/whl/{accelerator}/torch-0.4.0-{platform}-linux_x86_64.whl torchvision > /dev/null 2>&1\n",
        "import torch\n",
        "\n",
        "# Generate data\n",
        "N = 3000\n",
        "\n",
        "X = torch.empty( (N, 2) )\n",
        "Y = torch.empty(N)\n",
        "for i in range(N):\n",
        "    xi = torch.randn(2)\n",
        "    xi = xi / torch.norm(xi) # normalize to unit ball\n",
        "    yi = 1\n",
        "    l = torch.rand(1)\n",
        "    if i % 3 != 0:\n",
        "        l = l + 2\n",
        "        yi = -1\n",
        "    xi = l * xi\n",
        "    X[i] = xi\n",
        "    Y[i] = yi\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "x1 = X[:, 0]\n",
        "x2 = X[:, 1]\n",
        "\n",
        "from pylab import rcParams\n",
        "rcParams['font.size'] = 14\n",
        "plt.style.use('seaborn-white')\n",
        "rcParams['figure.figsize'] = 4,4\n",
        "\n",
        "\n",
        "def tocolor(x):\n",
        "    if x == 1: return \"r\"\n",
        "    else: return \"b\"\n",
        "\n",
        "colors = list(map( tocolor, Y ))\n",
        "_ = plt.scatter(x1, x2, c=colors, s=2)\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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v1ClIxp07zfe9+SZ8wNWrpFWvXq0RmdZw546Un37Ku+XIgTAw5GVeRdgEQTrg0iVmv3Xr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\nFChQQET/Azcenwz4yYqfAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f196a3f0ef0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "tmYdaN4m6hnd",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Define a ResNet module in Pytorch"
      ]
    },
    {
      "metadata": {
        "id": "-zCGuFLw3jH2",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class ResNet(torch.nn.Module):\n",
        "    def __init__(self, dim):\n",
        "        \n",
        "        super(ResNet, self).__init__()\n",
        "        \n",
        "        self.linear1 = torch.nn.Linear(dim, dim)\n",
        "        self.nonlinear = torch.nn.ReLU()\n",
        "\n",
        "    def forward(self, x):\n",
        "        \n",
        "        return self.nonlinear(self.linear1(x)) + x"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "DmU8RYJhRCYz",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Then, a deep net."
      ]
    },
    {
      "metadata": {
        "id": "7hR7jgUV7iEY",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "class DeepNet(torch.nn.Module):\n",
        "    def __init__(self, deep, dim ):\n",
        "        super(DeepNet, self).__init__()\n",
        "        \n",
        "        self.layers = []\n",
        "        self.deep = deep\n",
        "        \n",
        "        self.seq = torch.nn.Sequential()\n",
        "        for i in range(deep):\n",
        "            self.seq.add_module(\"res_%d\"%(i+1), ResNet(dim) )\n",
        "\n",
        "        self.output = torch.nn.Linear(dim, 1)\n",
        "            \n",
        "    def forward(self, x):\n",
        "        out = self.seq(x)\n",
        "        return torch.tanh( self.output(out))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ydUH2H8KY4po",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
        "\n",
        "net = DeepNet(4, 2).to(device)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "vaCvSDMV82A3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1530
        },
        "outputId": "504f095b-fcdd-47f8-a0a5-81cc027e9122"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "\n",
        "print(net)\n",
        "#@title\n",
        "!pip install git+https://github.com/szagoruyko/pytorchviz > /dev/null 2>&1\n",
        "!apt-get install graphviz > /dev/null 2>&1\n",
        "from torchviz import make_dot, make_dot_from_trace\n",
        "x = torch.randn(1,2)\n",
        "x = x.to(device)\n",
        "y = net(x)\n",
        "\n",
        "trace, _ = torch.jit.get_trace_graph(net, x)\n",
        "make_dot_from_trace(trace)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "DeepNet(\n",
            "  (seq): Sequential(\n",
            "    (res_1): ResNet(\n",
            "      (linear1): Linear(in_features=2, out_features=2, bias=True)\n",
            "      (nonlinear): ReLU()\n",
            "    )\n",
            "    (res_2): ResNet(\n",
            "      (linear1): Linear(in_features=2, out_features=2, bias=True)\n",
            "      (nonlinear): ReLU()\n",
            "    )\n",
            "    (res_3): ResNet(\n",
            "      (linear1): Linear(in_features=2, out_features=2, bias=True)\n",
            "      (nonlinear): ReLU()\n",
            "    )\n",
            "    (res_4): ResNet(\n",
            "      (linear1): Linear(in_features=2, out_features=2, bias=True)\n",
            "      (nonlinear): ReLU()\n",
            "    )\n",
            "  )\n",
            "  (output): Linear(in_features=2, out_features=1, bias=True)\n",
            ")\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f1967ac3748>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 271
        }
      ]
    },
    {
      "metadata": {
        "id": "MbjhpoeqRKfC",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Now, we use logistic loss function (for $y_i \\in \\left\\{-1, 1\\right\\}$):\n",
        "$$\n",
        "\\textrm{loss} = \\frac 1 n \\sum_{i=1}^n \\log\\left( 1+  e^{ - y_i \\hat y_i}\\right)\n",
        "$$ where $\\hat y_i = \\textrm{net}(x_i)$."
      ]
    },
    {
      "metadata": {
        "id": "y-FgDpri83_g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "5a2567f0-844f-4b34-fb0c-9b146137b8c8"
      },
      "cell_type": "code",
      "source": [
        "criterion = torch.nn.SoftMarginLoss()\n",
        "\n",
        "learning_rate = 0.005\n",
        "optimizer = torch.optim.Adam(net.parameters(), lr=learning_rate)\n",
        "\n",
        "X = X.to(device)\n",
        "Y = Y.to(device)\n",
        "\n",
        "for it in range(5000):\n",
        "    output = net(X)\n",
        "\n",
        "    loss = criterion(output, Y.view(N,1))\n",
        "    \n",
        "    optimizer.zero_grad()\n",
        "    loss.backward()\n",
        "\n",
        "    optimizer.step()\n",
        "    if it % 1000 == 0:\n",
        "        print(\"loss: \", loss.item())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "loss:  0.8421573042869568\n",
            "loss:  0.31732770800590515\n",
            "loss:  0.3143801987171173\n",
            "loss:  0.3137434422969818\n",
            "loss:  0.31350356340408325\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "d7aws0F7S9bR",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Finally, we plot the output values of input points $(a, b)$ for all  $a, b \\in [-5, 5]$:"
      ]
    },
    {
      "metadata": {
        "id": "4arWbqiK9tKB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 310
        },
        "outputId": "4f8d366d-37ff-443e-83b0-ebdad82735b9"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "rcParams['figure.figsize'] = 5,5\n",
        "\n",
        "a = np.random.random((100, 100))\n",
        "myX = torch.empty( (100*100, 2))\n",
        "c = 0\n",
        "for i in range(100):\n",
        "    for j in range(100):\n",
        "        a = i / 100.0\n",
        "        b = j / 100.0\n",
        "        a = 5 * 2*(a - 0.5)\n",
        "        b = 5 * 2*(b - 0.5)\n",
        "        \n",
        "        myX[c, 0] = a\n",
        "        myX[c, 1] = b\n",
        "        c = c + 1\n",
        "\n",
        "myX =myX.to(device)\n",
        "out = net(myX)\n",
        "heatmap = out.view(100,100).data.cpu().numpy()\n",
        "\n",
        "im = plt.imshow(heatmap, interpolation='nearest', extent=[-5, 5, -5, 5], \\\n",
        "           cmap=plt.get_cmap(\"binary\"), origin='lower')\n",
        "plt.colorbar(im)\n",
        "_ = plt.scatter(x1, x2, c=colors, s=2)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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S26GDVKcOZOTmJg0dii9Qwv/WoAGk16qVVLUqJPPAA5Bgw4YQ2JIlTjUXEiINHszf0aNR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\nYVtYWIiCggK0Urrhy6FWqzFjxgzExsaia9euhuPXrl2DTqc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Nm1bHo6qa+vK5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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f1967abc128>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}