Initialization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initialization\n",
    "\n",
    "Welcome to the first assignment of \"Improving Deep Neural Networks\". \n",
    "\n",
    "Training your neural network requires specifying an initial value of the weights. A well chosen initialization method will help learning.  \n",
    "\n",
    "If you completed the previous course of this specialization, you probably followed our instructions for weight initialization, and it has worked out so far. But how do you choose the initialization for a new neural network? In this notebook, you will see how different initializations lead to different results. \n",
    "\n",
    "A well chosen initialization can:\n",
    "- Speed up the convergence of gradient descent\n",
    "- Increase the odds of gradient descent converging to a lower training (and generalization) error \n",
    "\n",
    "To get started, run the following cell to load the packages and the planar dataset you will try to classify."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IkLa7oFaGDTyLhO0bsykushEZdfaKeA+kFfHZu6twOY89F7nZZbz+3CL++/m1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TAAAg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\nY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f001c6d5358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "from init_utils import sigmoid, relu, compute_loss, forward_propagation, backward_propagation\n",
    "from init_utils import update_parameters, predict, load_dataset, plot_decision_boundary, predict_dec\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'\n",
    "\n",
    "# load image dataset: blue/red dots in circles\n",
    "train_X, train_Y, test_X, test_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You would like a classifier to separate the blue dots from the red dots."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Neural Network model "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will use a 3-layer neural network (already implemented for you). Here are the initialization methods you will experiment with:  \n",
    "- *Zeros initialization* --  setting `initialization = \"zeros\"` in the input argument.\n",
    "- *Random initialization* -- setting `initialization = \"random\"` in the input argument. This initializes the weights to large random values.  \n",
    "- *He initialization* -- setting `initialization = \"he\"` in the input argument. This initializes the weights to random values scaled according to a paper by He et al., 2015. \n",
    "\n",
    "**Instructions**: Please quickly read over the code below, and run it. In the next part you will implement the three initialization methods that this `model()` calls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, learning_rate = 0.01, num_iterations = 15000, print_cost = True, initialization = \"he\"):\n",
    "    \"\"\"\n",
    "    Implements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (containing 0 for red dots; 1 for blue dots), of shape (1, number of examples)\n",
    "    learning_rate -- learning rate for gradient descent \n",
    "    num_iterations -- number of iterations to run gradient descent\n",
    "    print_cost -- if True, print the cost every 1000 iterations\n",
    "    initialization -- flag to choose which initialization to use (\"zeros\",\"random\" or \"he\")\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- parameters learnt by the model\n",
    "    \"\"\"\n",
    "        \n",
    "    grads = {}\n",
    "    costs = [] # to keep track of the loss\n",
    "    m = X.shape[1] # number of examples\n",
    "    layers_dims = [X.shape[0], 10, 5, 1]\n",
    "    \n",
    "    # Initialize parameters dictionary.\n",
    "    if initialization == \"zeros\":\n",
    "        parameters = initialize_parameters_zeros(layers_dims)\n",
    "    elif initialization == \"random\":\n",
    "        parameters = initialize_parameters_random(layers_dims)\n",
    "    elif initialization == \"he\":\n",
    "        parameters = initialize_parameters_he(layers_dims)\n",
    "\n",
    "    # Loop (gradient descent)\n",
    "\n",
    "    for i in range(0, num_iterations):\n",
    "\n",
    "        # Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.\n",
    "        a3, cache = forward_propagation(X, parameters)\n",
    "        \n",
    "        # Loss\n",
    "        cost = compute_loss(a3, Y)\n",
    "\n",
    "        # Backward propagation.\n",
    "        grads = backward_propagation(X, Y, cache)\n",
    "        \n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads, learning_rate)\n",
    "        \n",
    "        # Print the loss every 1000 iterations\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print(\"Cost after iteration {}: {}\".format(i, cost))\n",
    "            costs.append(cost)\n",
    "            \n",
    "    # plot the loss\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('iterations (per hundreds)')\n",
    "    plt.title(\"Learning rate =\" + str(learning_rate))\n",
    "    plt.show()\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Zero initialization\n",
    "\n",
    "There are two types of parameters to initialize in a neural network:\n",
    "- the weight matrices $(W^{[1]}, W^{[2]}, W^{[3]}, ..., W^{[L-1]}, W^{[L]})$\n",
    "- the bias vectors $(b^{[1]}, b^{[2]}, b^{[3]}, ..., b^{[L-1]}, b^{[L]})$\n",
    "\n",
    "**Exercise**: Implement the following function to initialize all parameters to zeros. You'll see later that this does not work well since it fails to \"break symmetry\", but lets try it anyway and see what happens. Use np.zeros((..,..)) with the correct shapes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_parameters_zeros \n",
    "\n",
    "def initialize_parameters_zeros(layers_dims):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    layer_dims -- python array (list) containing the size of each layer.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your parameters \"W1\", \"b1\", ..., \"WL\", \"bL\":\n",
    "                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])\n",
    "                    b1 -- bias vector of shape (layers_dims[1], 1)\n",
    "                    ...\n",
    "                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])\n",
    "                    bL -- bias vector of shape (layers_dims[L], 1)\n",
    "    \"\"\"\n",
    "    \n",
    "    parameters = {}\n",
    "    L = len(layers_dims)            # number of layers in the network\n",
    "    \n",
    "    for l in range(1, L):\n",
    "        ### START CODE HERE ### (≈ 2 lines of code)\n",
    "        parameters['W' + str(l)] = np.zeros((layers_dims[l],layers_dims[l-1]))\n",
    "        parameters['b' + str(l)] = np.zeros((layers_dims[l],1))\n",
    "        ### END CODE HERE ###\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "b1 = [[ 0.]\n",
      " [ 0.]]\n",
      "W2 = [[ 0.  0.]]\n",
      "b2 = [[ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_parameters_zeros([3,2,1])\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td>\n",
    "    **W1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **b1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.]\n",
    " [ 0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **W2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.  0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **b2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following code to train your model on 15,000 iterations using zeros initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.6931471805599453\n",
      "Cost after iteration 1000: 0.6931471805599453\n",
      "Cost after iteration 2000: 0.6931471805599453\n",
      "Cost after iteration 3000: 0.6931471805599453\n",
      "Cost after iteration 4000: 0.6931471805599453\n",
      "Cost after iteration 5000: 0.6931471805599453\n",
      "Cost after iteration 6000: 0.6931471805599453\n",
      "Cost after iteration 7000: 0.6931471805599453\n",
      "Cost after iteration 8000: 0.6931471805599453\n",
      "Cost after iteration 9000: 0.6931471805599453\n",
      "Cost after iteration 10000: 0.6931471805599455\n",
      "Cost after iteration 11000: 0.6931471805599453\n",
      "Cost after iteration 12000: 0.6931471805599453\n",
      "Cost after iteration 13000: 0.6931471805599453\n",
      "Cost after iteration 14000: 0.6931471805599453\n"
     ]
    },
    {
     "data": {
      "image/png": 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2q5wMrKu87i7bqmYCu0q6QdJySSeX7SuBwyTtLmkSxW2kprbaiaQFkrokdfX09AxxOBER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\nERGNlzCMiIjG+/8qs5fH0fJiOQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0008140e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On the train set:\n",
      "Accuracy: 0.5\n",
      "On the test set:\n",
      "Accuracy: 0.5\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, initialization = \"zeros\")\n",
    "print (\"On the train set:\")\n",
    "predictions_train = predict(train_X, train_Y, parameters)\n",
    "print (\"On the test set:\")\n",
    "predictions_test = predict(test_X, test_Y, parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance is really bad, and the cost does not really decrease, and the algorithm performs no better than random guessing. Why? Lets look at the details of the predictions and the decision boundary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictions_train = [[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 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 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 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 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 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 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 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 0\n",
      "  0 0 0 0]]\n",
      "predictions_test = [[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 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 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]]\n"
     ]
    }
   ],
   "source": [
    "print (\"predictions_train = \" + str(predictions_train))\n",
    "print (\"predictions_test = \" + str(predictions_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LCAy4qX9jwe/z3pzC+xM/CnOpWS4L+4z+3P2HJJxOndPYpUsiygKaGbM+PyxZ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\nC363uAqGAFWIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00080547f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Model with Zeros initialization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,1.5])\n",
    "axes.set_ylim([-1.5,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is predicting 0 for every example. \n",
    "\n",
    "In general, initializing all the weights to zero results in the network failing to break symmetry. This means that every neuron in each layer will learn the same thing, and you might as well be training a neural network with $n^{[l]}=1$ for every layer, and the network is no more powerful than a linear classifier such as logistic regression. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The weights $W^{[l]}$ should be initialized randomly to break symmetry. \n",
    "- It is however okay to initialize the biases $b^{[l]}$ to zeros. Symmetry is still broken so long as $W^{[l]}$ is initialized randomly. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Random initialization\n",
    "\n",
    "To break symmetry, lets intialize the weights randomly. Following random initialization, each neuron can then proceed to learn a different function of its inputs. In this exercise, you will see what happens if the weights are intialized randomly, but to very large values. \n",
    "\n",
    "**Exercise**: Implement the following function to initialize your weights to large random values (scaled by \\*10) and your biases to zeros. Use `np.random.randn(..,..) * 10` for weights and `np.zeros((.., ..))` for biases. We are using a fixed `np.random.seed(..)` to make sure your \"random\" weights  match ours, so don't worry if running several times your code gives you always the same initial values for the parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_parameters_random\n",
    "\n",
    "def initialize_parameters_random(layers_dims):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    layer_dims -- python array (list) containing the size of each layer.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your parameters \"W1\", \"b1\", ..., \"WL\", \"bL\":\n",
    "                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])\n",
    "                    b1 -- bias vector of shape (layers_dims[1], 1)\n",
    "                    ...\n",
    "                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])\n",
    "                    bL -- bias vector of shape (layers_dims[L], 1)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(3)               # This seed makes sure your \"random\" numbers will be the as ours\n",
    "    parameters = {}\n",
    "    L = len(layers_dims)            # integer representing the number of layers\n",
    "    \n",
    "    for l in range(1, L):\n",
    "        ### START CODE HERE ### (≈ 2 lines of code)\n",
    "        parameters['W' + str(l)] = np.random.randn(layers_dims[l],layers_dims[l-1])*10\n",
    "        parameters['b' + str(l)] = np.zeros((layers_dims[l],1))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 17.88628473   4.36509851   0.96497468]\n",
      " [-18.63492703  -2.77388203  -3.54758979]]\n",
      "b1 = [[ 0.]\n",
      " [ 0.]]\n",
      "W2 = [[-0.82741481 -6.27000677]]\n",
      "b2 = [[ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_parameters_random([3, 2, 1])\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td>\n",
    "    **W1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 17.88628473   4.36509851   0.96497468]\n",
    " [-18.63492703  -2.77388203  -3.54758979]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **b1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.]\n",
    " [ 0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **W2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[-0.82741481 -6.27000677]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **b2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following code to train your model on 15,000 iterations using random initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "parameters = model(train_X, train_Y, initialization = \"random\")\n",
    "print (\"On the train set:\")\n",
    "predictions_train = predict(train_X, train_Y, parameters)\n",
    "print (\"On the test set:\")\n",
    "predictions_test = predict(test_X, test_Y, parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you see \"inf\" as the cost after the iteration 0, this is because of numerical roundoff; a more numerically sophisticated implementation would fix this. But this isn't worth worrying about for our purposes. \n",
    "\n",
    "Anyway, it looks like you have broken symmetry, and this gives better results. than before. The model is no longer outputting all 0s. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print (predictions_train)\n",
    "print (predictions_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.title(\"Model with large random initialization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,1.5])\n",
    "axes.set_ylim([-1.5,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observations**:\n",
    "- The cost starts very high. This is because with large random-valued weights, the last activation (sigmoid) outputs results that are very close to 0 or 1 for some examples, and when it gets that example wrong it incurs a very high loss for that example. Indeed, when $\\log(a^{[3]}) = \\log(0)$, the loss goes to infinity.\n",
    "- Poor initialization can lead to vanishing/exploding gradients, which also slows down the optimization algorithm. \n",
    "- If you train this network longer you will see better results, but initializing with overly large random numbers slows down the optimization.\n",
    "\n",
    "<font color='blue'>\n",
    "**In summary**:\n",
    "- Initializing weights to very large random values does not work well. \n",
    "- Hopefully intializing with small random values does better. The important question is: how small should be these random values be? Lets find out in the next part! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - He initialization\n",
    "\n",
    "Finally, try \"He Initialization\"; this is named for the first author of He et al., 2015. (If you have heard of \"Xavier initialization\", this is similar except Xavier initialization uses a scaling factor for the weights $W^{[l]}$ of `sqrt(1./layers_dims[l-1])` where He initialization would use `sqrt(2./layers_dims[l-1])`.)\n",
    "\n",
    "**Exercise**: Implement the following function to initialize your parameters with He initialization.\n",
    "\n",
    "**Hint**: This function is similar to the previous `initialize_parameters_random(...)`. The only difference is that instead of multiplying `np.random.randn(..,..)` by 10, you will multiply it by $\\sqrt{\\frac{2}{\\text{dimension of the previous layer}}}$, which is what He initialization recommends for layers with a ReLU activation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_parameters_he\n",
    "\n",
    "def initialize_parameters_he(layers_dims):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    layer_dims -- python array (list) containing the size of each layer.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your parameters \"W1\", \"b1\", ..., \"WL\", \"bL\":\n",
    "                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])\n",
    "                    b1 -- bias vector of shape (layers_dims[1], 1)\n",
    "                    ...\n",
    "                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])\n",
    "                    bL -- bias vector of shape (layers_dims[L], 1)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(3)\n",
    "    parameters = {}\n",
    "    L = len(layers_dims) - 1 # integer representing the number of layers\n",
    "     \n",
    "    for l in range(1, L + 1):\n",
    "        ### START CODE HERE ### (≈ 2 lines of code)\n",
    "        parameters['W' + str(l)] = np.random.randn(layers_dims[l],layers_dims[l-1])*np.sqrt(2/layers_dims[l-1])\n",
    "        parameters['b' + str(l)] = np.zeros((layers_dims[l],1))\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.78862847  0.43650985]\n",
      " [ 0.09649747 -1.8634927 ]\n",
      " [-0.2773882  -0.35475898]\n",
      " [-0.08274148 -0.62700068]]\n",
      "b1 = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "W2 = [[-0.03098412 -0.33744411 -0.92904268  0.62552248]]\n",
      "b2 = [[ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_parameters_he([2, 4, 1])\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td>\n",
    "    **W1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 1.78862847  0.43650985]\n",
    " [ 0.09649747 -1.8634927 ]\n",
    " [-0.2773882  -0.35475898]\n",
    " [-0.08274148 -0.62700068]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **b1**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]\n",
    " [ 0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **W2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[-0.03098412 -0.33744411 -0.92904268  0.62552248]]\n",
    "    </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td>\n",
    "    **b2**\n",
    "    </td>\n",
    "        <td>\n",
    "    [[ 0.]]\n",
    "    </td>\n",
    "    </tr>\n",
    "\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following code to train your model on 15,000 iterations using He initialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "parameters = model(train_X, train_Y, initialization = \"he\")\n",
    "print (\"On the train set:\")\n",
    "predictions_train = predict(train_X, train_Y, parameters)\n",
    "print (\"On the test set:\")\n",
    "predictions_test = predict(test_X, test_Y, parameters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "plt.title(\"Model with He initialization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,1.5])\n",
    "axes.set_ylim([-1.5,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observations**:\n",
    "- The model with He initialization separates the blue and the red dots very well in a small number of iterations.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 5 - Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "You have seen three different types of initializations. For the same number of iterations and same hyperparameters the comparison is:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **Model**\n",
    "        </td>\n",
    "        <td>\n",
    "        **Train accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **Problem/Comment**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        3-layer NN with zeros initialization\n",
    "        </td>\n",
    "        <td>\n",
    "        50%\n",
    "        </td>\n",
    "        <td>\n",
    "        fails to break symmetry\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        3-layer NN with large random initialization\n",
    "        </td>\n",
    "        <td>\n",
    "        83%\n",
    "        </td>\n",
    "        <td>\n",
    "        too large weights \n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        3-layer NN with He initialization\n",
    "        </td>\n",
    "        <td>\n",
    "        99%\n",
    "        </td>\n",
    "        <td>\n",
    "        recommended method\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember from this notebook**:\n",
    "- Different initializations lead to different results\n",
    "- Random initialization is used to break symmetry and make sure different hidden units can learn different things\n",
    "- Don't intialize to values that are too large\n",
    "- He initialization works well for networks with ReLU activations. "
   ]
  }
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