08_neural_networks.ipynb

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   "source": [
    "# IGNORE THIS CELL WHICH CUSTOMIZES LAYOUT AND STYLING OF THE NOTEBOOK !\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import seaborn as sns\n",
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    "mpl.rcParams['lines.linewidth'] = 3\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "%config IPCompleter.greedy=True\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore', category=FutureWarning)\n",
    "from IPython.core.display import HTML; HTML(open(\"custom.html\", \"r\").read())"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 8: Introduction to Neural Networks\n",
    "\n",
    "\n",
    "\n",
    "<img src=\"./images/3042en.jpg\" title=\"made at imgflip.com\" width=35%/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## History of Neural networks\n",
    "\n",
    "\n",
    "1943 - Threshold Logic\n",
    "\n",
    "1940s - Hebbian Learning\n",
    "\n",
    "1958 - Perceptron\n",
    "\n",
    "1980s - Neocognitron\n",
    "\n",
    "1982 - Hopfield Network\n",
    "\n",
    "1989 - Convolutional neural network (CNN) kernels trained via backpropagation\n",
    "\n",
    "1997 - Long-short term memory (LSTM) model\n",
    "\n",
    "1998 - LeNet-5\n",
    "\n",
    "2014 - Gated Recurrent Units (GRU), Generative Adversarial Networks (GAN)\n",
    "\n",
    "2015 - ResNet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why the boom now?\n",
    "* Data\n",
    "* Data\n",
    "* Data\n",
    "* Availability of GPUs\n",
    "* Algorithmic developments which allow for efficient training and making networks networks\n",
    "* Development of high-level libraries/APIs have made the field much more accessible than it was a decade ago"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feed-Forward neural network\n",
    "<center>\n",
    "<figure>\n",
    "<img src=\"./images/neuralnets/neural_net_ex.svg\" width=\"700\"/>\n",
    "<figcaption>A 3 layer densely connected Neural Network (By convention the input layer is not counted).</figcaption>\n",
    "</figure>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building blocks\n",
    "### Perceptron\n",
    "\n",
    "The smallest unit of a neural network is a **perceptron** like node.\n",
    "\n",
    "**What is a Perceptron?**\n",
    "\n",
    "It is a simple function which can have multiple inputs and has a single output.\n",
    "\n",
    "<center>\n",
    "<figure>\n",
    "<img src=\"./images/neuralnets/perceptron_ex.svg\" width=\"400\"/>\n",
    "<figcaption>A simple perceptron with 3 inputs and 1 output.</figcaption>\n",
    "</figure>\n",
    "</center>\n",
    "\n",
    "\n",
    "It works as follows: \n",
    "\n",
    "Step 1: A **weighted sum** of the inputs is calculated\n",
    "\n",
    "\\begin{equation*}\n",
    "weighted\\_sum = w_{1} x_{1} + w_{2} x_{2} + w_{3} x_{3} + ...\n",
    "\\end{equation*}\n",
    "\n",
    "Step 2: A **step** activation function is applied\n",
    "\n",
    "$$\n",
    "f = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            0 & \\quad weighted\\_sum < threshold \\\\\n",
    "            1 & \\quad weighted\\_sum \\geq threshold\n",
    "        \\end{array}\n",
    "    \\right.\n",
    "$$\n",
    "\n",
    "You can see that this is also a linear classifier as the ones we introduced in script 02."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 392
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the step function\n",
    "x = np.arange(-2,2.1,0.01)\n",
    "y = np.zeros(len(x))\n",
    "threshold = 0.\n",
    "y[x>threshold] = 1.\n",
    "step_plot = sns.lineplot(x, y).set_title('Step function') ;\n",
    "plt.xlabel('weighted_sum') ;\n",
    "plt.ylabel('f(weighted_sum)') ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perceptron(X, w, threshold=1):\n",
    "    # This function computes sum(w_i*x_i) and\n",
    "    # applies a perceptron activation\n",
    "    linear_sum = np.dot(np.asarray(X).T, w)\n",
    "    output = np.zeros(len(linear_sum), dtype=np.int8)\n",
    "    output[linear_sum >= threshold] = 1\n",
    "    return output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Boolean AND\n",
    "\n",
    "| x$_1$ | x$_2$ | output |\n",
    "| --- | --- | --- |\n",
    "| 0 | 0 | 0 |\n",
    "| 1 | 0 | 0 |\n",
    "| 0 | 1 | 0 |\n",
    "| 1 | 1 | 1 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perceptron output for x1, x2 =  0 , 0  is  0\n",
      "Perceptron output for x1, x2 =  1 , 0  is  0\n",
      "Perceptron output for x1, x2 =  0 , 1  is  0\n",
      "Perceptron output for x1, x2 =  1 , 1  is  1\n"
     ]
    }
   ],
   "source": [
    "# Calculating Boolean AND using a perceptron\n",
    "threshold = 1.5\n",
    "# (w1, w2)\n",
    "w = [1, 1]\n",
    "# (x1, x2) pairs\n",
    "x1 = [0, 1, 0, 1]\n",
    "x2 = [0, 0, 1, 1]\n",
    "# Calling the perceptron function\n",
    "output = perceptron([x1, x2], w, threshold)\n",
    "for i in range(len(output)):\n",
    "    print(\"Perceptron output for x1, x2 = \", x1[i], \",\", x2[i],\n",
    "          \" is \", output[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this simple case we can rewrite our equation to $x_2 = ...... $ which describes a line in 2D:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def perceptron_DB(x1, x2, w, threshold):\n",
    "    # Plotting the decision boundary of the perceptron\n",
    "    plt.scatter(x1, x2, color=\"black\")\n",
    "    plt.xlim(-1,2)\n",
    "    plt.ylim(-1,2)\n",
    "    # The decision boundary is a line given by\n",
    "    # w_1*x_1+w_2*x_2-threshold=0\n",
    "    x1 = np.arange(-3, 4)\n",
    "    x2 = (threshold - x1*w[0])/w[1]\n",
    "    sns.lineplot(x1, x2, **{\"color\": \"black\"})\n",
    "    plt.xlabel(\"x$_1$\", fontsize=16)\n",
    "    plt.ylabel(\"x$_2$\", fontsize=16)\n",
    "    # Coloring the regions\n",
    "    pts_tmp = np.arange(-2, 2.1, 0.02)\n",
    "    points = np.array(np.meshgrid(pts_tmp, pts_tmp)).T.reshape(-1, 2)\n",
    "    outputs = perceptron(points.T, w, threshold)\n",
    "    plt.plot(points[:, 0][outputs == 0], points[:, 1][outputs == 0],\n",
    "             \"o\",\n",
    "             color=\"steelblue\",\n",
    "             markersize=1,\n",
    "             alpha=0.04,\n",
    "             )\n",
    "    plt.plot(points[:, 0][outputs == 1], points[:, 1][outputs == 1],\n",
    "             \"o\",\n",
    "             color=\"chocolate\",\n",
    "             markersize=1,\n",
    "             alpha=0.04,\n",
    "             )\n",
    "    plt.title(\"Blue color = 0 and Chocolate = 1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 284,
       "width": 406
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the perceptron decision boundary\n",
    "perceptron_DB(x1, x2, w, threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise section\n",
    "* Compute a Boolean \"OR\" using a perceptron\n",
    "\n",
    "Hint: copy the code from the \"AND\" example and edit the weights and/or threshold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Boolean OR\n",
    "\n",
    "| x$_1$ | x$_2$ | output |\n",
    "| --- | --- | --- |\n",
    "| 0 | 0 | 0 |\n",
    "| 1 | 0 | 1 |\n",
    "| 0 | 1 | 1 |\n",
    "| 1 | 1 | 1 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculating Boolean OR using a perceptron\n",
    "# Enter code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true,
    "tags": [
     "solution"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perceptron output for x1, x2 =  0 , 0  is  0\n",
      "Perceptron output for x1, x2 =  1 , 0  is  1\n",
      "Perceptron output for x1, x2 =  0 , 1  is  1\n",
      "Perceptron output for x1, x2 =  1 , 1  is  1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 284,
       "width": 406
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "# Calculating Boolean OR using a perceptron\n",
    "threshold=0.6\n",
    "# (w1, w2)\n",
    "w=[1,1]\n",
    "# (x1, x2) pairs\n",
    "x1 = [0, 1, 0, 1]\n",
    "x2 = [0, 0, 1, 1]\n",
    "output = perceptron([x1, x2], w, threshold)\n",
    "for i in range(len(output)):\n",
    "    print(\"Perceptron output for x1, x2 = \", x1[i], \",\", x2[i],\n",
    "          \" is \", output[i])\n",
    "perceptron_DB(x1, x2, w, threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise section\n",
    "* Create a NAND gate using a perceptron\n",
    "\n",
    "#### Boolean NAND\n",
    "\n",
    "| x$_1$ | x$_2$ | output |\n",
    "| --- | --- | --- |\n",
    "| 0 | 0 | 1 |\n",
    "| 1 | 0 | 1 |\n",
    "| 0 | 1 | 1 |\n",
    "| 1 | 1 | 0 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculating Boolean NAND using a perceptron\n",
    "# Enter code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": [
     "solution"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perceptron output for x1, x2 =  0 , 0  is  1\n",
      "Perceptron output for x1, x2 =  1 , 0  is  1\n",
      "Perceptron output for x1, x2 =  0 , 1  is  1\n",
      "Perceptron output for x1, x2 =  1 , 1  is  0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 284,
       "width": 406
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "# Calculating Boolean NAND using a perceptron\n",
    "import matplotlib.pyplot as plt\n",
    "threshold=-1.5\n",
    "# (w1, w2)\n",
    "w=[-1,-1]\n",
    "# (x1, x2) pairs\n",
    "x1 = [0, 1, 0, 1]\n",
    "x2 = [0, 0, 1, 1]\n",
    "output = perceptron([x1, x2], w, threshold)\n",
    "for i in range(len(output)):\n",
    "    print(\"Perceptron output for x1, x2 = \", x1[i], \",\", x2[i],\n",
    "          \" is \", output[i])\n",
    "perceptron_DB(x1, x2, w, threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, a single perceptron can compute \"AND\", \"OR\" and \"NOT\" boolean functions.\n",
    "\n",
    "However, it cannot compute some other boolean functions such as \"XOR\".\n",
    "\n",
    "**WHAT CAN WE DO?**\n",
    "\n",
    "\n",
    "Hint: Think about what is the significance of the NAND gate we have created above?\n",
    "\n",
    "Answer: We said a single perceptron can't compute a \"XOR\" function. We didn't say that about **multiple Perceptrons** put together."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**XOR function using multiple perceptrons**\n",
    "\n",
    "<center>\n",
    "<figure>\n",
    "<img src=\"./images/neuralnets/perceptron_XOR.svg\" width=\"400\"/>\n",
    "<figcaption>Multiple perceptrons connected together to output a XOR function.</figcaption>\n",
    "</figure>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multi-layer perceptrons\n",
    "\n",
    "The normal densely connected neural network is sometimes also called \"Multi-layer\" perceptron."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning\n",
    "\n",
    "We know that we can compute complicated functions by combining a number of perceptrons.\n",
    "\n",
    "In the perceptron examples we had set the model parameters (weights and threshold) by hand.\n",
    "\n",
    "This is something we definitely **DO NOT** want to do or even can do for big networks.\n",
    "\n",
    "We want some algorithm to set/learn the model parameters for us!\n",
    "\n",
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <i class=\"fa fa-info-circle\"></i>&nbsp; <strong>Threshold -> bias</strong>  \n",
    "    \n",
    "Before we go further we need to introduce one change. The threshold which we saw in the step activation function above is moved to the left side of the equation and is called **bias**.\n",
    "\n",
    "$$\n",
    "f = \\left\\{\n",
    "        \\begin{array}{ll}\n",
    "            0 & \\quad weighted\\_sum + bias < 0 \\\\\n",
    "            1 & \\quad weighted\\_sum + bias \\geq 0\n",
    "        \\end{array}\n",
    "       \\quad \\quad  \\mathrm{where}, bias = -threshold\n",
    "    \\right.\n",
    "$$\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to algorithmically set/learn the weights and bias we need to choose an appropriate loss function for the problem at hand and solve an optimization problem.\n",
    "We will explain below what this means.\n",
    "\n",
    "\n",
    "### Loss function\n",
    "\n",
    "To learn using an algorithm we need to define a quantity/function which allows us to measure how close or far are the predictions of our network/setup from reality or the supplied labels. This is done by choosing a so-called \"Loss function\" (as in the case for other machine learning algorithms).\n",
    "\n",
    "Once we have this function, we need an algorithm to update the weights of the network such that this loss function decreases. \n",
    "As one can already imagine the choice of an appropriate loss function is critical to the success of the model. \n",
    "\n",
    "Fortunately, for classification and regression (which cover a large variety of problems) these loss functions are well known. \n",
    "\n",
    "**Crossentropy** and **mean squared error** loss functions are often used for standard classification and regression problems, respectively.\n",
    "\n",
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <i class=\"fa fa-info-circle\"></i>&nbsp; As we have seen before, <strong>mean squared error</strong> is defined as \n",
    "\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} \\left((y_1 - \\hat{y}_1)^2 + (y_2 - \\hat{y}_2)^2 + ... + (y_n - \\hat{y}_n)^2 \\right)\n",
    "$$\n",
    "\n",
    "\n",
    "</div>\n",
    "\n",
    "### Gradient based learning\n",
    "\n",
    "As mentioned above, once we have chosen a loss function, we want to solve an **optimization problem** which minimizes this loss by updating the parameters (weights and biases) of the network. This is how the learning takes in a NN, and the \"knowledge\" is stored as the weights and biases.\n",
    "\n",
    "The most popular optimization methods used in Neural Network training are **Gradient-descent (GD)** type methods, such as gradient-descent itself, RMSprop and Adam. \n",
    "\n",
    "**Gradient-descent** uses partial derivatives of the loss function with respect to the network weights and a learning rate to updates the weights such that the loss function decreases and after some iterations reaches its (Global) minimum value.\n",
    "\n",
    "First, the loss function and its derivative are computed at the output node, and this signal is propagated backwards, using the chain rule, in the network to compute the partial derivatives. Hence, this method is called **Backpropagation**.\n",
    "\n",
    "One way to perform a single GD pass is to compute the partial derivatives using **all the samples** in our data, computing average derivatives and using them to update the weights. This is called **Batch gradient descent**. However, in deep learning we mostly work with massive datasets and using batch gradient descent can make the training very slow!\n",
    "\n",
    "The other extreme is to randomly shuffle the dataset and advance a pass of GD with the gradients computed using only **one sample** at a time. This is called **Stochastic gradient descent**.\n",
    "\n",
    "<center>\n",
    "<figure>\n",
    "<img src=\"./images/stochastic-vs-batch-gradient-descent.png\" width=\"600\"/>\n",
    "<figcaption>Source: <a href=\"https://wikidocs.net/3413\">https://wikidocs.net/3413</a></figcaption>\n",
    "</figure>\n",
    "</center>\n",
    "\n",
    "\n",
    "In practice, an approach in-between these two is used. The entire dataset is divided into **m batches** and these are used one by one to compute the derivatives and apply GD. This technique is called **Mini-batch gradient descent**. \n",
    "\n",
    "<div class=\"alert alert-block alert-warning\">\n",
    "<p><i class=\"fa fa-warning\"></i>&nbsp;\n",
    "One pass through the entire training dataset is called 1 epoch of training.\n",
    "</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(10, 4)) ;\n",
    "\n",
    "pts=np.arange(-20,20, 0.1) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Activation Functions\n",
    "\n",
    "In order to train the network we need to move away from Perceptron's **step** activation function because it can not be used for training using the gradient-descent and back-propagation algorithms among other drawbacks.\n",
    "\n",
    "Non-Linear functions such as:\n",
    "\n",
    "* Sigmoid\n",
    "\n",
    "\\begin{equation*}\n",
    "f(z) = \\frac{1}{1+e^{-z}} \\quad \\quad \\mathrm{where}, z = weighted\\_sum + bias\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 254,
       "width": 376
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(pts, 1/(1+np.exp(-pts))) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* tanh\n",
    "\n",
    "\\begin{equation*}\n",
    "f(z) = \\frac{e^{z} - e^{-z}}{e^{z} + e^{-z}}\\quad \\quad \\mathrm{where}, z = weighted\\_sum + bias\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 254,
       "width": 389
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(pts, np.tanh(pts*np.pi)) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* **ReLU (Rectified linear unit)**\n",
    "\n",
    "\\begin{equation*}\n",
    "f(z) = \\mathrm{max}(0,z)   \\quad \\quad \\mathrm{where}, z = weighted\\_sum + bias\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 254,
       "width": 383
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pts_relu=[max(0,i) for i in pts];\n",
    "plt.plot(pts, pts_relu) ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "are some of the commonly used as activation functions. Such non-linear activation functions allow the network to learn complex representations of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "<p><i class=\"fa fa-warning\"></i>&nbsp;\n",
    "ReLU is very popular and is widely used nowadays. There also exist other variations of ReLU, e.g. \"leaky ReLU\".\n",
    "</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<p><i class=\"fa fa-warning\"></i>&nbsp;\n",
    "Why don't we just use a simple linear activation function?\n",
    "    \n",
    "Linear activations are **NOT** used because it can be mathematically shown that if they are used then the output is just a linear function of the input. So we cannot learn interesting and complex functions by adding any number of hidden layers.\n",
    "\n",
    "The only exception when we do want to use a linear activation is for the output layer of a network when solving a regression problem.\n",
    "\n",
    "</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise section\n",
    "\n",
    "### Google Playground\n",
    "\n",
    "A great tool from Google to develop a feeling for the workings of neural networks.\n",
    "\n",
    "https://playground.tensorflow.org/\n",
    "\n",
    "<img src=\"./images/neuralnets/google_playground.png\"/>\n",
    "\n",
    "**Walkthrough by instructor**\n",
    "\n",
    "Some concepts to look at:\n",
    "\n",
    "* Simple vs Complex models (Effect of network size)\n",
    "* Optimization results\n",
    "* Effect of activation functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Keras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is Keras?\n",
    "\n",
    "* It is a high level API to create and work with neural networks\n",
    "* Supports multiple backends such as **TensorFlow** from Google, **Theano** (Although Theano is dead now) and **CNTK** (Microsoft Cognitive Toolkit)\n",
    "* Very good for creating neural nets quickly and hides away a lot of tedious work\n",
    "* Has been incorporated into official TensorFlow (which obviously only works with tensforflow) and as of TensorFlow 2.0 this will the main api to use it\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "<figure>\n",
    "<img src=\"./images/neuralnets/neural_net_keras_1.svg\" width=\"700\"/>\n",
    "<figcaption>Building this model in Keras</figcaption>\n",
    "</figure>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /Users/tarunchadha/anaconda3/envs/mlw-2/lib/python3.6/site-packages/tensorflow/python/framework/op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Colocations handled automatically by placer.\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 4)                 12        \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 4)                 20        \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 1)                 5         \n",
      "_________________________________________________________________\n",
      "activation_1 (Activation)    (None, 1)                 0         \n",
      "=================================================================\n",
      "Total params: 37\n",
      "Trainable params: 37\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Say hello to keras\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation\n",
    "\n",
    "# Creating a model\n",
    "model = Sequential()\n",
    "\n",
    "# Adding layers to this model\n",
    "# 1st Hidden layer\n",
    "# A Dense/fully-connected layer which takes as input a \n",
    "# feature array of shape (samples, num_features)\n",
    "# Here input_shape = (2,) means that the layer expects an input with num_features = 2\n",
    "# and the sample size could be anything\n",
    "# The activation function for this layer is set to \"relu\"\n",
    "model.add(Dense(units=4, input_shape=(2,), activation=\"relu\"))\n",
    "\n",
    "# 2nd Hidden layer\n",
    "# This is also a fully-connected layer and we do not need to specify the\n",
    "# shape of the input anymore (We need to do that only for the first layer)\n",
    "# NOTE: Now we didn't add the activation seperately. Instead we just added it\n",
    "# while calling Dense(). This and the way used for the first layer are Equivalent!\n",