Optimization_methods_v1b.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color='darkblue'> Updates to Assignment <font>\n",
    "\n",
    "#### If you were working on a previous version\n",
    "* The current notebook filename is version \"Optimization_methods_v1b\". \n",
    "* You can find your work in the file directory as version \"Optimization methods'.\n",
    "* To see the file directory, click on the Coursera logo at the top left of the notebook.\n",
    "\n",
    "#### List of Updates\n",
    "* op_utils is now opt_utils_v1a.  Assertion statement in `initialize_parameters` is fixed.\n",
    "* opt_utils_v1a: `compute_cost` function now accumulates total cost of the batch without taking the average (average is taken for entire epoch instead).\n",
    "* In `model` function, the total cost per mini-batch is accumulated, and the average of the entire epoch is taken as the average cost. So the plot of the cost function over time is now a smooth downward curve instead of an oscillating curve.\n",
    "* Print statements used to check each function are reformatted, and 'expected output` is reformatted to match the format of the print statements (for easier visual comparisons)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils_v1a import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils_v1a import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\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'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "A simple optimization method in machine learning is gradient descent (GD). When you take gradient steps with respect to all $m$ examples on each step, it is also called Batch Gradient Descent. \n",
    "\n",
    "**Warm-up exercise**: Implement the gradient descent update rule. The  gradient descent rule is, for $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "where L is the number of layers and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary. Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * grads[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 =\n",
      "[[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 =\n",
      "[[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 =\n",
      "[[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 =\n",
      "[[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 =\\n\" + str(parameters[\"W1\"]))\n",
    "print(\"b1 =\\n\" + str(parameters[\"b1\"]))\n",
    "print(\"W2 =\\n\" + str(parameters[\"W2\"]))\n",
    "print(\"b2 =\\n\" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "W1 =\n",
    "[[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]]\n",
    "b1 =\n",
    "[[ 1.74604067]\n",
    " [-0.75184921]]\n",
    "W2 =\n",
    "[[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
    "b2 =\n",
    "[[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variant of this is Stochastic Gradient Descent (SGD), which is equivalent to mini-batch gradient descent where each mini-batch has just 1 example. The update rule that you have just implemented does not change. What changes is that you would be computing gradients on just one training example at a time, rather than on the whole training set. The code examples below illustrate the difference between stochastic gradient descent and (batch) gradient descent. \n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost += compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost += compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Stochastic Gradient Descent, you use only 1 training example before updating the gradients. When the training set is large, SGD can be faster. But the parameters will \"oscillate\" toward the minimum rather than converge smoothly. Here is an illustration of this: \n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" denotes a minimum of the cost. SGD leads to many oscillations to reach convergence. But each step is a lot faster to compute for SGD than for GD, as it uses only one training example (vs. the whole batch for GD). </center></caption>\n",
    "\n",
    "**Note** also that implementing SGD requires 3 for-loops in total:\n",
    "1. Over the number of iterations\n",
    "2. Over the $m$ training examples\n",
    "3. Over the layers (to update all parameters, from $(W^{[1]},b^{[1]})$ to $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "In practice, you'll often get faster results if you do not use neither the whole training set, nor only one training example, to perform each update. Mini-batch gradient descent uses an intermediate number of examples for each step. With mini-batch gradient descent, you loop over the mini-batches instead of looping over individual training examples.\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" denotes a minimum of the cost. Using mini-batches in your optimization algorithm often leads to faster optimization. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The difference between gradient descent, mini-batch gradient descent and stochastic gradient descent is the number of examples you use to perform one update step.\n",
    "- You have to tune a learning rate hyperparameter $\\alpha$.\n",
    "- With a well-turned mini-batch size, usually it outperforms either gradient descent or stochastic gradient descent (particularly when the training set is large)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "Let's learn how to build mini-batches from the training set (X, Y).\n",
    "\n",
    "There are two steps:\n",
    "- **Shuffle**: Create a shuffled version of the training set (X, Y) as shown below. Each column of X and Y represents a training example. Note that the random shuffling is done synchronously between X and Y. Such that after the shuffling the $i^{th}$ column of X is the example corresponding to the $i^{th}$ label in Y. The shuffling step ensures that examples will be split randomly into different mini-batches. \n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **Partition**: Partition the shuffled (X, Y) into mini-batches of size `mini_batch_size` (here 64). Note that the number of training examples is not always divisible by `mini_batch_size`. The last mini batch might be smaller, but you don't need to worry about this. When the final mini-batch is smaller than the full `mini_batch_size`, it will look like this: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**Exercise**: Implement `random_mini_batches`. We coded the shuffling part for you. To help you with the partitioning step, we give you the following code that selects the indexes for the $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "Note that the last mini-batch might end up smaller than `mini_batch_size=64`. Let $\\lfloor s \\rfloor$ represents $s$ rounded down to the nearest integer (this is `math.floor(s)` in Python). If the total number of examples is not a multiple of `mini_batch_size=64` then there will be $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches with a full 64 examples, and the number of examples in the final mini-batch will be ($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, k * mini_batch_size : (k + 1) * mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, k * mini_batch_size : (k + 1) * mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, num_complete_minibatches * mini_batch_size:]\n",
    "        mini_batch_Y = shuffled_Y[:, num_complete_minibatches * mini_batch_size:]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 20)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 20)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Shuffling and Partitioning are the two steps required to build mini-batches\n",
    "- Powers of two are often chosen to be the mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**Figure 3**</u><font color='purple'>: The red arrows shows the direction taken by one step of mini-batch gradient descent with momentum. The blue points show the direction of the gradient (with respect to the current mini-batch) on each step. Rather than just following the gradient, we let the gradient influence $v$ and then take a step in the direction of $v$.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**Exercise**: Initialize the velocity. The velocity, $v$, is a python dictionary that needs to be initialized with arrays of zeros. Its keys are the same as those in the `grads` dictionary, that is:\n",
    "for $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**Note** that the iterator l starts at 0 in the for loop while the first parameters are v[\"dW1\"] and v[\"db1\"] (that's a \"one\" on the superscript). This is why we are shifting l to l+1 in the `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\"+str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\"+str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] =\n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] =\n",
      "[[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] =\n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] =\n",
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] =\\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] =\\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] =\\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] =\\n\" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "v[\"dW1\"] =\n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db1\"] =\n",
    "[[ 0.]\n",
    " [ 0.]]\n",
    "v[\"dW2\"] =\n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db2\"] =\n",
    "[[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with momentum. The momentum update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "where L is the number of layers, $\\beta$ is the momentum and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary.  Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$ (that's a \"one\" on the superscript). So you will need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    \n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "         # compute velocities\n",
    "        v[\"dW\" + str(l+1)] = beta * v[\"dW\" + str(l+1)] + (1 - beta) * grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta * v[\"db\" + str(l+1)] + (1 - beta) * grads[\"db\" + str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * v[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * v[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = \n",
      "[[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = \n",
      "[[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = \n",
      "[[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = \n",
      "[[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = \n",
      "[[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = \n",
      "[[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = \n",
      "[[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = v[[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \\n\" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \\n\" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \\n\" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \\n\" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = v\" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "W1 = \n",
    "[[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]]\n",
    "b1 = \n",
    "[[ 1.74493465]\n",
    " [-0.76027113]]\n",
    "W2 = \n",
    "[[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
    "b2 = \n",
    "[[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]]\n",
    "v[\"dW1\"] = \n",
    "[[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]]\n",
    "v[\"db1\"] = \n",
    "[[-0.01228902]\n",
    " [-0.09357694]]\n",
    "v[\"dW2\"] = \n",
    "[[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]]\n",
    "v[\"db2\"] = v[[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** that:\n",
    "- The velocity is initialized with zeros. So the algorithm will take a few iterations to \"build up\" velocity and start to take bigger steps.\n",
    "- If $\\beta = 0$, then this just becomes standard gradient descent without momentum. \n",
    "\n",
    "**How do you choose $\\beta$?**\n",
    "\n",
    "- The larger the momentum $\\beta$ is, the smoother the update because the more we take the past gradients into account. But if $\\beta$ is too big, it could also smooth out the updates too much. \n",
    "- Common values for $\\beta$ range from 0.8 to 0.999. If you don't feel inclined to tune this, $\\beta = 0.9$ is often a reasonable default. \n",
    "- Tuning the optimal $\\beta$ for your model might need trying several values to see what works best in term of reducing the value of the cost function $J$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Momentum takes past gradients into account to smooth out the steps of gradient descent. It can be applied with batch gradient descent, mini-batch gradient descent or stochastic gradient descent.\n",
    "- You have to tune a momentum hyperparameter $\\beta$ and a learning rate $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam is one of the most effective optimization algorithms for training neural networks. It combines ideas from RMSProp (described in lecture) and Momentum. \n",
    "\n",
    "**How does Adam work?**\n",
    "1. It calculates an exponentially weighted average of past gradients, and stores it in variables $v$ (before bias correction) and $v^{corrected}$ (with bias correction). \n",
    "2. It calculates an exponentially weighted average of the squares of the past gradients, and  stores it in variables $s$ (before bias correction) and $s^{corrected}$ (with bias correction). \n",
    "3. It updates parameters in a direction based on combining information from \"1\" and \"2\".\n",
    "\n",
    "The update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "where:\n",
    "- t counts the number of steps taken of Adam \n",
    "- L is the number of layers\n",
    "- $\\beta_1$ and $\\beta_2$ are hyperparameters that control the two exponentially weighted averages. \n",
    "- $\\alpha$ is the learning rate\n",
    "- $\\varepsilon$ is a very small number to avoid dividing by zero\n",
    "\n",
    "As usual, we will store all parameters in the `parameters` dictionary  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Initialize the Adam variables $v, s$ which keep track of the past information.\n",
    "\n",
    "**Instruction**: The variables $v, s$ are python dictionaries that need to be initialized with arrays of zeros. Their keys are the same as for `grads`, that is:\n",
    "for $l = 1, ..., L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    " \n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = \n",
      "[[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = \n",
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW1\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db1\"] = \n",
      "[[ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW2\"] = \n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db2\"] = \n",
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \\n\" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \\n\" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \\n\" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \\n\" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \\n\" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "v[\"dW1\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db1\"] = \n",
    "[[ 0.]\n",
    " [ 0.]]\n",
    "v[\"dW2\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "v[\"db2\"] = \n",
    "[[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]]\n",
    "s[\"dW1\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "s[\"db1\"] = \n",
    "[[ 0.]\n",
    " [ 0.]]\n",
    "s[\"dW2\"] = \n",
    "[[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]]\n",
    "s[\"db2\"] = \n",
    "[[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with Adam. Recall the general update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "\n",
    "**Note** that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = beta1 * v[\"dW\" + str(l+1)] + (1 - beta1) * grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta1 * v[\"db\" + str(l+1)] + (1 - beta1) * grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l+1)] = v[\"dW\" + str(l+1)] / (1 - beta1)\n",
    "        v_corrected[\"db\" + str(l+1)] = v[\"db\" + str(l+1)] / (1 - beta1)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l+1)] = beta2 * s[\"dW\" + str(l+1)] + (1 - beta2) * (grads[\"dW\" + str(l+1)] * grads[\"dW\" + str(l+1)])\n",
    "        s[\"db\" + str(l+1)] = beta2 * s[\"db\" + str(l+1)] + (1 - beta2) * (grads[\"db\" + str(l+1)] * grads[\"db\" + str(l+1)])\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l+1)] = s[\"dW\" + str(l+1)] / (1 - beta2)\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l+1)] / (1 - beta2)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * v_corrected[\"dW\" + str(l+1)] / (np.sqrt(s_corrected[\"dW\" + str(l+1)]) + epsilon)\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * v_corrected[\"db\" + str(l+1)] / (np.sqrt(s_corrected[\"db\" + str(l+1)]) + epsilon)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = \n",
      "[[ 1.63434536 -0.62175641 -0.53817175]\n",
      " [-1.08296862  0.85540763 -2.2915387 ]]\n",
      "b1 = \n",
      "[[ 1.75481176]\n",
      " [-0.7512069 ]]\n",
      "W2 = \n",
      "[[ 0.3290391  -0.25937038  1.47210794]\n",
      " [-2.05014071 -0.3124172  -0.37405435]\n",
      " [ 1.14376944 -1.08989128 -0.16242821]]\n",
      "b2 = \n",
      "[[-0.88785842]\n",
      " [ 0.03221375]\n",
      " [ 0.57281521]]\n",
      "v[\"dW1\"] = \n",
      "[[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = \n",
      "[[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = \n",
      "[[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = \n",
      "[[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n",
      "s[\"dW1\"] = \n",
      "[[ 0.00121136  0.00131039  0.00081287]\n",
      " [ 0.0002525   0.00081154  0.00046748]]\n",
      "s[\"db1\"] = \n",
      "[[  1.51020075e-05]\n",
      " [  8.75664434e-04]]\n",
      "s[\"dW2\"] = \n",
      "[[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
      " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
      " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]]\n",
      "s[\"db2\"] = \n",
      "[[  5.49507194e-05]\n",
      " [  2.75494327e-03]\n",
      " [  5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \\n\" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \\n\" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \\n\" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \\n\" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \\n\" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \\n\" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \\n\" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \\n\" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \\n\" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \\n\" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \\n\" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \\n\" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "```\n",
    "W1 = \n",
    "[[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]]\n",
    "b1 = \n",
    "[[ 1.75225313]\n",
    " [-0.75376553]]\n",
    "W2 = \n",
    "[[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]]\n",
    "b2 = \n",
    "[[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]]\n",
    "v[\"dW1\"] = \n",
    "[[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]]\n",
    "v[\"db1\"] = \n",
    "[[-0.01228902]\n",
    " [-0.09357694]]\n",
    "v[\"dW2\"] = \n",
    "[[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]]\n",
    "v[\"db2\"] = \n",
    "[[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]\n",
    "s[\"dW1\"] = \n",
    "[[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]]\n",
    "s[\"db1\"] = \n",
    "[[  1.51020075e-05]\n",
    " [  8.75664434e-04]]\n",
    "s[\"dW2\"] = \n",
    "[[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]]\n",
    "s[\"db2\"] = \n",
    "[[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You now have three working optimization algorithms (mini-batch gradient descent, Momentum, Adam). Let's implement a model with each of these optimizers and observe the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model with different optimization algorithms\n",
    "\n",
    "Lets use the following \"moons\" dataset to test the different optimization methods. (The dataset is named \"moons\" because the data from each of the two classes looks a bit like a crescent-shaped moon.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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pOWkUwU3qEtmtJb0/fpResx/xuC68Y1OfiT+B9aMuqz234tQsEn9ZR8qqHcgq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I8dQMdp/sebcSSfp+77GZdTx1HWW/bVJ1t48JmpxMSdCuKH9ufw9AO/4HR69TYL8ux8+OZ60lJy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\nv5qYYyZ0Z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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6f9129400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already implemented a 3-layer neural network. You will train it with: \n",
    "- Mini-batch **Gradient Descent**: it will call your function:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: it will call your functions:\n",
    "    - `initialize_velocity()` and `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: it will call your functions:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    m = X.shape[1]                   # number of training examples\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "        cost_total = 0\n",
    "        \n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost and add to the cost total\n",
    "            cost_total += compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        cost_avg = cost_total / m\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost_avg))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost_avg)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will now run this 3 layer neural network with each of the 3 optimization methods.\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "Run the following code to see how the model does with mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.702405\n",
      "Cost after epoch 1000: 0.668101\n",
      "Cost after epoch 2000: 0.635288\n",
      "Cost after epoch 3000: 0.600491\n",
      "Cost after epoch 4000: 0.573367\n",
      "Cost after epoch 5000: 0.551977\n",
      "Cost after epoch 6000: 0.532370\n",
      "Cost after epoch 7000: 0.514007\n",
      "Cost after epoch 8000: 0.496472\n",
      "Cost after epoch 9000: 0.468014\n"
     ]
    },
    {
     "data": {
      "image/png": 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rV+Xmno3p26q2nlmUmKMwFJGoOnQ0izfmrOe5aatZt/MgadXLcWO3RgxKT6Wy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\n93+o7NbUCU7wmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7243f7668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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QUloyb2BY3dRC5J6ncEoKy5abWuwg6h15vIgMZcShw3WUzlwNIZ4QOrsOVpLNKTWP+3re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zz0/W/4jZ7NT8RL9+zphpLyC8fvLD5y+Ge6c/cWo2t75Ryjy1uMrlWbttjsLHQaW6pEE5fs0hml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\nioiIhFCiFBERCfH/50bmP+Yj+ssAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6f066e940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "Run the following code to see how the model does with momentum. Because this example is relatively simple, the gains from using momemtum are small; but for more complex problems you might see bigger gains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.702413\n",
      "Cost after epoch 1000: 0.668167\n",
      "Cost after epoch 2000: 0.635388\n",
      "Cost after epoch 3000: 0.600591\n",
      "Cost after epoch 4000: 0.573444\n",
      "Cost after epoch 5000: 0.552058\n",
      "Cost after epoch 6000: 0.532458\n",
      "Cost after epoch 7000: 0.514101\n",
      "Cost after epoch 8000: 0.496652\n",
      "Cost after epoch 9000: 0.468160\n"
     ]
    },
    {
     "data": {
      "image/png": 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08Df8pCkMf5IGLHf3le6eBYwGBkW5pqhx943uPif4eS+hP2QNCR2T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\ne/8fvl8UGzM29/QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7031cb780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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vH0vDbK0EVB2vC/msS6lYoj++v3Ntx3NzXOg/gZL6fabsNImQRb5hbJ5h2gpz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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6f010fba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "Run the following code to see how the model does with Adam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.702130\n",
      "Cost after epoch 1000: 0.318100\n",
      "Cost after epoch 2000: 0.205118\n",
      "Cost after epoch 3000: 0.160727\n",
      "Cost after epoch 4000: 0.147537\n",
      "Cost after epoch 5000: 0.142568\n",
      "Cost after epoch 6000: 0.140468\n",
      "Cost after epoch 7000: 0.139397\n",
      "Cost after epoch 8000: 0.138789\n",
      "Cost after epoch 9000: 0.137847\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7243f7898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.943333333333\n"
     ]
    },
    {
     "data": {
      "image/png": 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yC+lZXMPCNyyMwMcg4DtXf5+pK0mWF109PLnFMHX2Kk7N2KQz+jiCQJHNmYyO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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6effcca90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4 - Summary\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum usually helps, but given the small learning rate and the simplistic dataset, its impact is almost negligeable. Also, the huge oscillations you see in the cost come from the fact that some minibatches are more difficult thans others for the optimization algorithm.\n",
    "\n",
    "Adam on the other hand, clearly outperforms mini-batch gradient descent and Momentum. If you run the model for more epochs on this simple dataset, all three methods will lead to very good results. However, you've seen that Adam converges a lot faster.\n",
    "\n",
    "Some advantages of Adam include:\n",
    "- Relatively low memory requirements (though higher than gradient descent and gradient descent with momentum) \n",
    "- Usually works well even with little tuning of hyperparameters (except $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  }
 ],
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