NN.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is backpropagation?\\\n",
    "Ans: backpropagation is a method of learning that uses a gradient descent algorithm to find the optimal weights of a neural network.\n",
    "\n",
    "What is forward propagation?\\\n",
    "Ans: forward propagation is the process of passing an input through a neural network to get the output.\n",
    "\n",
    "What is gradient descent?\\\n",
    "Ans: gradient descent is an algorithm that uses a gradient to find the optimal weights of a neural network.\n",
    "\n",
    "What is activation function?\\\n",
    "Ans: activation function is a function that takes an input and returns an output.\n",
    "\n",
    "Why we need activation function?\\\n",
    "Ans: activation function is used to make sure that the output is between 0 and 1.\n",
    "\n",
    "Why we will sigmoid function?\\\n",
    "ans: The main reason why we use sigmoid function is because it exists between (0 to 1). Therefore, it is especially used for models where we have to predict the probability as an output.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Neural Network from scratch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load dataset 0 mnist\n",
    "from matplotlib import image\n",
    "image_path = 'trainingSet/0'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4132\n"
     ]
    }
   ],
   "source": [
    "#Show how many images are in the folder\n",
    "print(len(os.listdir(image_path)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1f9d98a7fd0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#show one image\n",
    "image_file = os.path.join(image_path, os.listdir(image_path)[0])\n",
    "img = image.imread(image_file)\n",
    "plt.imshow(img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Image binarization\n",
    "def binarize(img):\n",
    "    img = img.astype(np.float32)\n",
    "    img = np.where(img < 0.5, 0, 1)\n",
    "    return img\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the matrix\n",
    "plt.imshow(img.reshape(28,28), cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 0 means black\n",
    "#### 1 means white\n",
    "#### Pixel values are between 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1\n",
      "  1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0\n",
      "  1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0\n",
      "  0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0\n",
      "  0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1\n",
      "  1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      "  1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0\n",
      "  0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1\n",
      "  1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1\n",
      "  1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0\n",
      "  0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0\n",
      "  1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0\n",
      "  1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1\n",
      "  1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0\n",
      "  0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1\n",
      "  1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1\n",
      "  1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1\n",
      "  0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0\n",
      "  0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      "  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      "  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      "  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "#show the binary matrix using 0 and 1\n",
    "print(img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0]\n",
      " [0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0]\n",
      " [0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0]\n",
      " [0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0]\n",
      " [1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0]\n",
      " [1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0]\n",
      " [0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0]\n",
      " [1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0]\n",
      " [0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0]\n",
      " [0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0]\n",
      " [1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0]\n",
      " [0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0]\n",
      " [1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0]\n",
      " [0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0]\n",
      " [0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0]\n",
      " [1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0]\n",
      " [0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0]\n",
      " [0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0]\n",
      " [0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0]\n",
      " [1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0]\n",
      " [1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0]\n",
      " [0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0]\n",
      " [1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "# Our matrix is a vector of 28x28x1 so we need to reshape it to 28x28\n",
    "img = img.reshape(28,28)\n",
    "print(img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define sigmoid function\n",
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define derivative of sigmoid function\n",
    "def sigmoid_derivative(x):\n",
    "    return x*(1-x)\n",
    "# we need derivatives of sigmoid function to calculate the error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.22035917e-01 9.87040435e-01 6.76155903e-02 7.34244683e-01\n",
      "  2.37233003e-01 3.56973817e-02 9.40687749e-01 7.42954848e-01\n",
      "  9.09994936e-01 1.90658613e-01 3.83571915e-01 8.13778195e-01\n",
      "  8.53232859e-01 3.01865112e-01 7.91210853e-02 1.97338516e-01\n",
      "  1.29090986e-01 2.48578799e-01 9.18695261e-01 5.20227420e-01\n",
      "  2.44588801e-01 5.52337962e-01 3.63105746e-01 7.21029413e-01\n",
      "  8.88520485e-03 7.98328784e-01 8.79469160e-01 4.92507568e-01]\n",
      " [7.20599837e-01 7.10646113e-01 3.30557828e-01 7.45597434e-01\n",
      "  8.37976421e-01 8.86574430e-01 3.78407553e-02 9.62467034e-02\n",
      "  9.54449267e-01 5.18663634e-01 5.79398912e-01 8.98981057e-01\n",
      "  4.88731218e-01 4.23550059e-01 2.86300206e-01 3.15180521e-01\n",
      "  3.70984268e-01 2.16580111e-01 2.11985314e-01 4.34127937e-01\n",
      "  3.64400484e-01 3.58317187e-01 4.07703245e-01 8.63951441e-01\n",
      "  4.41693622e-01 7.65731604e-02 3.27880711e-01 3.31612847e-01]\n",
      " [5.80939586e-01 8.68315219e-01 3.22212172e-01 7.64854180e-01\n",
      "  5.18577583e-01 7.97286241e-01 8.73280853e-02 6.56507204e-01\n",
      "  7.41418396e-01 6.53730028e-01 2.16053236e-01 9.26391959e-01\n",
      "  1.14007932e-01 8.78132105e-01 2.39899811e-01 7.60732334e-02\n",
      "  5.63796984e-01 8.44660737e-02 8.15855596e-01 1.87397614e-01\n",
      "  3.92242952e-01 3.04988484e-01 7.44681321e-01 9.61204470e-01\n",
      "  7.84536921e-01 4.79286450e-01 3.02614116e-02 8.70078704e-01]\n",
      " [2.85715543e-01 5.38361629e-01 6.79203573e-01 6.39090728e-01\n",
      "  2.66849147e-01 6.94223992e-01 2.56454524e-01 8.25536405e-01\n",
      "  2.05816517e-01 9.74966645e-01 3.89347915e-01 8.64226108e-01\n",
      "  8.75633385e-01 9.75748799e-01 2.21377908e-01 3.82660982e-01\n",
      "  9.08184396e-01 5.66135998e-01 3.57194579e-01 2.26097588e-01\n",
      "  9.04898059e-01 4.08441528e-01 2.62090187e-01 8.08292177e-01\n",
      "  6.37896776e-01 5.56568641e-01 2.82308085e-01 1.66969189e-01]\n",
      " [8.20704030e-01 6.93199765e-01 3.35569026e-01 3.08442137e-01\n",
      "  8.51334161e-01 5.56810862e-01 6.53454851e-01 7.37291242e-01\n",
      "  4.51415323e-01 5.52932456e-02 2.13619135e-01 3.63997987e-01\n",
      "  9.88977666e-01 5.76706874e-01 5.83332331e-01 3.90072326e-01\n",
      "  5.72353198e-01 1.10846341e-01 5.12280405e-01 1.58721199e-01\n",
      "  9.53883702e-01 2.11421951e-01 6.72192298e-01 8.40500219e-01\n",
      "  2.50055115e-01 1.10319068e-01 6.39807696e-01 8.78452961e-01]\n",
      " [4.63287464e-01 6.21290022e-02 1.47257998e-01 9.75493051e-01\n",
      "  1.29225205e-01 1.62360675e-02 8.33099428e-01 1.63414177e-01\n",
      "  2.79092634e-01 7.64170781e-01 7.69962556e-01 5.18746125e-02\n",
      "  3.07050866e-01 9.83484157e-01 7.31112029e-01 9.25572466e-01\n",
      "  4.90824743e-01 4.75159962e-02 2.85295968e-01 1.25232709e-02\n",
      "  5.50289215e-01 9.58109288e-01 9.94168507e-01 7.48927603e-01\n",
      "  9.32168165e-01 5.61191313e-02 1.64261308e-01 7.13600579e-01]\n",
      " [2.16404242e-01 1.67309616e-01 9.40404813e-01 1.01121181e-01\n",
      "  3.71996968e-01 5.89670725e-01 5.57680789e-01 8.51137701e-02\n",
      "  3.75810515e-01 7.71989801e-01 5.30140053e-01 6.07335333e-01\n",
      "  6.06071316e-01 1.61007208e-01 2.33072774e-01 7.91509152e-01\n",
      "  4.27633178e-01 6.15758491e-01 6.03707756e-01 1.00024609e-03\n",
      "  7.26806083e-02 8.15912695e-01 7.52662155e-01 4.79978473e-01\n",
      "  6.67881068e-01 6.83869230e-01 4.69550970e-01 8.67330145e-01]\n",
      " [9.84030644e-02 1.69090633e-01 2.06515318e-01 7.47765567e-01\n",
      "  6.72789499e-01 1.60424369e-01 4.84791763e-01 9.97887670e-01\n",
      "  3.34891940e-01 6.76227307e-01 7.58843046e-01 4.75450118e-01\n",
      "  7.80730440e-01 5.65936170e-01 2.35348657e-01 8.97769542e-01\n",
      "  6.02295780e-01 4.82991884e-01 6.91846410e-01 5.09116043e-01\n",
      "  8.99553434e-01 6.83648651e-01 2.52088113e-01 8.79137055e-01\n",
      "  2.39474778e-01 5.46497542e-01 7.25113356e-01 3.26886485e-01]\n",
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      "  7.88194358e-01 4.29779021e-01 1.84734047e-01 9.89607034e-01\n",
      "  2.85291818e-01 4.78424695e-01 2.83051058e-02 8.89363614e-02\n",
      "  4.76849857e-01 5.27365662e-01 3.57419958e-01 6.48272272e-01\n",
      "  5.83071562e-01 8.48638271e-01 3.67799677e-01 9.40077828e-03\n",
      "  1.62203394e-01 8.10033023e-03 7.43829135e-01 3.58104835e-01\n",
      "  6.58839569e-01 5.59182855e-01 6.53795959e-01 1.77922916e-01]\n",
      " [1.44146330e-01 5.95402476e-01 9.25224984e-01 9.47499764e-01\n",
      "  7.03461114e-01 8.54675120e-01 5.68654380e-01 3.34250945e-02\n",
      "  7.97577912e-01 2.70480873e-01 6.45725854e-01 9.09565415e-01\n",
      "  2.07515213e-01 3.85350416e-01 7.98760344e-01 4.52321110e-01\n",
      "  4.70834800e-01 3.05716396e-01 1.20019286e-01 2.61003548e-01\n",
      "  2.78470685e-01 7.56325761e-01 3.82494194e-01 8.01656109e-01\n",
      "  4.25413081e-01 6.78280433e-01 6.86172230e-01 9.02718387e-01]\n",
      " [1.10223427e-01 4.56592179e-01 5.59657910e-01 3.61954798e-01\n",
      "  7.12437142e-01 3.11443521e-01 4.69793166e-01 6.22220958e-01\n",
      "  3.06644133e-01 5.09390948e-01 1.66325922e-01 7.05238100e-01\n",
      "  3.17841804e-01 7.63054841e-02 1.54867844e-01 7.19883805e-01\n",
      "  8.24593271e-01 1.11749600e-01 2.73850765e-02 8.69665296e-01\n",
      "  1.81695439e-01 2.98957063e-01 4.79691711e-02 9.43301915e-01\n",
      "  7.21459747e-01 4.65664733e-01 8.50831326e-01 2.07586710e-01]\n",
      " [2.24010645e-01 6.15231650e-01 4.56024798e-01 1.25384478e-01\n",
      "  7.13297829e-01 8.83197755e-01 1.45680609e-01 7.24980671e-01\n",
      "  7.93812506e-01 9.95808964e-01 3.70579730e-01 9.15287768e-01\n",
      "  7.59545442e-01 5.43092939e-01 5.41593093e-01 2.20828692e-01\n",
      "  8.37009395e-01 7.60691967e-01 7.12835737e-01 4.02025046e-01\n",
      "  3.99443766e-01 2.79712680e-01 9.19295435e-01 9.53892174e-01\n",
      "  4.95430619e-01 1.47805646e-01 5.94169259e-01 8.98777040e-01]\n",
      " [7.52543109e-01 9.38637607e-01 6.15232483e-01 6.14192824e-01\n",
      "  1.86016772e-01 8.20509427e-01 3.98295303e-01 4.82320378e-01\n",
      "  7.61707497e-01 5.18659568e-01 8.44006818e-01 7.70980065e-01\n",
      "  9.26710346e-01 7.82850003e-01 2.86485701e-01 2.94930629e-01\n",
      "  9.20674568e-01 8.26785548e-01 3.11022518e-01 3.47033365e-01\n",
      "  2.28401032e-01 8.17612515e-03 7.51901396e-01 9.30349508e-01\n",
      "  6.74399019e-01 7.66378778e-01 8.26415208e-01 1.88236576e-01]\n",
      " [2.26775951e-01 6.10286347e-01 2.23631236e-01 4.84481445e-01\n",
      "  9.16766514e-01 7.81151044e-01 1.82059269e-01 2.28993318e-01\n",
      "  4.51559907e-01 1.51918770e-01 4.36283973e-01 4.66195029e-01\n",
      "  5.35600053e-01 4.66573332e-01 6.28602085e-01 9.78748399e-01\n",
      "  7.63528138e-01 8.91335094e-01 8.78516000e-01 8.92549708e-01\n",
      "  4.62597127e-01 7.13393570e-01 3.32801758e-02 1.28287790e-01\n",
      "  9.53152361e-01 9.68243124e-02 9.16098114e-01 9.51548827e-01]\n",
      " [8.78839867e-01 8.61441182e-02 9.31467531e-01 5.06521093e-01\n",
      "  6.77403555e-01 5.57063243e-01 8.54522880e-03 3.35660313e-01\n",
      "  4.49149119e-01 5.24237100e-01 1.38514550e-01 1.40883819e-01\n",
      "  4.52597889e-01 1.50941660e-01 1.79405957e-01 1.66413333e-01\n",
      "  7.06279734e-01 8.52700302e-01 7.10757340e-01 3.76993584e-03\n",
      "  8.45876980e-01 6.90818313e-01 1.21838778e-01 5.63421952e-01\n",
      "  9.48023298e-01 3.10206811e-01 3.03783026e-02 9.51396706e-01]\n",
      " [2.95550514e-01 3.81357405e-01 1.49790639e-01 2.98881001e-01\n",
      "  2.62763833e-01 8.80630987e-01 8.87794775e-01 7.94978229e-01\n",
      "  1.38232742e-02 7.34777489e-01 7.14435268e-01 9.48795001e-01\n",
      "  1.91392459e-01 6.00340520e-02 5.98110362e-01 2.73586645e-01\n",
      "  9.52190268e-01 1.51120820e-01 9.79099079e-01 8.36144171e-01\n",
      "  6.77789084e-01 7.34575119e-01 9.45381226e-01 3.46811881e-01\n",
      "  9.65335074e-01 5.11654930e-01 5.17617478e-01 8.61146289e-01]\n",
      " [2.66923552e-01 8.34737286e-01 5.74102776e-01 4.64198912e-02\n",
      "  5.58750308e-01 3.05668151e-01 8.94270536e-01 8.17944994e-01\n",
      "  7.54977294e-01 2.57270271e-01 6.89994633e-01 6.93331372e-01\n",
      "  4.75894085e-02 1.45054029e-01 1.64596276e-01 9.36474168e-04\n",
      "  9.65698749e-01 1.97541163e-01 7.54933642e-01 4.97071605e-01\n",
      "  4.34929850e-01 1.78723876e-01 6.24490191e-01 3.24030204e-01\n",
      "  2.70296966e-01 4.94415296e-01 2.33032382e-01 1.47321499e-01]\n",
      " [2.67481265e-01 7.81699778e-02 8.90009193e-01 4.47079104e-01\n",
      "  9.77326423e-01 2.15295590e-01 1.80783262e-01 3.91519611e-01\n",
      "  9.26257049e-01 6.96187116e-01 6.36917151e-01 5.37430270e-01\n",
      "  5.91484824e-01 8.00042066e-01 8.45575352e-01 5.61688254e-01\n",
      "  6.01012710e-01 5.86970886e-01 4.74884050e-01 2.97305338e-01\n",
      "  1.42454570e-01 3.51908842e-01 3.87459075e-01 6.50149609e-01\n",
      "  8.28058280e-01 2.57212369e-01 6.77028420e-01 5.59967887e-01]\n",
      " [6.50352148e-01 5.25534415e-01 7.23913746e-01 9.40441354e-01\n",
      "  9.13475328e-01 9.78273839e-01 9.73804530e-01 5.97618111e-01\n",
      "  5.88859280e-01 1.75057341e-01 3.31588186e-01 3.82601775e-01\n",
      "  5.53410226e-02 4.62594369e-01 8.08335882e-01 5.19813372e-01\n",
      "  5.95132849e-02 2.24946050e-01 9.77212946e-02 1.92166171e-01\n",
      "  9.36577403e-01 3.13911639e-01 3.05194030e-01 3.45878749e-02\n",
      "  1.92837575e-01 2.76440427e-01 2.19971247e-01 7.99597391e-01]\n",
      " [1.44855075e-01 7.01525672e-01 2.42158961e-01 6.48070434e-01\n",
      "  3.41876472e-02 1.94723418e-01 2.83361282e-01 7.64343610e-01\n",
      "  5.00197007e-01 3.22452952e-01 1.97098192e-01 8.26466495e-01\n",
      "  2.22790692e-01 4.19298993e-02 1.57848597e-01 8.80629616e-01\n",
      "  1.72719556e-01 7.35398943e-01 9.17731935e-01 3.24431284e-01\n",
      "  1.25293421e-01 1.12178176e-01 9.94258742e-01 8.97229132e-01\n",
      "  9.19837261e-01 2.46836692e-02 4.04016302e-01 2.58603935e-01]\n",
      " [3.00513583e-01 9.38322438e-01 6.87184173e-01 8.03977846e-01\n",
      "  3.51689581e-01 6.12237636e-01 8.49868348e-01 4.31123678e-01\n",
      "  1.39775341e-03 5.85049715e-01 5.04531039e-01 2.27584987e-01\n",
      "  9.52275680e-01 2.57004209e-01 3.08900068e-01 7.06566778e-01\n",
      "  8.21470485e-01 3.70839383e-02 8.40385949e-01 3.36196071e-01\n",
      "  5.50631908e-01 5.09838847e-01 7.31782896e-01 7.66529311e-01\n",
      "  7.45615826e-01 6.95069045e-01 7.57656372e-01 5.97961247e-01]\n",
      " [2.04175026e-01 3.72250063e-01 8.96654600e-01 9.94744489e-01\n",
      "  3.98566114e-01 9.19012257e-01 4.92721640e-01 2.94805292e-01\n",
      "  2.93719551e-01 3.96214360e-01 6.46102744e-01 5.46260855e-01\n",
      "  3.72209991e-01 2.61612648e-01 8.46472305e-01 1.50003209e-02\n",
      "  4.58235161e-02 8.30624245e-01 7.93292560e-01 5.23318155e-01\n",
      "  3.23135704e-01 1.90535681e-01 5.92297727e-02 1.58861070e-02\n",
      "  3.89474973e-02 4.89691953e-01 4.05410240e-01 5.27773281e-01]\n",
      " [4.55916249e-01 1.36160433e-01 1.82277527e-02 8.27298509e-01\n",
      "  7.68511372e-01 2.28844798e-01 3.08373281e-01 1.90109726e-01\n",
      "  7.16607390e-01 7.28738948e-01 1.65707780e-01 3.29755885e-01\n",
      "  4.47560453e-01 5.54030813e-01 7.77692642e-02 3.94271492e-02\n",
      "  5.04390278e-01 1.04586076e-02 7.14509912e-01 2.50635116e-01\n",
      "  6.98111088e-02 4.32720379e-01 9.22664720e-01 3.70057452e-01\n",
      "  5.95566356e-01 2.09826088e-01 3.02760250e-01 2.42184951e-01]\n",
      " [6.23062470e-01 2.50513647e-02 6.87258242e-02 2.29656150e-01\n",
      "  8.27690372e-01 3.12565987e-01 8.93150228e-01 4.46085893e-01\n",
      "  6.05860830e-01 2.96789204e-01 5.91375838e-01 7.52973745e-01\n",
      "  5.85281961e-01 1.35375065e-01 2.02814284e-01 1.26552045e-01\n",
      "  6.41721396e-01 8.11996595e-01 8.88944571e-01 1.69438389e-01\n",
      "  6.34622310e-01 4.44782410e-02 6.24365571e-01 1.55712662e-01\n",
      "  3.46573096e-01 8.09725220e-01 6.30058617e-01 4.84352900e-01]\n",
      " [8.27994435e-01 1.04148376e-01 1.59947506e-01 4.76871383e-01\n",
      "  2.08750737e-01 1.25467594e-01 9.90257197e-01 4.15750048e-03\n",
      "  5.04205448e-01 1.33949432e-01 8.24879231e-01 9.34968895e-03\n",
      "  8.69849009e-01 6.13131126e-01 7.73960365e-01 7.62364171e-02\n",
      "  8.41298625e-01 5.45838920e-01 9.13355242e-01 7.51090533e-02\n",
      "  5.47789750e-01 3.82708364e-01 7.81205493e-01 9.63452816e-01\n",
      "  3.87942117e-01 2.60337866e-01 3.72824573e-01 9.09507788e-01]\n",
      " [9.82667153e-01 6.98809002e-01 6.99778706e-01 3.64954814e-01\n",
      "  1.03597290e-01 6.76946750e-01 9.38461052e-01 6.63886251e-01\n",
      "  3.92533013e-01 2.19235018e-01 6.13630229e-01 2.32369114e-01\n",
      "  7.43591217e-01 7.93739752e-01 5.49072875e-01 3.88526774e-01\n",
      "  4.69634497e-01 2.23801525e-01 5.23295812e-01 4.16998262e-01\n",
      "  1.42046494e-01 6.85655690e-01 8.41100056e-01 6.53071855e-01\n",
      "  5.21622258e-01 8.96277104e-01 4.96500731e-01 1.09726956e-01]\n",
      " [7.40118042e-01 6.94452732e-01 8.64132144e-01 5.53583150e-01\n",
      "  1.62563809e-01 2.15150341e-02 1.45007139e-01 7.89888930e-01\n",
      "  5.46921949e-01 6.68231821e-02 9.47991195e-01 4.43233727e-01\n",
      "  2.64779044e-01 3.24634845e-01 5.87109833e-01 1.03827628e-01\n",
      "  2.06721029e-01 9.95958546e-01 8.96744756e-01 5.47039319e-01\n",
      "  7.58383882e-01 7.05354995e-01 3.45517783e-02 3.02773179e-01\n",
      "  6.29393691e-01 3.45317888e-01 7.43752657e-01 1.36862424e-01]\n",
      " [8.60924059e-01 3.82728549e-01 5.95068997e-01 9.06439975e-01\n",
      "  6.47275201e-01 2.62132492e-02 2.93468697e-01 8.61796926e-01\n",
      "  2.50298022e-01 6.49025643e-01 9.91751037e-02 1.83284309e-01\n",
      "  7.78548725e-01 1.70521542e-01 2.29733540e-02 1.79095047e-02\n",
      "  9.66490674e-01 7.89390703e-02 7.00189067e-01 3.25385467e-01\n",
      "  8.83047359e-01 6.77408726e-01 4.13603715e-01 9.75409262e-01\n",
      "  3.17084005e-01 9.28412786e-01 8.88166497e-01 1.01484727e-01]]\n"
     ]
    }
   ],
   "source": [
    "# making input layer with 28 neurons\n",
    "input_layer = np.random.rand(28,28)\n",
    "print(input_layer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.86108066 0.53514522 0.2794574  0.02769679 0.00847167 0.05338504\n",
      "  0.06408331 0.2999462  0.35563041 0.03493898 0.47366842 0.05366154\n",
      "  0.17966584 0.92357206 0.78868638 0.0520914  0.88059064 0.41647582\n",
      "  0.92222188 0.13319362 0.06766615 0.11335567 0.57607208 0.41871625\n",
      "  0.2483677  0.71664679 0.75341267 0.19962399]\n",
      " [0.51201686 0.57552881 0.60499895 0.55321007 0.26157151 0.39137208\n",
      "  0.612293   0.83372204 0.13526239 0.3792288  0.45651665 0.97420627\n",
      "  0.96226835 0.3676991  0.1569577  0.65285005 0.35916814 0.12347511\n",
      "  0.90006689 0.25830305 0.9676669  0.54420359 0.6069488  0.35031784\n",
      "  0.73818567 0.10660619 0.99334337 0.58245347]\n",
      " [0.02009255 0.35669414 0.76193311 0.37592126 0.56724092 0.89132929\n",
      "  0.39652981 0.99056396 0.45729537 0.14290007 0.06331952 0.26189282\n",
      "  0.68248418 0.1970635  0.05484605 0.41465412 0.49487889 0.08646555\n",
      "  0.68579176 0.36718576 0.68772324 0.8584882  0.91861857 0.57504559\n",
      "  0.33509785 0.05018666 0.21563962 0.3871166 ]\n",
      " [0.26524383 0.24196891 0.53692477 0.30496541 0.08020154 0.25306985\n",
      "  0.77811347 0.73484795 0.06621823 0.9620981  0.30728157 0.96778727\n",
      "  0.31904776 0.11255611 0.49318522 0.25489248 0.59487178 0.04352838\n",
      "  0.92309435 0.74815069 0.45242443 0.16541827 0.17471449 0.83634243\n",
      "  0.42722526 0.83780236 0.00462193 0.08429149]\n",
      " [0.84830983 0.21949821 0.24362133 0.58310631 0.22512704 0.64048248\n",
      "  0.43524692 0.17713061 0.02958663 0.19084835 0.47974655 0.39509881\n",
      "  0.18706383 0.30748555 0.70097982 0.51871323 0.79267603 0.51511482\n",
      "  0.14680703 0.72733917 0.59963427 0.08553698 0.15910302 0.64689065\n",
      "  0.48309828 0.23221812 0.82536225 0.27153929]\n",
      " [0.01678593 0.64986098 0.0510038  0.97126924 0.96650231 0.69007572\n",
      "  0.73583352 0.74623957 0.74161732 0.71927209 0.18487886 0.76605431\n",
      "  0.97572014 0.67739713 0.22736513 0.57025626 0.65582833 0.21486938\n",
      "  0.09799253 0.16809574 0.83195946 0.34741809 0.67140986 0.02186843\n",
      "  0.88623853 0.44420369 0.11484614 0.51950331]\n",
      " [0.79989843 0.36484263 0.73683961 0.92439675 0.72446181 0.85078408\n",
      "  0.11469241 0.36477238 0.57557262 0.30448741 0.63157134 0.75077924\n",
      "  0.81488346 0.40092478 0.18207586 0.96771725 0.60387318 0.30600741\n",
      "  0.69471967 0.2884859  0.73558143 0.77029239 0.48737786 0.63225386\n",
      "  0.92577835 0.98830707 0.11277924 0.20683881]\n",
      " [0.31021619 0.09305426 0.7875636  0.47184572 0.25406205 0.50245179\n",
      "  0.09550227 0.14598961 0.05985937 0.12588794 0.90589497 0.99146896\n",
      "  0.75511169 0.99787319 0.10812939 0.72069119 0.79556879 0.0331272\n",
      "  0.91689917 0.40381318 0.29388421 0.35846937 0.37521248 0.74879214\n",
      "  0.52062236 0.33142159 0.56873266 0.11024853]\n",
      " [0.63513027 0.67729338 0.75773329 0.3851185  0.04947639 0.57994949\n",
      "  0.19097636 0.81659941 0.6982708  0.15486714 0.14867026 0.4021675\n",
      "  0.94942089 0.96363128 0.5160892  0.52640861 0.27057523 0.40385957\n",
      "  0.33003034 0.1773733  0.78013934 0.34875551 0.95655801 0.86089113\n",
      "  0.31228543 0.10959721 0.75110015 0.17691934]\n",
      " [0.56014741 0.47717448 0.46964609 0.50825435 0.21234686 0.04435274\n",
      "  0.54079049 0.61453713 0.78357651 0.23090099 0.13578786 0.68262036\n",
      "  0.76915349 0.1055359  0.79600043 0.74203323 0.51576823 0.67848744\n",
      "  0.3884591  0.2067604  0.74157408 0.24654125 0.7222393  0.45919082\n",
      "  0.35511872 0.34173163 0.99995673 0.82549537]\n",
      " [0.29578307 0.72613363 0.3814134  0.91001132 0.19291252 0.27298236\n",
      "  0.94020948 0.75622471 0.70215802 0.99635785 0.93867965 0.24517164\n",
      "  0.13986404 0.27276395 0.31397979 0.08992249 0.61069411 0.94545453\n",
      "  0.70533157 0.69131178 0.18139109 0.86274369 0.88215397 0.06589915\n",
      "  0.1685909  0.72243883 0.79130347 0.91376811]\n",
      " [0.44395659 0.28133019 0.53485339 0.57417629 0.86201628 0.26796224\n",
      "  0.02363391 0.0259243  0.88169374 0.11765899 0.79791501 0.52162748\n",
      "  0.26754863 0.39222186 0.29758162 0.80979896 0.94121994 0.28781038\n",
      "  0.21157987 0.62073765 0.84973387 0.70550987 0.40884021 0.47316204\n",
      "  0.77680192 0.93646206 0.89221553 0.1984412 ]\n",
      " [0.38973158 0.62077895 0.45653979 0.92339137 0.38329245 0.95526134\n",
      "  0.06487022 0.92162731 0.65952573 0.13974593 0.06297757 0.97399195\n",
      "  0.06692405 0.32391083 0.50737445 0.19741569 0.04518408 0.84987213\n",
      "  0.19190115 0.08416043 0.95296148 0.53109749 0.59233458 0.76765696\n",
      "  0.99106447 0.77379099 0.73233895 0.13170617]\n",
      " [0.80504776 0.89721445 0.93176281 0.65661301 0.41099825 0.63609297\n",
      "  0.08269475 0.52380715 0.49951891 0.45439649 0.58816831 0.40027379\n",
      "  0.83423908 0.76627358 0.37165644 0.49143832 0.41873635 0.75997477\n",
      "  0.70080473 0.23915608 0.12361675 0.55714211 0.13916059 0.18603331\n",
      "  0.61280999 0.10746092 0.59994205 0.24214221]\n",
      " [0.16452759 0.75304462 0.88732857 0.37836717 0.09082692 0.15935938\n",
      "  0.02815583 0.09128245 0.76482201 0.59893107 0.63557556 0.92335554\n",
      "  0.70968572 0.38414887 0.01596943 0.63363819 0.34097502 0.48398632\n",
      "  0.94930714 0.60965574 0.28641634 0.81651058 0.28946432 0.22960524\n",
      "  0.95701234 0.14010605 0.28715318 0.48179673]\n",
      " [0.9275203  0.90593695 0.16191919 0.62515987 0.75338635 0.56547545\n",
      "  0.29394241 0.82971108 0.85224772 0.81722796 0.90199585 0.2708653\n",
      "  0.5384107  0.21193358 0.52003475 0.73701366 0.44329637 0.38079717\n",
      "  0.43432754 0.31869913 0.61912117 0.12448589 0.31758603 0.56616184\n",
      "  0.06830802 0.55016102 0.1210016  0.60356088]\n",
      " [0.45190727 0.32008828 0.53688603 0.12619074 0.68289891 0.39639142\n",
      "  0.40348921 0.12045243 0.07073755 0.63489307 0.41110701 0.86920721\n",
      "  0.82674063 0.98878309 0.72701871 0.1144256  0.76142336 0.51639253\n",
      "  0.98119666 0.54185301 0.14210856 0.33230955 0.84368648 0.37218591\n",
      "  0.48042075 0.36892893 0.8506944  0.31682227]\n",
      " [0.31795108 0.48129859 0.94527734 0.22006888 0.09521772 0.72582482\n",
      "  0.43673817 0.79901151 0.89618397 0.44765429 0.21296112 0.29921445\n",
      "  0.65038522 0.80782157 0.03726145 0.67413673 0.43041477 0.36533607\n",
      "  0.06739503 0.67504258 0.43559386 0.10530693 0.04641108 0.91392654\n",
      "  0.65080285 0.32336953 0.54887555 0.09442885]\n",
      " [0.21513231 0.80336129 0.82945831 0.88203601 0.68055899 0.05293142\n",
      "  0.62051854 0.15748952 0.28328929 0.72797815 0.09995506 0.38221735\n",
      "  0.16021256 0.90442358 0.44070702 0.41263375 0.54994521 0.34991584\n",
      "  0.88053282 0.48074372 0.35497489 0.64831285 0.97771246 0.48444292\n",
      "  0.07313706 0.47574924 0.22172499 0.72884954]\n",
      " [0.87243708 0.4641887  0.13158218 0.25608941 0.03585193 0.42127604\n",
      "  0.38450247 0.61033744 0.57979048 0.6416704  0.34752609 0.06898251\n",
      "  0.58964353 0.80370167 0.53224442 0.19782115 0.42616051 0.3509398\n",
      "  0.72486517 0.17747568 0.80289461 0.55720734 0.52645183 0.40915028\n",
      "  0.5146176  0.64167601 0.86611293 0.6388237 ]\n",
      " [0.27492311 0.9723935  0.98810178 0.92731516 0.95663683 0.59317612\n",
      "  0.02554123 0.65761816 0.65453181 0.10274847 0.40340132 0.80366408\n",
      "  0.63805167 0.27423921 0.82291118 0.10782584 0.83827387 0.76688212\n",
      "  0.53834987 0.38584422 0.97099809 0.60784227 0.06442986 0.58811653\n",
      "  0.404846   0.26337429 0.89893955 0.97094641]\n",
      " [0.55280583 0.66303495 0.13628067 0.6576605  0.36193973 0.93906847\n",
      "  0.2498071  0.34178496 0.39103066 0.98242685 0.75586841 0.70444356\n",
      "  0.72330497 0.34686929 0.0947335  0.60523645 0.26623249 0.25463592\n",
      "  0.34260996 0.83483792 0.92467954 0.5308995  0.4102582  0.44330684\n",
      "  0.9614979  0.44582426 0.00333711 0.65959395]\n",
      " [0.00644568 0.83675417 0.75212402 0.55346308 0.2562304  0.60440552\n",
      "  0.15085496 0.4669055  0.8488751  0.39490239 0.0312359  0.74300625\n",
      "  0.18066157 0.88701148 0.55343669 0.02172409 0.26160743 0.15451159\n",
      "  0.84964222 0.43614678 0.38437014 0.51582469 0.38779797 0.15793373\n",
      "  0.01254625 0.42059933 0.42659915 0.40823871]\n",
      " [0.16078979 0.96625741 0.44712679 0.87211048 0.61008055 0.84664334\n",
      "  0.99682376 0.30879057 0.59146657 0.85476647 0.86013673 0.00323612\n",
      "  0.30302862 0.1057217  0.57998127 0.03236882 0.56909527 0.80078816\n",
      "  0.66444938 0.23853446 0.6817548  0.04449991 0.25703829 0.56135023\n",
      "  0.52064869 0.22764178 0.09298859 0.18358577]\n",
      " [0.41104239 0.34896948 0.77676699 0.74010326 0.28671877 0.0368016\n",
      "  0.35825283 0.47108448 0.11573603 0.23046602 0.75427357 0.58332092\n",
      "  0.69563834 0.13209911 0.95869367 0.44949996 0.86372572 0.11078454\n",
      "  0.60601937 0.86055261 0.67713134 0.89303079 0.08131697 0.41360754\n",
      "  0.46427954 0.08599794 0.73244941 0.69849467]\n",
      " [0.4373373  0.61854002 0.74463883 0.96637541 0.17266803 0.65112247\n",
      "  0.61677619 0.17286642 0.62552692 0.89688948 0.67393584 0.08956894\n",
      "  0.85129236 0.625094   0.78584321 0.01403339 0.26664527 0.86181759\n",
      "  0.00180793 0.26783682 0.45347202 0.31490803 0.37686636 0.68669518\n",
      "  0.67865184 0.82436832 0.40572828 0.67409677]\n",
      " [0.84058857 0.67471403 0.6311599  0.23669109 0.99924488 0.93475495\n",
      "  0.54046334 0.88575575 0.59136746 0.80688079 0.56103198 0.03592839\n",
      "  0.98651021 0.8338628  0.61125326 0.7398871  0.67699619 0.58510183\n",
      "  0.74294233 0.22116938 0.54622111 0.59108051 0.16922917 0.24696099\n",
      "  0.55630742 0.62950665 0.69632194 0.3275449 ]\n",
      " [0.89333951 0.33838766 0.85226196 0.86101676 0.30103645 0.71636762\n",
      "  0.21005526 0.37176999 0.08048208 0.23913495 0.93122282 0.1626465\n",
      "  0.86537789 0.62408371 0.7011502  0.74946649 0.1782622  0.54223874\n",
      "  0.72096327 0.4873536  0.88910618 0.20600164 0.92355973 0.4759051\n",
      "  0.57045834 0.14416046 0.88662953 0.32419616]]\n"
     ]
    }
   ],
   "source": [
    "# define bias and weights\n",
    "bias = np.random.rand(1)\n",
    "weights = np.random.rand(28,28)\n",
    "print(weights) "
   ]
  }
 ],
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