Basics_NN_BackPropagation_ErrorCal_Gradient_weightsUpdation (1).ipynb

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      "source": [
        "# We are going to create a Neural Network from scratch, we will use this to solve a equation\n",
        "\n",
        "# lets say we have an equation\n",
        "# y = 3x1 + 4x2\n",
        "# x1, x2 are input  & y is the output\n",
        "\n",
        "\n",
        "# x1 | x2 |  y\n",
        "# 3  | 2  | 17\n",
        "\n",
        "\n",
        "# we have to build a model which will take input as `x1` & `x2`\n",
        "# corectly predict the output `y`\n",
        "\n",
        "x1 = 3\n",
        "x2 = 2\n",
        "y_actual = 17"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "n4JPQ2Tqpj2H"
      },
      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
      "source": [
        "# Phase I - Feed Forward Neural Network\n",
        "# 1.1 Assign random weights\n",
        "# 1.2 affine equation\n",
        "\n",
        "# we want 2 random weights\n",
        "w1 = np.random.randint(1, 10)\n",
        "w2 = np.random.randint(1, 10)\n",
        "w1, w2"
      ],
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        "id": "AcdyxIjjpnjY",
        "outputId": "f46ddd33-7d95-4e3e-c550-572df60e701f"
      },
      "execution_count": null,
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              "(9, 8)"
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          "metadata": {},
          "execution_count": 4
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# 1.2 Affine Equation\n",
        "y_pred = w1*x1 + w2*x2"
      ],
      "metadata": {
        "id": "0VEz53Scppie"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred"
      ],
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        "outputId": "30a20e5a-4ee2-4e89-c4d0-343e78ff9e33"
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "43"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Phase II - Error Calculation\n",
        "# 2.1 Calculate the error\n",
        "error = (y_pred - y_actual)**2"
      ],
      "metadata": {
        "id": "k4Lb0p4qpsJk"
      },
      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
      "source": [
        "error"
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          "metadata": {},
          "execution_count": 8
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    {
      "cell_type": "code",
      "source": [
        "# Phase III - Back Propagation\n",
        "# 3.1 Calculate the gradients\n",
        "# 3.2 weight updation\n",
        "\n",
        "dedw1 = 2*(y_pred - y_actual)*x1\n",
        "dedw2 = 2*(y_pred - y_actual)*x2"
      ],
      "metadata": {
        "id": "Yz5b8RjTpuu6"
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      "execution_count": null,
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      "cell_type": "code",
      "source": [
        "dedw1, dedw2"
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              "(156, 104)"
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          "metadata": {},
          "execution_count": 10
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    {
      "cell_type": "code",
      "source": [
        "# 3.2 Weight updation\n",
        "w1 = w1 - dedw1\n",
        "w2 = w2 - dedw2"
      ],
      "metadata": {
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      "execution_count": null,
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      "source": [
        "w1,w2"
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      "execution_count": null,
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-147, -96)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w1*x1 + w2*x2"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/"
        },
        "id": "eKNigSnwp1Ii",
        "outputId": "c3d59ef2-43d5-4441-bdd6-fd0bdab3aafa"
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      "execution_count": null,
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          "output_type": "execute_result",
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              "-633"
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          "metadata": {},
          "execution_count": 13
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    {
      "cell_type": "code",
      "source": [
        "# We never expected this is give correct results in just one iteration\n",
        "# we need to add more iteration"
      ],
      "metadata": {
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      },
      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
      "source": [
        "w1 = np.random.randint(1, 100)\n",
        "w2 = np.random.randint(1, 100)\n",
        "\n",
        "y_pred_list = []\n",
        "error_list = []\n",
        "w1_list = []\n",
        "w2_list = []\n",
        "lr = 0.01\n",
        "\n",
        "for epoch in range(1, 50):\n",
        "  # affine equation\n",
        "  y_pred = x1*w1 + x2*w2\n",
        "  y_pred_list.append(y_pred)\n",
        "  w1_list.append(w1)\n",
        "  w2_list.append(w2)\n",
        "\n",
        "  # error calc\n",
        "  error = (y_pred - y_actual)**2\n",
        "  error_list.append(error)\n",
        "\n",
        "  # gradient calc\n",
        "  dedw1 = 2*(y_pred - y_actual)*(x1)\n",
        "  dedw2 = 2*(y_pred - y_actual)*(x2)\n",
        "\n",
        "  # weight updation\n",
        "  w1 = w1 - lr*dedw1\n",
        "  w2 = w2 - lr*dedw2\n",
        "  print(f\"Iteration: {epoch} y_actual: {y_actual} & y_pred: {y_pred}\")"
      ],
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        "id": "HBt2SFzVp6FU",
        "outputId": "2038c572-4325-41aa-c91e-b554ecd93291"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 1 y_actual: 17 & y_pred: 202\n",
            "Iteration: 2 y_actual: 17 & y_pred: 153.89999999999998\n",
            "Iteration: 3 y_actual: 17 & y_pred: 118.306\n",
            "Iteration: 4 y_actual: 17 & y_pred: 91.96643999999999\n",
            "Iteration: 5 y_actual: 17 & y_pred: 72.47516560000001\n",
            "Iteration: 6 y_actual: 17 & y_pred: 58.05162254400001\n",
            "Iteration: 7 y_actual: 17 & y_pred: 47.37820068256\n",
            "Iteration: 8 y_actual: 17 & y_pred: 39.4798685050944\n",
            "Iteration: 9 y_actual: 17 & y_pred: 33.63510269376985\n",
            "Iteration: 10 y_actual: 17 & y_pred: 29.30997599338969\n",
            "Iteration: 11 y_actual: 17 & y_pred: 26.10938223510837\n",
            "Iteration: 12 y_actual: 17 & y_pred: 23.740942853980194\n",
            "Iteration: 13 y_actual: 17 & y_pred: 21.98829771194534\n",
            "Iteration: 14 y_actual: 17 & y_pred: 20.69134030683955\n",
            "Iteration: 15 y_actual: 17 & y_pred: 19.73159182706127\n",
            "Iteration: 16 y_actual: 17 & y_pred: 19.02137795202534\n",
            "Iteration: 17 y_actual: 17 & y_pred: 18.49581968449875\n",
            "Iteration: 18 y_actual: 17 & y_pred: 18.106906566529076\n",
            "Iteration: 19 y_actual: 17 & y_pred: 17.819110859231518\n",
            "Iteration: 20 y_actual: 17 & y_pred: 17.606142035831326\n",
            "Iteration: 21 y_actual: 17 & y_pred: 17.448545106515176\n",
            "Iteration: 22 y_actual: 17 & y_pred: 17.33192337882123\n",
            "Iteration: 23 y_actual: 17 & y_pred: 17.24562330032771\n",
            "Iteration: 24 y_actual: 17 & y_pred: 17.18176124224251\n",
            "Iteration: 25 y_actual: 17 & y_pred: 17.13450331925946\n",
            "Iteration: 26 y_actual: 17 & y_pred: 17.099532456252\n",
            "Iteration: 27 y_actual: 17 & y_pred: 17.073654017626485\n",
            "Iteration: 28 y_actual: 17 & y_pred: 17.054503973043598\n",
            "Iteration: 29 y_actual: 17 & y_pred: 17.040332940052263\n",
            "Iteration: 30 y_actual: 17 & y_pred: 17.029846375638677\n",
            "Iteration: 31 y_actual: 17 & y_pred: 17.02208631797262\n",
            "Iteration: 32 y_actual: 17 & y_pred: 17.01634387529974\n",
            "Iteration: 33 y_actual: 17 & y_pred: 17.012094467721806\n",
            "Iteration: 34 y_actual: 17 & y_pred: 17.008949906114136\n",
            "Iteration: 35 y_actual: 17 & y_pred: 17.006622930524458\n",
            "Iteration: 36 y_actual: 17 & y_pred: 17.004900968588103\n",
            "Iteration: 37 y_actual: 17 & y_pred: 17.003626716755193\n",
            "Iteration: 38 y_actual: 17 & y_pred: 17.002683770398846\n",
            "Iteration: 39 y_actual: 17 & y_pred: 17.001985990095147\n",
            "Iteration: 40 y_actual: 17 & y_pred: 17.001469632670407\n",
            "Iteration: 41 y_actual: 17 & y_pred: 17.001087528176107\n",
            "Iteration: 42 y_actual: 17 & y_pred: 17.00080477085032\n",
            "Iteration: 43 y_actual: 17 & y_pred: 17.000595530429234\n",
            "Iteration: 44 y_actual: 17 & y_pred: 17.000440692517632\n",
            "Iteration: 45 y_actual: 17 & y_pred: 17.00032611246305\n",
            "Iteration: 46 y_actual: 17 & y_pred: 17.00024132322266\n",
            "Iteration: 47 y_actual: 17 & y_pred: 17.00017857918477\n",
            "Iteration: 48 y_actual: 17 & y_pred: 17.000132148596727\n",
            "Iteration: 49 y_actual: 17 & y_pred: 17.00009778996158\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(20, 5))\n",
        "plt.plot(error_list)\n",
        "plt.title(\"Error Graph\")\n",
        "plt.xlabel(\"epochs\")\n",
        "plt.ylabel('error')\n",
        "plt.xticks(np.arange(0, 50))\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 348
        },
        "id": "uQcKNqtup8iY",
        "outputId": "871e4bea-7577-4f41-b632-6351179030e1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x500 with 1 Axes>"
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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "error"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r4ltOqvGp_s9",
        "outputId": "8d084fb0-dffd-43b7-97f8-50329be19095"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9.56287658563274e-09"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.subplot(1,2,1)\n",
        "plt.plot(w1_list)\n",
        "\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(w2_list)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "k_ciIb3WqCMd",
        "outputId": "59f069fb-63c0-45df-bd97-e0eab38d37c0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7d3a2cce8e50>]"
            ]
          },
          "metadata": {},
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "bzNzDwRmqD5r"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}