Lesson 3: the power and limitation of neural network.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "On neural networks approximation for any function.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/UDICatNCHU/PyTorch-SocialNetwork/blob/master/On_neural_networks_approximation_for_any_function.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jV2fuzXGXz_X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = [[-1,-5], [-2,-5], [-3.5,-5], [1,5], [2.1,5], [3.3, 5], [2.3, 5]]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RrfUDCjHYRWq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import numpy as np"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CwF3PaF9ZFA7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.array(data)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IJkpl7hTahxg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = data[:,0]\n",
        "y = data[:,1]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LbPWum59P6vi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        },
        "outputId": "6dc5f1de-e326-4bf8-d45f-b0ce91909ee2"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.scatter(x, y)\n",
        "plt.show()"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RhAkTfFzUv2PHjmnjxo368MMPVVpa6vecYSMWi6msrEwNDQ2SpIaGBpWVlXE5x7GtW7fq\n1KlT2r59u6LRqN9zBvTHH3+otbW19/OjR49q1KhRKigo8HFV3/gFKAN47rnndP78eeXk5CgSiWjp\n0qV6/PHH/Z7Vp0ceeUS5ubn/ClFdXV1WPtro0dDQoM2bN6ujo0O5ubm666679NFHH2Xdv1gvXLig\nVatWqaOjQ/n5+aqtrdV9993n96w+vfrqq/r666917do1FRYWqqCgQIcOHfJ7Vp/OnTunqqoqjRs3\nTnfeeackqbS0VNu3b/d5Wd+uXbum5cuX66+//lI4HNaoUaP00ksvafLkyX5Puy2CDwBGcEkHAIwg\n+ABgBMEHACMIPgAYQfABwAiCDwBGEHwAMILgA4AR/w9hNV8hs/EXuQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7zqfbsB2YcN-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x_tensor = torch.tensor(x, dtype=torch.float)\n",
        "y_tensor = torch.tensor(y, dtype=torch.float)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RPdgqR_retpF",
        "colab_type": "code",
        "outputId": "7e837103-d8a8-4a6e-f27e-a57dcc9999f9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 139
        }
      },
      "source": [
        "y_tensor.view(-1,1)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-5.],\n",
              "        [-5.],\n",
              "        [-5.],\n",
              "        [ 5.],\n",
              "        [ 5.],\n",
              "        [ 5.],\n",
              "        [ 5.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V5Dju17de7jm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NkKsNWNZYsVc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Net(torch.nn.Module):\n",
        "    def __init__(self, n_feature, size_hidden, n_output):\n",
        "        super(Net, self).__init__()\n",
        "        self.layer1 = torch.nn.Linear(n_feature, size_hidden)   # hidden layer\n",
        "        self.layer2 = torch.nn.Linear(size_hidden, n_output)   # output layer\n",
        "#         self.predict = torch.nn.Linear(n_feature, n_output)   # output layer        \n",
        "\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = torch.sigmoid(self.layer1(x))      # activation function for hidden layer\n",
        "#         x = self.layer1(x)      # without sigmoid      \n",
        "        x = self.layer2(x)             # linear output\n",
        "\n",
        "        return x\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T5BN7IrFbJ23",
        "colab_type": "code",
        "outputId": "9aa0c681-c0b3-420a-85a9-3cf089a8a14c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17351
        }
      },
      "source": [
        "net = Net(1, 1, 1)\n",
        "learning_rate = 0.01\n",
        "optimizer = torch.optim.Adam(net.parameters(), lr=learning_rate)\n",
        "criterion = torch.nn.MSELoss(reduction='sum')  # this is for regression mean squared loss\n",
        "\n",
        "running_loss = 0.0\n",
        "for epoch in range(1000):\n",
        "  inputs = x_tensor.view(-1,1)\n",
        "  labels = y_tensor.view(-1,1)\n",
        "  optimizer.zero_grad()\n",
        "  outputs = net(inputs)\n",
        "  loss = criterion(outputs, labels)\n",
        "  loss.backward()\n",
        "  optimizer.step()  \n",
        "  running_loss += loss.item()\n",
        "  print('Epoch {}'.format(epoch+1), \"loss: \",running_loss)\n",
        "  running_loss = 0.0\n",
        "  "
      ],
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1 loss:  179.1348876953125\n",
            "Epoch 2 loss:  178.7306671142578\n",
            "Epoch 3 loss:  178.33567810058594\n",
            "Epoch 4 loss:  177.9501953125\n",
            "Epoch 5 loss:  177.574462890625\n",
            "Epoch 6 loss:  177.208740234375\n",
            "Epoch 7 loss:  176.8532257080078\n",
            "Epoch 8 loss:  176.50814819335938\n",
            "Epoch 9 loss:  176.17367553710938\n",
            "Epoch 10 loss:  175.8499755859375\n",
            "Epoch 11 loss:  175.53720092773438\n",
            "Epoch 12 loss:  175.23545837402344\n",
            "Epoch 13 loss:  174.94482421875\n",
            "Epoch 14 loss:  174.66539001464844\n",
            "Epoch 15 loss:  174.3971405029297\n",
            "Epoch 16 loss:  174.1400909423828\n",
            "Epoch 17 loss:  173.8942108154297\n",
            "Epoch 18 loss:  173.65940856933594\n",
            "Epoch 19 loss:  173.435546875\n",
            "Epoch 20 loss:  173.22251892089844\n",
            "Epoch 21 loss:  173.0200958251953\n",
            "Epoch 22 loss:  172.82803344726562\n",
            "Epoch 23 loss:  172.64608764648438\n",
            "Epoch 24 loss:  172.4739227294922\n",
            "Epoch 25 loss:  172.31118774414062\n",
            "Epoch 26 loss:  172.15750122070312\n",
            "Epoch 27 loss:  172.01242065429688\n",
            "Epoch 28 loss:  171.87545776367188\n",
            "Epoch 29 loss:  171.7461395263672\n",
            "Epoch 30 loss:  171.62391662597656\n",
            "Epoch 31 loss:  171.5082244873047\n",
            "Epoch 32 loss:  171.3984832763672\n",
            "Epoch 33 loss:  171.29408264160156\n",
            "Epoch 34 loss:  171.19439697265625\n",
            "Epoch 35 loss:  171.0987548828125\n",
            "Epoch 36 loss:  171.00653076171875\n",
            "Epoch 37 loss:  170.9170684814453\n",
            "Epoch 38 loss:  170.82968139648438\n",
            "Epoch 39 loss:  170.7437286376953\n",
            "Epoch 40 loss:  170.65855407714844\n",
            "Epoch 41 loss:  170.573486328125\n",
            "Epoch 42 loss:  170.48789978027344\n",
            "Epoch 43 loss:  170.40118408203125\n",
            "Epoch 44 loss:  170.31271362304688\n",
            "Epoch 45 loss:  170.221923828125\n",
            "Epoch 46 loss:  170.1282196044922\n",
            "Epoch 47 loss:  170.0310821533203\n",
            "Epoch 48 loss:  169.92996215820312\n",
            "Epoch 49 loss:  169.8243865966797\n",
            "Epoch 50 loss:  169.7138671875\n",
            "Epoch 51 loss:  169.5979461669922\n",
            "Epoch 52 loss:  169.47621154785156\n",
            "Epoch 53 loss:  169.3482208251953\n",
            "Epoch 54 loss:  169.21363830566406\n",
            "Epoch 55 loss:  169.07208251953125\n",
            "Epoch 56 loss:  168.92320251464844\n",
            "Epoch 57 loss:  168.76670837402344\n",
            "Epoch 58 loss:  168.60231018066406\n",
            "Epoch 59 loss:  168.42971801757812\n",
            "Epoch 60 loss:  168.2487030029297\n",
            "Epoch 61 loss:  168.0590362548828\n",
            "Epoch 62 loss:  167.8605194091797\n",
            "Epoch 63 loss:  167.6529998779297\n",
            "Epoch 64 loss:  167.43629455566406\n",
            "Epoch 65 loss:  167.21029663085938\n",
            "Epoch 66 loss:  166.9748992919922\n",
            "Epoch 67 loss:  166.7300262451172\n",
            "Epoch 68 loss:  166.4756317138672\n",
            "Epoch 69 loss:  166.21168518066406\n",
            "Epoch 70 loss:  165.93820190429688\n",
            "Epoch 71 loss:  165.65518188476562\n",
            "Epoch 72 loss:  165.36270141601562\n",
            "Epoch 73 loss:  165.06082153320312\n",
            "Epoch 74 loss:  164.74961853027344\n",
            "Epoch 75 loss:  164.42922973632812\n",
            "Epoch 76 loss:  164.0997772216797\n",
            "Epoch 77 loss:  163.76141357421875\n",
            "Epoch 78 loss:  163.41432189941406\n",
            "Epoch 79 loss:  163.05865478515625\n",
            "Epoch 80 loss:  162.6946563720703\n",
            "Epoch 81 loss:  162.32247924804688\n",
            "Epoch 82 loss:  161.94239807128906\n",
            "Epoch 83 loss:  161.5546112060547\n",
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            "Epoch 846 loss:  9.907549858093262\n",
            "Epoch 847 loss:  9.864069938659668\n",
            "Epoch 848 loss:  9.820744514465332\n",
            "Epoch 849 loss:  9.777582168579102\n",
            "Epoch 850 loss:  9.734580039978027\n",
            "Epoch 851 loss:  9.691739082336426\n",
            "Epoch 852 loss:  9.649065017700195\n",
            "Epoch 853 loss:  9.606546401977539\n",
            "Epoch 854 loss:  9.564188957214355\n",
            "Epoch 855 loss:  9.521986961364746\n",
            "Epoch 856 loss:  9.47994613647461\n",
            "Epoch 857 loss:  9.43805980682373\n",
            "Epoch 858 loss:  9.396340370178223\n",
            "Epoch 859 loss:  9.354764938354492\n",
            "Epoch 860 loss:  9.31335735321045\n",
            "Epoch 861 loss:  9.272102355957031\n",
            "Epoch 862 loss:  9.230999946594238\n",
            "Epoch 863 loss:  9.19005298614502\n",
            "Epoch 864 loss:  9.149263381958008\n",
            "Epoch 865 loss:  9.108627319335938\n",
            "Epoch 866 loss:  9.068143844604492\n",
            "Epoch 867 loss:  9.027817726135254\n",
            "Epoch 868 loss:  8.987639427185059\n",
            "Epoch 869 loss:  8.947614669799805\n",
            "Epoch 870 loss:  8.907744407653809\n",
            "Epoch 871 loss:  8.868023872375488\n",
            "Epoch 872 loss:  8.828453063964844\n",
            "Epoch 873 loss:  8.789037704467773\n",
            "Epoch 874 loss:  8.749767303466797\n",
            "Epoch 875 loss:  8.710646629333496\n",
            "Epoch 876 loss:  8.671680450439453\n",
            "Epoch 877 loss:  8.632858276367188\n",
            "Epoch 878 loss:  8.594184875488281\n",
            "Epoch 879 loss:  8.555659294128418\n",
            "Epoch 880 loss:  8.517281532287598\n",
            "Epoch 881 loss:  8.479053497314453\n",
            "Epoch 882 loss:  8.44096565246582\n",
            "Epoch 883 loss:  8.403027534484863\n",
            "Epoch 884 loss:  8.365229606628418\n",
            "Epoch 885 loss:  8.32758617401123\n",
            "Epoch 886 loss:  8.290082931518555\n",
            "Epoch 887 loss:  8.252720832824707\n",
            "Epoch 888 loss:  8.215505599975586\n",
            "Epoch 889 loss:  8.178433418273926\n",
            "Epoch 890 loss:  8.141507148742676\n",
            "Epoch 891 loss:  8.104721069335938\n",
            "Epoch 892 loss:  8.068077087402344\n",
            "Epoch 893 loss:  8.031574249267578\n",
            "Epoch 894 loss:  7.995209217071533\n",
            "Epoch 895 loss:  7.958988189697266\n",
            "Epoch 896 loss:  7.922906875610352\n",
            "Epoch 897 loss:  7.886966228485107\n",
            "Epoch 898 loss:  7.851161003112793\n",
            "Epoch 899 loss:  7.815496444702148\n",
            "Epoch 900 loss:  7.779967784881592\n",
            "Epoch 901 loss:  7.7445783615112305\n",
            "Epoch 902 loss:  7.70932674407959\n",
            "Epoch 903 loss:  7.674216270446777\n",
            "Epoch 904 loss:  7.639238357543945\n",
            "Epoch 905 loss:  7.604396343231201\n",
            "Epoch 906 loss:  7.569694519042969\n",
            "Epoch 907 loss:  7.535125255584717\n",
            "Epoch 908 loss:  7.500689506530762\n",
            "Epoch 909 loss:  7.466394424438477\n",
            "Epoch 910 loss:  7.432234764099121\n",
            "Epoch 911 loss:  7.398200988769531\n",
            "Epoch 912 loss:  7.3642988204956055\n",
            "Epoch 913 loss:  7.330534934997559\n",
            "Epoch 914 loss:  7.296900749206543\n",
            "Epoch 915 loss:  7.263400077819824\n",
            "Epoch 916 loss:  7.230029106140137\n",
            "Epoch 917 loss:  7.196793556213379\n",
            "Epoch 918 loss:  7.163684844970703\n",
            "Epoch 919 loss:  7.130709171295166\n",
            "Epoch 920 loss:  7.097867488861084\n",
            "Epoch 921 loss:  7.065150260925293\n",
            "Epoch 922 loss:  7.032564640045166\n",
            "Epoch 923 loss:  7.000110149383545\n",
            "Epoch 924 loss:  6.967776775360107\n",
            "Epoch 925 loss:  6.935574054718018\n",
            "Epoch 926 loss:  6.903497219085693\n",
            "Epoch 927 loss:  6.871547698974609\n",
            "Epoch 928 loss:  6.839730739593506\n",
            "Epoch 929 loss:  6.808035373687744\n",
            "Epoch 930 loss:  6.776468753814697\n",
            "Epoch 931 loss:  6.745023250579834\n",
            "Epoch 932 loss:  6.713702201843262\n",
            "Epoch 933 loss:  6.682509422302246\n",
            "Epoch 934 loss:  6.65144157409668\n",
            "Epoch 935 loss:  6.6204938888549805\n",
            "Epoch 936 loss:  6.589675426483154\n",
            "Epoch 937 loss:  6.5589728355407715\n",
            "Epoch 938 loss:  6.528396129608154\n",
            "Epoch 939 loss:  6.497940540313721\n",
            "Epoch 940 loss:  6.467611312866211\n",
            "Epoch 941 loss:  6.437403678894043\n",
            "Epoch 942 loss:  6.40731143951416\n",
            "Epoch 943 loss:  6.377338886260986\n",
            "Epoch 944 loss:  6.347492694854736\n",
            "Epoch 945 loss:  6.3177642822265625\n",
            "Epoch 946 loss:  6.288161277770996\n",
            "Epoch 947 loss:  6.2586669921875\n",
            "Epoch 948 loss:  6.229298114776611\n",
            "Epoch 949 loss:  6.200046062469482\n",
            "Epoch 950 loss:  6.170907020568848\n",
            "Epoch 951 loss:  6.141889572143555\n",
            "Epoch 952 loss:  6.112987995147705\n",
            "Epoch 953 loss:  6.084209442138672\n",
            "Epoch 954 loss:  6.055540561676025\n",
            "Epoch 955 loss:  6.026988983154297\n",
            "Epoch 956 loss:  5.998555660247803\n",
            "Epoch 957 loss:  5.970239639282227\n",
            "Epoch 958 loss:  5.942032337188721\n",
            "Epoch 959 loss:  5.913944721221924\n",
            "Epoch 960 loss:  5.885969638824463\n",
            "Epoch 961 loss:  5.858107089996338\n",
            "Epoch 962 loss:  5.830358505249023\n",
            "Epoch 963 loss:  5.802727699279785\n",
            "Epoch 964 loss:  5.775198936462402\n",
            "Epoch 965 loss:  5.747788906097412\n",
            "Epoch 966 loss:  5.720491886138916\n",
            "Epoch 967 loss:  5.693303108215332\n",
            "Epoch 968 loss:  5.666230201721191\n",
            "Epoch 969 loss:  5.6392598152160645\n",
            "Epoch 970 loss:  5.6124067306518555\n",
            "Epoch 971 loss:  5.585663795471191\n",
            "Epoch 972 loss:  5.55902624130249\n",
            "Epoch 973 loss:  5.532501697540283\n",
            "Epoch 974 loss:  5.506086826324463\n",
            "Epoch 975 loss:  5.479776859283447\n",
            "Epoch 976 loss:  5.453580856323242\n",
            "Epoch 977 loss:  5.427487373352051\n",
            "Epoch 978 loss:  5.401503086090088\n",
            "Epoch 979 loss:  5.37562370300293\n",
            "Epoch 980 loss:  5.349852085113525\n",
            "Epoch 981 loss:  5.324190139770508\n",
            "Epoch 982 loss:  5.2986345291137695\n",
            "Epoch 983 loss:  5.2731852531433105\n",
            "Epoch 984 loss:  5.247831344604492\n",
            "Epoch 985 loss:  5.222592353820801\n",
            "Epoch 986 loss:  5.197453022003174\n",
            "Epoch 987 loss:  5.172420501708984\n",
            "Epoch 988 loss:  5.14749002456665\n",
            "Epoch 989 loss:  5.1226654052734375\n",
            "Epoch 990 loss:  5.097942352294922\n",
            "Epoch 991 loss:  5.0733256340026855\n",
            "Epoch 992 loss:  5.048805236816406\n",
            "Epoch 993 loss:  5.024392127990723\n",
            "Epoch 994 loss:  5.000079154968262\n",
            "Epoch 995 loss:  4.9758687019348145\n",
            "Epoch 996 loss:  4.951755523681641\n",
            "Epoch 997 loss:  4.927750110626221\n",
            "Epoch 998 loss:  4.903839588165283\n",
            "Epoch 999 loss:  4.880032539367676\n",
            "Epoch 1000 loss:  4.856325149536133\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OeZL6uS5diUe",
        "colab_type": "code",
        "outputId": "ca270a9e-3338-4012-eb79-8e5026e3e443",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "net(torch.tensor([3.0]).view(-1,1))"
      ],
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[4.4759]], grad_fn=<AddmmBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kt4WsvyRXgrd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 884
        },
        "outputId": "0ce00315-0dd6-4d18-ac7b-05a5b6fe7779"
      },
      "source": [
        "p_x = [ i for i in range(-25,25)]\n",
        "p_y = [ net(torch.tensor([y], dtype=torch.float).view(-1,1)).item() for y in p_x ]\n",
        "p_y"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[-4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162924766540527,\n",
              " -4.162919998168945,\n",
              " -4.162752151489258,\n",
              " -4.156876087188721,\n",
              " -3.955916166305542,\n",
              " -0.16800236701965332,\n",
              " 4.198738098144531,\n",
              " 4.467990875244141,\n",
              " 4.475929260253906,\n",
              " 4.476157188415527,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426,\n",
              " 4.476162910461426]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8bGH1m1MXgQP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        },
        "outputId": "ffc82f2a-6115-4dd5-895e-538af5012da7"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.scatter(p_x, p_y)\n",
        "plt.show()"
      ],
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Xu++++7xYLOZLna4dPnzYO3r0qLdkyRLvww8/7HHsnXfe8V544QXP8zzv+PHj3h133OG1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\n8X8uu3lTMfbktAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zTGEBzPCVFx2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = [[-1,-50], [-2,-50], [-3,-50], [-4,-50], [1,50], [2,50], [3, 50], [4, 50], [5,50], [6, 100], [7, 100], [8, 100]]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kQ9EkLOjZcsX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = [[-1,-5], [-2,-5], [-3,-5], [-4,-5], [1,5], [2,5], [3, 5], [4, 5], [5,5], [6, 10], [7, 10], [8, 10]]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CezqNR1DVFu9",
        "colab_type": "code",
        "outputId": "57ce2edf-2498-438c-cf87-d3a4f14f72a6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        }
      },
      "source": [
        "\n",
        "data = np.array(data)\n",
        "x = data[:,0]\n",
        "y = data[:,1]\n",
        "\n",
        "x_tensor = torch.tensor(x, dtype=torch.float)\n",
        "y_tensor = torch.tensor(y, dtype=torch.float)\n",
        "\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.scatter(x, y)\n",
        "plt.show()"
      ],
      "execution_count": 209,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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d1etu7pMpPQC4X1oGftWsYmVnnTt6dpZXVbOK065PpvQA4H5pedP27I3GRD/Z8uc+iXq6\nJRm7JGMPAO4X1+fhm8Tn4bOLG2XKHhK7uFGyPw8/LS/pAACiR+ADgCUIfACwBIEPAJZwzVM6Xq8n\nJce6Dbu4T6bsIbGLG8W6RyzHueYpHQBAYnFJBwAsQeADgCUIfACwBIEPAJYg8AHAEgQ+AFiCwAcA\nSxD4AGAJAh8ALJFRgX/o0CGVlJTorbfeSvUoMVu1apXmzZunyspK3XXXXfr2229TPVJU2tvbVV1d\nrblz56q6ulonTpxI9Ugx6evr0wMPPKC5c+dq/vz5Wrp0qXp7e1M9Vlzq6+s1depUHT9+PNWjxGxw\ncFArVqzQrbfeqvnz5+vZZ59N9UgxOXDggG6//Xbddtttqqys1EcffZScxk6GCIfDzh133OEsWbLE\n2blzZ6rHidnHH3/sDA0Njfx6zpw5KZ4oOosWLXJ2797tOI7j7N6921m0aFGKJ4pNX1+fc/DgwZGf\n161b5zz11FMpnCg+R44ccRYvXuzMnj3b+e6771I9TszWrFnjvPDCC04kEnEcx3F6enpSPFH0IpGI\nM2PGjJH/DkePHnVKS0ud4eHhhPfOmDP8devWafHixcrLy0v1KHGZPXu2Ro0aJUkqLS1VV1eXIpFI\niqc6P6FQSG1tbaqoqJAkVVRUqK2tLS3PjHNzczVz5syRn0tLS9XR0ZHCiWI3NDSk1atXa+XKlake\nJS4DAwPavXu3li1bJo/njw8OmzhxYoqnio3X61U4/Mc3XYXDYRUUFMjrTXwcu+bTMuPR3NyscDis\nefPm6ZNPPkn1OMY0Njbq5ptvTsr/CCZ0dnZq0qRJ8vl8kiSfz6eCggJ1dnYqPz8/xdPFLhKJ6O23\n31Z5eXmqR4nJxo0bVVlZqaKiolSPEpeTJ08qNzdX9fX1OnTokMaNG6dly5ZpxowZqR4tKh6PR6+9\n9poefvhhjR07VgMDA2poaEhK77QI/AULFvzj2dWHH36oDRs2aOvWrUmeKjb/tsvnn38+EpZNTU3a\ns2ePGhsbkzke/saaNWs0duxY1dTUpHqUqH311Vc6cuSIHn/88VSPErfh4WGdPHlSV1xxhZ588kl9\n8803euihh7R//36NHx/dd7um0pkzZ7RlyxZt2rRJZWVl+vLLL7V8+XI1NTVp3LhxCe2dFoH/7rvv\n/uPvHT58WD09Pbrzzjsl/XGz7cCBA/r111+1dOnSZI143v5tl7P279+vV199Vdu2bUurf7IWFhbq\n1KlTGh4els/n0/DwsLq7u1VYWJjq0WJWV1enn376SZs3b06bf2n92RdffKFgMKg5c+ZIkrq6urR4\n8WKtXbtWN954Y4qni05hYaGysrJGLhleffXVysvLU3t7u6ZPn57i6c7f0aNH1d3drbKyMklSWVmZ\nxowZo2AwqKuuuiqxzRN+lyDJnnzyybS/aTt79mznxIkTqR4lJjU1NefctK2pqUnxRLHbsGGDU1NT\n4/z++++pHsWYdL9pe9999zmffvqp4ziO8+OPPzrXXXed89tvv6V4quh0d3c711xzjRMMBh3HcZwf\nfvjBufbaa52+vr6E9864L0Cpra3VtGnT0vKf35J0/fXXa9SoUedc8962bVva3IwOBoOqra1Vf3+/\ncnJyVFdXp8mTJ6d6rKh9//33qqio0GWXXaYLLrhAklRUVKQ33ngjxZPFp7y8XJs3b9aUKVNSPUpM\nTp48qaefflq//vqrsrKytHz5cs2aNSvVY0Xt/fff15tvvjly8/nRRx/VLbfckvC+GRf4AIC/l34X\nJQEAMSHwAcASBD4AWILABwBLEPgAYAkCHwAsQeADgCUIfACwxP8Ac92vsT96iJwAAAAASUVORK5C\nYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tcq3SB07WQve",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Net2(torch.nn.Module):\n",
        "    def __init__(self, n_feature, size_hidden, n_output):\n",
        "        super(Net2, self).__init__()\n",
        "        self.layer1 = torch.nn.Linear(n_feature, size_hidden)   # hidden layer\n",
        "        self.layer2 = torch.nn.Linear(size_hidden, n_output)   # output layer\n",
        "#         self.predict = torch.nn.Linear(n_feature, n_output)   # output layer        \n",
        "\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = torch.sigmoid(self.layer1(x))      # activation function for hidden layer\n",
        "#         x = self.layer1(x)      # without sigmoid      \n",
        "        x = self.layer2(x)             # linear output\n",
        "\n",
        "        return x\n",
        "net2 = Net2(1, 2, 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-660DFF6VFru",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "07a06b1d-f51e-40ce-ddde-12c8bfa282ff"
      },
      "source": [
        "learning_rate = 0.1\n",
        "optimizer = torch.optim.Adam(net2.parameters(), lr=learning_rate)\n",
        "criterion = torch.nn.MSELoss(reduction='sum')  # this is for regression mean squared loss\n",
        "\n",
        "running_loss = 0.0\n",
        "for epoch in range(10000):\n",
        "  inputs = x_tensor.view(-1,1)\n",
        "  labels = y_tensor.view(-1,1)\n",
        "  optimizer.zero_grad()\n",
        "  outputs = net2(inputs)\n",
        "  loss = criterion(outputs, labels)\n",
        "  loss.backward()\n",
        "  optimizer.step()  \n",
        "  running_loss += loss.item()\n",
        "#   print('Epoch {}'.format(epoch+1), \"loss: \",running_loss)\n",
        "  running_loss = 0.0\n",
        "print(loss.item())"
      ],
      "execution_count": 211,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.001309102401137352\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "daPVger2VfYn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "a89c574a-169a-4783-8378-ff0c32856022"
      },
      "source": [
        "net2(torch.tensor([200.0]).view(-1,1))"
      ],
      "execution_count": 214,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[10.0112]], grad_fn=<AddmmBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 214
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-_YUCi6qVFoE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        },
        "outputId": "d3d590a8-96dd-4a65-bb9d-0a7c5363623d"
      },
      "source": [
        "p_x = [ i for i in np.arange(-10,10, 0.1)]\n",
        "p_y = [ net2(torch.tensor([y], dtype=torch.float).view(-1,1)).item() for y in p_x ]\n",
        "import matplotlib.pyplot as plt\n",
        "plt.scatter(p_x, p_y)\n",
        "plt.show()"
      ],
      "execution_count": 213,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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A83CUDnCGUQWDJImjdNArUfjAl4wqGNRe/JJ1F9wCwsWUDgDYBIUPADZB4QOATVD4AGAT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\n+ABgE/8PZL/TqaJh0goAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SwngN48qVFkd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q1ZaHJDHYAC-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "z = y*y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1i7uAuDqZI__",
        "colab_type": "code",
        "outputId": "0c0d990c-6030-4158-83d9-91ac12dbde41",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "z"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([64.], grad_fn=<MulBackward0>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 303
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6-zYriNwVFhm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "z.backward()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A0kLcfVhVFd0",
        "colab_type": "code",
        "outputId": "6790bd67-bbba-446f-d150-0e7e426ab939",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "x.grad"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([192.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 305
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MOnY1x4fVFa0",
        "colab_type": "code",
        "outputId": "8ae7fda7-4141-4890-bfc3-71ad0a23438a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "x.grad"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([192.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 306
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "906ifGZ0Xxad",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t87dVE72XxQi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rEoCXLpHUmmd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j68mMSn2gt09",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = torch.tensor([1,2,3,4,5], dtype=torch.float, requires_grad=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3uMdpoGbABDx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "parameters = torch.tensor([1,1,1,1,1], dtype=torch.float, requires_grad=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-SpFhdp9F83X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "result = (x*parameters).sum()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WctytTuWHC6X",
        "colab_type": "code",
        "outputId": "b6bdcb0d-9e69-4b1b-ce11-efb56c0d2eb9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "result"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(15., grad_fn=<SumBackward0>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 172
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aGY7nggtGptA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "error = torch.zeros_like(result)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sDzUJhC5HGVx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "error = torch.abs(result - error)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XEoFOE2_G2IR",
        "colab_type": "code",
        "outputId": "1add8df1-d720-437b-a21c-dfb50296614d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "error"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(15., grad_fn=<AbsBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 175
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XjrEj-ZZGwEX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "error.backward()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "camk8CGaGRqD",
        "colab_type": "code",
        "outputId": "dfdd898c-959f-4a03-f27c-4b9be4390ac9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "parameters.grad"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1., 2., 3., 4., 5.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 177
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GttiyQcHGU1E",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mndFUFQvGUUX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sAkxIk64KH6M",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-eYbSMXUKHg5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "APESWE_IJ0v2",
        "colab_type": "code",
        "outputId": "f3af55c8-dad7-4266-f177-f2556425dcdc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "(x*parameters).sum()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(14.4500, grad_fn=<SumBackward0>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 184
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UBRR9zjaAfZo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = x.view(1,-1).clone().detach()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "esle3uZHEvv3",
        "colab_type": "code",
        "outputId": "cfd8f8c6-0c8e-417c-8c21-7bd5419ef452",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "x.requires_grad_(True)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2., 3., 4., 5.]], requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 107
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bSkorkcIE2FL",
        "colab_type": "code",
        "outputId": "f983d585-51bb-4eb0-ea30-938d03d6bf8b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2., 3., 4., 5.]], requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 108
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iZa-cFhoD_iV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6djWBInAAhPh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "parameters = parameters.view(-1,1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X4Wkmz_sDVtT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "parameters.requires_grad_= True"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rVwBXnWGENAm",
        "colab_type": "code",
        "outputId": "b779d5f9-deb8-4341-af9c-01522e192f56",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "x"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2., 3., 4., 5.]], grad_fn=<ViewBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "by1mAtauAJ2r",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "result = torch.mm(x, parameters)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CmdxCPB1DXvA",
        "colab_type": "code",
        "outputId": "5c136c33-9827-4f45-bec4-fcccbf300f60",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "x"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2., 3., 4., 5.]], grad_fn=<ViewBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9r0AcAdaAN1n",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y = x.pow(2).sum()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AgUjvEHvDOR-",
        "colab_type": "code",
        "outputId": "aa3be7ae-6075-4b9f-c844-ed297f54ee33",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "y"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(55., grad_fn=<SumBackward0>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 111
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-BPQSFH2A7NI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y.backward()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MjkaufNBBWiy",
        "colab_type": "code",
        "outputId": "a8427dca-1714-488a-f240-cc7683d7e4d2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "print(x.grad)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([[ 2.,  4.,  6.,  8., 10.]])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ndg2-ek_B9Ks",
        "colab_type": "code",
        "outputId": "c5ea42a1-471b-409e-fef8-fdf11f07f8e9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "xx = torch.tensor([[1., -1.]], requires_grad=True)\n",
        "out = xx.pow(2).sum()\n",
        "out.backward()\n",
        "xx.grad"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 2., -2.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 114
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fzOWitZADLYd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}