back_propagation_2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "back propagation 2.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Shibu Mohapatra\n",
        "\n",
        "Artificial Intelligence"
      ],
      "metadata": {
        "id": "IDGVUX9hlWk6"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IMH2FkL6EH0S"
      },
      "source": [
        "**Program for back propagation algorithm, then user will provide the inputsps according to requirement & display the output.**"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from random import random\n",
        "import numpy as np\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "filename = \"/content/trainingdata.csv\"\n",
        "raw_data = open(filename, 'rt')\n",
        "data = np.genfromtxt(raw_data, delimiter=' ', dtype= 'float', names = True)\n",
        "col_len = np.size(data,0)"
      ],
      "metadata": {
        "id": "9kSqEU7J6sty"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def activation(weighted_sum):\n",
        "    return(1/(1 + math.exp(-weighted_sum)))\n",
        "\n",
        "def initialize(no_hidden):\n",
        "    ct = 0\n",
        "    x = 2\n",
        "    n = no_hidden\n",
        "    print(\"-----------------------------------------------------------------------------\")\n",
        "    print(\"Initializing neural network with \", n, \"hidden neurons, 1 input and 1 output.\")\n",
        "    print(\"-----------------------------------------------------------------------------\")\n",
        "\n",
        "    #Assigning Random weights for Input-Hidden layers\n",
        "    weights_input = [[0 for i in range(x)] for j in range(n)]\n",
        "    for i in range(n):\n",
        "        for j in range(2):\n",
        "            weights_input[i][j] = random()\n",
        "\n",
        "    #Assigning Random weights for Hidden-Output layers\n",
        "    weights_output = [0 for i in range(n + 1)]\n",
        "    for j in range(n + 1):\n",
        "        weights_output[j] = random()\n",
        "\n",
        "    print(\"Weights have been assigned random values as follows: \", weights_input, weights_output)\n",
        "    print(\"-----------------------------------------------------------------------------\")\n",
        "\n",
        "    sum_input = 0\n",
        "    sum_output = 0\n",
        "    out_neuron_in_hid = [[0 for i in range(col_len)] for j in range(n)]\n",
        "    out_neuron_hid_out = [0 for p in range(col_len)]\n",
        "    delta_out_hidden = [0 for p in range(col_len)]\n",
        "    delta_hidden_in = [[0 for i in range(col_len)] for j in range(n)]\n",
        "    Error_sum = 2\n",
        "    J = [0 for p in range(col_len)]\n",
        "    Loss = []\n",
        "    step = 0.1\n",
        "\n",
        "    # Algorithm starts here -> While -> for L -> for loops etc.\n",
        "    while(Error_sum > 0.1):\n",
        "        ct += 1\n",
        "        Error_sum = 0\n",
        "        for d_loop in range(col_len):\n",
        "\n",
        "            # Calculating output for input-hidden layer\n",
        "            for i in range(n):\n",
        "                for j in range(2):\n",
        "                    if (j == 0):\n",
        "                        sum_input = sum_input + weights_input[i][j] * 1\n",
        "                    else:\n",
        "                        sum_input = sum_input + weights_input[i][j] * data[d_loop][0]\n",
        "                out_neuron_in_hid[i][d_loop] = activation(sum_input)\n",
        "                sum_input = 0\n",
        "\n",
        "            #Calculating output for hidden-output layer\n",
        "            for j in range(n + 1):\n",
        "                if (j == 0):\n",
        "                    sum_output = sum_output + weights_output[j] * 1\n",
        "                else:\n",
        "                    sum_output = sum_output + weights_output[j] * out_neuron_in_hid[j - 1][d_loop]\n",
        "            out_neuron_hid_out[d_loop] = activation(sum_output)\n",
        "            sum_output = 0\n",
        "\n",
        "            #Delta Output-Hidden weights\n",
        "            delta_out_hidden[d_loop] = (data[d_loop][1] - out_neuron_hid_out[d_loop]) * (out_neuron_hid_out[d_loop] * (1 - out_neuron_hid_out[d_loop]))\n",
        "\n",
        "            #Delta Hidden-Input weights\n",
        "            for i in range(n):\n",
        "                delta_hidden_in[i][d_loop] = (delta_out_hidden[d_loop]*weights_output[i+1])*(out_neuron_in_hid[i][d_loop]*(1-out_neuron_in_hid[i][d_loop]))\n",
        "      \n",
        "            #Weight Updating\n",
        "            for j in range(n):\n",
        "                if(j==0):\n",
        "                    weights_output[j] = weights_output[j] + step*delta_out_hidden[d_loop]\n",
        "                else:\n",
        "                    weights_output[j] = weights_output[j] + step * delta_out_hidden[d_loop]*out_neuron_in_hid[j][d_loop]\n",
        "            #print(\"Weight output\", weights_output)\n",
        "\n",
        "            for j in range(n):\n",
        "                for k in range(2):\n",
        "                    if(k==0):\n",
        "                        weights_input[j][k] = weights_input[j][k] + step*delta_hidden_in[j][d_loop]*1\n",
        "                    else:\n",
        "                        weights_input[j][k] = weights_input[j][k] + step*delta_hidden_in[j][d_loop]*data[d_loop][0]\n",
        "            #print(\"Weight input\", weights_input)\n",
        "\n",
        "            #Loss Function\n",
        "            J[d_loop] = (data[d_loop][1] - out_neuron_hid_out[d_loop]) ** 2\n",
        "            Error_sum += J[d_loop]\n",
        "        Loss.append(Error_sum)\n",
        "        print(\"-----------------------------------------------------------------------------\")\n",
        "        print(\"Training error for epoch \", ct, \": \", Error_sum)\n",
        "\n",
        "    #Closing training data file\n",
        "    raw_data.close()\n",
        "    #print(\"Loss: \", Loss)\n",
        "\n",
        "    #Calling predict function for testing data\n",
        "    predict(n, weights_input, weights_output)\n",
        "\n",
        "    #Plotting Training error over epochs\n",
        "    plt.plot(Loss)\n",
        "    plt.ylabel('Training Error/Loss')\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "Ongcc5QQ8G87"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def predict(no_of_hidden, weights_input, weights_output):\n",
        "    n = no_of_hidden\n",
        "\n",
        "    #Opening testing data\n",
        "    filename = \"/content/testingdata.csv\"\n",
        "    raw_data2 = open(filename, 'rt')\n",
        "    data2 = np.genfromtxt(raw_data2, delimiter=' ', dtype='float')\n",
        "\n",
        "    col_len = np.size(data2, 0)\n",
        "    J2 = [0 for p in range(col_len)]\n",
        "    # Loss_train = []\n",
        "    # Error_sum2 = 0\n",
        "    sum_input = 0\n",
        "    sum_output = 0\n",
        "    out_neuron_in_hid = [[0 for i in range(col_len)] for j in range(n)]\n",
        "    out_neuron_hid_out = [0 for p in range(col_len)]\n",
        "    ct = 0\n",
        "    for d_loop in range(col_len):\n",
        "        ct += 1\n",
        "        for i in range(n):\n",
        "            for j in range(2):\n",
        "                if (j == 0):\n",
        "                    sum_input = sum_input + weights_input[i][j] * 1\n",
        "                else:\n",
        "                    sum_input = sum_input + weights_input[i][j] * data2[d_loop][0]\n",
        "            out_neuron_in_hid[i][d_loop] = activation(sum_input)\n",
        "            sum_input = 0\n",
        "\n",
        "        for j in range(n + 1):\n",
        "            if (j == 0):\n",
        "                sum_output = sum_output + weights_output[j] * 1\n",
        "            else:\n",
        "                sum_output = sum_output + weights_output[j] * out_neuron_in_hid[j - 1][d_loop]\n",
        "        out_neuron_hid_out[d_loop] = activation(sum_output)\n",
        "        sum_output = 0\n",
        "\n",
        "        J2[d_loop] = (data[d_loop][1] - out_neuron_hid_out[d_loop]) ** 2\n",
        "\n",
        "    Avg_error = 0\n",
        "    Sum_error = 0\n",
        "    for i in range(col_len):\n",
        "        Sum_error += J2[i]\n",
        "    Avg_error = (Sum_error/(col_len))\n",
        "\n",
        "    print(\"-----------------------------------------------------------------------------\")\n",
        "    print(\"Comparison between actual and predicted outputs:\")\n",
        "    print(\"-----------------------------------------------------------------------------\")\n",
        "    \n",
        "    for i in range(col_len):\n",
        "        print(data2[i][1], out_neuron_hid_out[i])\n",
        "    print(\"-----------------------------------------------------------------------------\")\n",
        "    print(\"Testing Loss (Sum): \", Sum_error)\n",
        "    print(\"-----------------------------------------------------------------------------\")\n",
        "\n",
        "    #Plotting Prediction and Actual outputs\n",
        "    y = [0 for j in range(col_len)]\n",
        "    for i in range(col_len):\n",
        "        y[i] = data[i][1]\n",
        "    plt.plot(y)\n",
        "    plt.plot(out_neuron_hid_out)\n",
        "    plt.ylabel('Y vs. Predicted Y')\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "btSiZvad8wkk"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def main():\n",
        "    no_of_hidden = input(\"Enter the number of hidden neurons: \")\n",
        "    initialize(int(no_of_hidden))\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "KYjXE_gi9AK9",
        "outputId": "fe3940fb-d771-4ea1-fcc3-f4ade59ffc21"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Enter the number of hidden neurons: 2\n",
            "-----------------------------------------------------------------------------\n",
            "Initializing neural network with  2 hidden neurons, 1 input and 1 output.\n",
            "-----------------------------------------------------------------------------\n",
            "Weights have been assigned random values as follows:  [[0.9371658733197922, 0.46180067682721504], [0.3919273929942928, 0.49787581782488877]] [0.24404207124165112, 0.07173535895120131, 0.11776231113987845]\n",
            "-----------------------------------------------------------------------------\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  1 :  9.122407921199208\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  2 :  8.608695924970746\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  3 :  8.06978066524327\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  4 :  7.513103806881015\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  5 :  6.9635490620562575\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  6 :  6.439534809918472\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  7 :  5.950711423265221\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  8 :  5.5007788411093\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  9 :  5.089986216227342\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  10 :  4.716718555247193\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  11 :  4.378436215210306\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  12 :  4.072219767610568\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  13 :  3.795079981604886\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  14 :  3.5441282609156186\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  15 :  3.316664290543148\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  16 :  3.110214882373352\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  17 :  2.9225444837796366\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  18 :  2.7516497099522055\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  19 :  2.595745365622041\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  20 :  2.4532464419252955\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  21 :  2.3227487482417883\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  22 :  2.203009715432598\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  23 :  2.092930215514056\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  24 :  1.9915378194852922\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  25 :  1.8979716591383458\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  26 :  1.8114689077087063\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  27 :  1.7313528089335894\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  28 :  1.6570221396586884\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  29 :  1.587941971801179\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  30 :  1.523635595203858\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  31 :  1.463677467335811\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  32 :  1.4076870648984416\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  33 :  1.3553235236890186\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  34 :  1.3062809650407876\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  35 :  1.2602844189083304\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  36 :  1.2170862647069152\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  37 :  1.1764631211018608\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  38 :  1.138213124989349\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  39 :  1.102153547915457\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  40 :  1.068118705199458\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  41 :  1.0359581191406977\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  42 :  1.0055349029869427\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  43 :  0.9767243369186559\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  44 :  0.949412611247148\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  45 :  0.9234957154169862\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  46 :  0.8988784543187219\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  47 :  0.8754735759225799\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  48 :  0.8532009963950503\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  49 :  0.8319871107086301\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  50 :  0.8117641783436185\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  51 :  0.7924697750473405\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  52 :  0.7740463027925117\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  53 :  0.7564405510900394\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  54 :  0.739603303686014\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  55 :  0.7234889854276987\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  56 :  0.708055344736352\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  57 :  0.6932631676900396\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  58 :  0.6790760202097073\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  59 :  0.6654600152673085\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  60 :  0.6523836024046745\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  61 :  0.6398173771738326\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  62 :  0.6277339083902036\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  63 :  0.6161075813352089\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  64 :  0.604914455259061\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  65 :  0.5941321337220918\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  66 :  0.5837396464774535\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  67 :  0.573717341742365\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  68 :  0.5640467878320415\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  69 :  0.554710683242176\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  70 :  0.5456927743643514\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  71 :  0.5369777801057185\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  72 :  0.528551322761146\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  73 :  0.5203998645540686\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  74 :  0.5125106493225572\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  75 :  0.5048716488806257\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  76 :  0.4974715136323275\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  77 :  0.4902995270584754\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  78 :  0.4833455637334729\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  79 :  0.4766000505633432\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  80 :  0.47005393096599846\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  81 :  0.46369863174162934\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  82 :  0.4575260324050307\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  83 :  0.45152843677320925\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  84 :  0.44569854662085706\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  85 :  0.4400294372335894\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  86 :  0.434514534704395\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  87 :  0.42914759483273335\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  88 :  0.4239226834983299\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  89 :  0.4188341583930602\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  90 :  0.4138766520046004\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  91 :  0.409045055754753\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  92 :  0.4043345052037678\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  93 :  0.39974036623954273\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  94 :  0.39525822217746487\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  95 :  0.39088386170288575\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  96 :  0.3866132675938855\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  97 :  0.38244260616711157\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  98 :  0.3783682173941603\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  99 :  0.37438660564021303\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  100 :  0.370494430980518\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  101 :  0.36668850105384587\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  102 :  0.3629657634152577\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  103 :  0.35932329835347787\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  104 :  0.35575831214084713\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  105 :  0.35226813068628343\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  106 :  0.3488501935639611\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  107 :  0.345502048392433\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  108 :  0.34222134554083916\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  109 :  0.3390058331405947\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  110 :  0.33585335238249536\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  111 :  0.3327618330806886\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  112 :  0.32972928948626934\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  113 :  0.32675381633451483\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  114 :  0.32383358511089994\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  115 :  0.3209668405220974\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  116 :  0.3181518971591101\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  117 :  0.3153871363406094\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  118 :  0.31267100312532803\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  119 :  0.3100020034831743\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  120 :  0.30737870161538966\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  121 :  0.30479971741472794\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  122 :  0.30226372405727775\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  123 :  0.29976944571803854\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  124 :  0.2973156554029324\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  125 :  0.2949011728903883\n",
            "-----------------------------------------------------------------------------\n",
            "Training error for epoch  126 :  0.2925248627760732\n",
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            "Training error for epoch  341 :  0.10017076084229298\n",
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            "Training error for epoch  342 :  0.09987049358456013\n",
            "-----------------------------------------------------------------------------\n",
            "Comparison between actual and predicted outputs:\n",
            "-----------------------------------------------------------------------------\n",
            "0.0184590475 0.06426366013841031\n",
            "0.00832518621 0.06428779711947073\n",
            "0.0073701677 0.06432202822526473\n",
            "0.00661010715 0.06437058747488977\n",
            "0.00344520607 0.06443949266952916\n",
            "0.00783351459 0.06453730301248559\n",
            "0.0105461859 0.06467620406039275\n",
            "0.0193736518 0.06487356677973834\n",
            "0.0109788559 0.06515419849431471\n",
            "0.0159958988 0.06555361376560362\n",
            "0.0175447195 0.06612282865483343\n",
            "0.0083489074 0.06693546843700394\n",
            "0.0258112869 0.06809846014940807\n",
            "0.0194590711 0.06976841021163123\n",
            "0.0312062555 0.07217722295647874\n",
            "0.0257936882 0.07567309608488072\n",
            "0.0454947476 0.0807875620042462\n",
            "0.0589743223 0.08834686085241716\n",
            "0.079759559 0.09965715252842439\n",
            "0.102841541 0.11680321105960643\n",
            "0.151681186 0.1430825358480194\n",
            "0.19942967 0.18345633471007208\n",
            "0.27388532 0.2444139497142721\n",
            "0.354939003 0.3317098834361683\n",
            "0.460865 0.44450231997417483\n",
            "0.55595422 0.569496652602192\n",
            "0.66319559 0.6851912269456578\n",
            "0.748931815 0.7759187363566337\n",
            "0.808931624 0.8390554195092095\n",
            "0.861212065 0.8801909426750525\n",
            "0.901987608 0.9063584666596335\n",
            "0.941374286 0.9230260418495849\n",
            "0.961602335 0.9337823398602756\n",
            "0.978881823 0.9408397851004732\n",
            "0.990488817 0.945544251466958\n",
            "0.993331186 0.9487226117264729\n",
            "1.00927789 0.9508929324605381\n",
            "1.01263728 0.9523870212385358\n",
            "1.00871382 0.9534218237831077\n",
            "1.01365678 0.9541417101704024\n",
            "1.01476942 0.9546441298945264\n",
            "1.00797002 0.9549955901108724\n",
            "1.01855198 0.9552418592383797\n",
            "1.00890106 0.9554146280379204\n",
            "1.01896529 0.9555359383521801\n",
            "1.01403998 0.9556211707787631\n",
            "1.01924727 0.9556810828771113\n",
            "1.01529249 0.9557232113898951\n",
            "1.00950134 0.9557528429358144\n",
            "1.00211468 0.9557736890246802\n",
            "-----------------------------------------------------------------------------\n",
            "Testing Loss (Sum):  0.1152863415575075\n",
            "-----------------------------------------------------------------------------\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}