camp_XOR_mlp.ipynb

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   "source": [
    "<a target=\"_blank\" href=\"https://colab.research.google.com/github/cyneuro/ML_camp/blob/main/camp_XOR_mlp.ipynb\">\n",
    "  <img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
    "</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hpyp0-XhZNlq"
   },
   "source": [
    "# CLASSIFYING XOR\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tDWMT_fRaNWt"
   },
   "source": [
    "## Review Activity - Framing the Problem\n",
    "\n",
    "**Linear Regression**\n",
    "\n",
    "1. Define the linear regression problem in words. (What are we trying to do?)\n",
    "2. Now, define the problem in mathematical terms. (What are we adjusting? What are we minimizing?)\n",
    "3. Sketch the details of the problem/math and write pseudocode for an algorithm to implement this.\n",
    "\n",
    "*Notation*:\n",
    "  * Output (value): $y$\n",
    "  * Input (feature): $x$\n",
    "  * Parameters: $m, b$\n",
    "\n",
    "**Logistic Regression**\n",
    "\n",
    "1. Define the logistic regression problem in words.\n",
    "2. Define the problem in mathematical terms.\n",
    "  * How do we draw a line?\n",
    "  * What does that line determine, and how?\n",
    "3. Sketch the details of the problem/math and write pseudocode for an algorithm to implement this.\n",
    "\n",
    "*Notation*:\n",
    "  * Output (class): $y$\n",
    "  * Input (features): $(x_1, x_2)$\n",
    "  * Parameters: $\\theta_0, \\theta_1, \\theta_2$\n"
   ]
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   "source": [
    "## Logic Gates\n",
    "\n",
    "XOR (exclusive OR) is a type of ***logic gate***.\n",
    "<br>\n",
    "Logic gates take two inputs (or more) and produce a boolean output, **true** ($1$) or **false** ($0$).\n",
    "<br>\n",
    "\n",
    "Let's assume any logic gates we use take inputs $A$ and $B$ ($0$ or $1$) and produce an output $Y$ ($0$ or $1$).\n",
    "\n",
    "#### **AND**\n",
    "\n",
    "The **AND** gate, as its name suggests, only returns $1$ when *both* inputs are $1$. If either or both of the inputs, $A$ and $B$, are $0$, then the gate outputs $0$.\n",
    "<table width=25%>\n",
    "  <tr>\n",
    "    <th colspan=3>AND</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <th>$A$</th>\n",
    "    <th>$B$</th>\n",
    "    <th>$Y$</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "</table>\n",
    "<br>\n",
    "\n",
    "#### **OR**\n",
    "\n",
    "The **OR** gate returns $1$ if *any* input is $1$. If $A$ is $1$, *or* $B$, *or* both, $Y=1$. Only if both inputs are $0$ does OR output $0$.\n",
    "<table width=25%>\n",
    "  <tr>\n",
    "    <th colspan=3>OR</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <th>$A$</th>\n",
    "    <th>$B$</th>\n",
    "    <th>$Y$</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "</table>\n",
    "\n",
    "#### **NAND and NOR**\n",
    "\n",
    "**NAND** and **NOR** are short for ***NOT AND*** and ***NOT OR***, i.e. they are the *inverses* of AND and OR.\n",
    "<br>\n",
    "NAND — Anything with a $0$ as either input outputs $1$. If $A$ and $B$ are both $1$, $A$ NAND $B = 0$.\n",
    "<br>\n",
    "NOR — Anything with a $1$ as either input outputs $0$. If $A$ and $B$ are both $0$, $A$ NOR $B = 1$.\n",
    "<table width=25%>\n",
    "  <tr>\n",
    "    <th colspan=3>NAND</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <th>$A$</th>\n",
    "    <th>$B$</th>\n",
    "    <th>$Y$</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "</table>\n",
    "<br>\n",
    "\n",
    "<table width=25%>\n",
    "  <tr>\n",
    "    <th colspan=3>NOR</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <th>$A$</th>\n",
    "    <th>$B$</th>\n",
    "    <th>$Y$</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "</table>\n",
    "\n",
    "#### **XOR**\n",
    "\n",
    "**XOR** means \"exclusive OR\", it outputs $1$ when *only one* input is $1$.\n",
    "<br>\n",
    "It *exclusively* allows one, and only one, of the inputs to be $1$ to output $1$.\n",
    "<table width=25%>\n",
    "  <tr>\n",
    "    <th colspan=3>XOR</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <th>$A$</th>\n",
    "    <th>$B$</th>\n",
    "    <th>$Y$</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "</table>\n",
    "\n",
    "You can think of XOR like two light switches that control the same light bulb. For the light to turn on, only one of the switches can be flipped up."
   ]
  },
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   "metadata": {
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   "source": [
    "## Classifying logic gates\n",
    "\n",
    "Take a look at the plots of XOR, AND, and OR below.\n",
    "\n",
    "If you can recall, in the Logistic Regression tutorial we used one perceptron to separate data into two classes with a single line.\n",
    "\n",
    "Is it possible to separate the data of each of these logic gates with one line?\n",
    "<br>\n",
    "If not, how many lines do you need?"
   ]
  },
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   "outputs": [
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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# XOR\n",
    "XOR_X = [[0, 0], [0, 1], [1, 0], [1, 1]]\n",
    "XOR_y = [0, 1, 1, 0]\n",
    "\n",
    "XOR_classes = {0 : [], 1 : []}\n",
    "for x_i, y_i in zip(XOR_X, XOR_y):\n",
    "  XOR_classes[y_i].append(x_i)\n",
    "\n",
    "# AND\n",
    "AND_X = [[0, 0], [0, 1], [1, 0], [1, 1]]\n",
    "AND_y = [0, 0, 0, 1]\n",
    "\n",
    "AND_classes = {0 : [], 1 : []}\n",
    "for x_i, y_i in zip(AND_X, AND_y):\n",
    "  AND_classes[y_i].append(x_i)\n",
    "\n",
    "# OR\n",
    "OR_X = [[0, 0], [0, 1], [1, 0], [1, 1]]\n",
    "OR_y = [0, 1, 1, 1]\n",
    "\n",
    "OR_classes = {0 : [], 1 : []}\n",
    "for x_i, y_i in zip(OR_X, OR_y):\n",
    "  OR_classes[y_i].append(x_i)\n",
    "\n",
    "# Plotting\n",
    "\n",
    "fig, axs = plt.subplots(1, 3)\n",
    "\n",
    "# XOR\n",
    "axs[0].set_title('XOR')\n",
    "axs[0].set_xlabel('x1')\n",
    "axs[0].set_ylabel('x2')\n",
    "axs[0].scatter(*np.array(XOR_classes[0]).T, s=100, color='tab:blue', label='Class 0')\n",
    "axs[0].scatter(*np.array(XOR_classes[1]).T, s=100, color='tab:red', label='Class 1')\n",
    "\n",
    "# AND\n",
    "axs[1].set_title('AND')\n",
    "axs[1].set_xlabel('x1')\n",
    "axs[1].set_ylabel('x2')\n",
    "axs[1].scatter(*np.array(AND_classes[0]).T, s=100, color='tab:blue')\n",
    "axs[1].scatter(*np.array(AND_classes[1]).T, s=100, color='tab:red')\n",
    "\n",
    "# OR\n",
    "axs[2].set_title('OR')\n",
    "axs[2].set_xlabel('x1')\n",
    "axs[2].set_ylabel('x2')\n",
    "axs[2].scatter(*np.array(OR_classes[0]).T, s=100, color='tab:blue')\n",
    "axs[2].scatter(*np.array(OR_classes[1]).T, s=100, color='tab:red')\n",
    "\n",
    "for ax in axs:\n",
    "  ax.grid()\n",
    "  ax.set_aspect('equal')\n",
    "  ax.set_xlim([-0.5, 1.5])\n",
    "  ax.set_ylim([-0.5, 1.5])\n",
    "\n",
    "plt.subplots_adjust(wspace = 0.75)\n",
    "fig.legend(loc='upper center')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fElowmStZe-u"
   },
   "source": [
    "Let's try to use a single perceptron to classify each of these and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 405
    },
    "id": "1aXTeTA9ZYWe",
    "outputId": "813a70fe-f10e-46cd-d6ce-843282e04685"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-83-1d6bb0973ffa>:22: RuntimeWarning: invalid value encountered in true_divide\n",
      "  y_pred = (-theta_1 * x_in - theta_0) / theta_2\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title **Challenge: What went wrong with the XOR plot and how can we fix it?**\n",
    "from sklearn.linear_model import Perceptron\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.lines import Line2D\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Plotting function\n",
    "\n",
    "def plot_perceptron(model, classes, ax, title):\n",
    "  # Plot dataset\n",
    "  ax.scatter(*np.asarray(classes[0]).T, color='tab:blue', s=100)\n",
    "  ax.scatter(*np.asarray(classes[1]).T, color='tab:red', s=100)\n",
    "\n",
    "  # Plot decision boundary\n",
    "  # Get θ-values from the model\n",
    "  theta_0 = model.intercept_[0]\n",
    "  theta_1, theta_2 = model.coef_[0]\n",
    "\n",
    "  x_in = np.linspace(-0.5, 1.5, 50)\n",
    "  y_pred = (-theta_1 * x_in - theta_0) / theta_2\n",
    "\n",
    "  ax.plot(x_in, y_pred, color='tab:green')\n",
    "\n",
    "  ax.set_title(title)\n",
    "  ax.set_xlim([-0.5, 1.5])\n",
    "  ax.set_ylim([-0.5, 1.5])\n",
    "  ax.set_xlabel('x1')\n",
    "  ax.set_ylabel('x2')\n",
    "  ax.grid()\n",
    "  ax.set_aspect('equal')\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Data\n",
    "\n",
    "# XOR\n",
    "XOR_X = np.array(\n",
    "        [[0, 0],\n",
    "         [0, 1],\n",
    "         [1, 0],\n",
    "         [1, 1]])\n",
    "\n",
    "XOR_y = np.array([0, 1, 1, 0])\n",
    "\n",
    "XOR_classes = {0 : [], 1 : []}\n",
    "for x_i, y_i in zip(XOR_X, XOR_y):\n",
    "  XOR_classes[y_i].append(x_i)\n",
    "\n",
    "# AND\n",
    "AND_X = np.array(\n",
    "        [[0, 0],\n",
    "         [0, 1],\n",
    "         [1, 0],\n",
    "         [1, 1]])\n",
    "\n",
    "AND_y = np.array([0, 0, 0, 1])\n",
    "\n",
    "AND_classes = {0 : [], 1 : []}\n",
    "for x_i, y_i in zip(AND_X, AND_y):\n",
    "  AND_classes[y_i].append(x_i)\n",
    "\n",
    "# OR\n",
    "OR_X = np.array(\n",
    "       [[0, 0],\n",
    "        [0, 1],\n",
    "        [1, 0],\n",
    "        [1, 1]])\n",
    "\n",
    "OR_y = np.array([0, 1, 1, 1])\n",
    "\n",
    "OR_classes = {0 : [], 1 : []}\n",
    "for x_i, y_i in zip(OR_X, OR_y):\n",
    "  OR_classes[y_i].append(x_i)\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Create a Perceptron and fit it to each dataset\n",
    "\n",
    "model = Perceptron()\n",
    "\n",
    "# Set up plot\n",
    "fig, axs = plt.subplots(1, 3)\n",
    "\n",
    "# Fit the perceptron to the XOR dataset and plot\n",
    "model.fit(XOR_X, XOR_y)\n",
    "plot_perceptron(model, XOR_classes, axs[0], 'XOR')\n",
    "\n",
    "# Fit the perceptron to the AND dataset and plot\n",
    "model.fit(AND_X, AND_y)\n",
    "plot_perceptron(model, AND_classes, axs[1], 'AND')\n",
    "\n",
    "# Fit the perceptron to the OR dataset and plot\n",
    "model.fit(OR_X, OR_y)\n",
    "plot_perceptron(model, OR_classes, axs[2], 'OR')\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Adjust plot legend\n",
    "\n",
    "plt.subplots_adjust(wspace = 0.75)\n",
    "\n",
    "# Create a legend for the whole figure\n",
    "legend_elements = [Line2D([0], [0], marker='o', color='w', markerfacecolor='tab:blue', markersize=10, label='Class 0'),\n",
    "                   Line2D([0], [0], marker='o', color='w', markerfacecolor='tab:red', markersize=10, label='Class 1'),\n",
    "                   Line2D([0], [0], color='tab:green', lw=2, label='Decision Boundary')]\n",
    "fig.legend(handles=legend_elements, loc='upper center')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Hz_eqClPSTl5"
   },
   "source": [
    "### Introducing Multilayered Perceptrons\n",
    "\n",
    "Unlike AND and OR, XOR *cannot* be classified using one line.\n",
    "<br>\n",
    "No matter where you place the line, at least one point will be incorrectly classified.\n",
    "<br></br>\n",
    "However, what if we were able to draw *two* lines?\n",
    "<br></br>\n",
    "That's where the **Multilayered Perceptron (MLP)** comes in.\n",
    "<br>\n",
    "MLPs are exactly what they sound like: **layers of perceptrons that take inputs from the previous layer and output to the next layer, passing through each layer until a single output is found in the final layer.**\n",
    "<br></br>\n",
    "**Let's see what that looks like visually:**\n",
    "\n",
    "A *single* perceptron, as shown in the AND and OR plots above, can only draw *one* line.\n",
    "\n",
    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)\n",
    "<br></br>\n",
    "However, if we use the *combined* output of *two* perceptrons, we can classify the XOR problem with two lines.\n",
    "\n",
    "In the diagram, for the sake of simplicity, each perceptron is condensed into a single circle ($h_1$, $h_2$) that takes in inputs ($x_0, x_1, x_2$) and computes an output ($\\hat{y}$).\n",
    "\n",
    "The weighted sum ($∑$) and sigmoid activation functions ($σ(z)$) for each perceptron won't be shown but still exist as part of the computation within the circle.\n",
    "\n",
    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)\n",
    "<br></br>\n",
    "So, what exactly is happening in this MLP layout?\n",
    "\n",
    "The model is divided into three layers: the ***input layer***, the ***hidden layer***, and the ***output layer***.\n",
    "\n",
    "1. Both perceptrons, $h_1$ and $h_2$, receive data from the input layer ($x_0, x_1, x_2$). **Remember, $x_0$ is for *bias* and *always* equals $1$.**\n",
    "2. $h_1$ and $h_2$ then compute a weighted sum ($z$) on the inputs with their respective weights ($\\theta_0, \\theta_1, \\theta_2$), shown as colored arrows connecting perceptrons).\n",
    "3. The perceptrons then *squash* their weighted sums with the sigmoid function ($\\sigma(z)$), obtaining their outputs. We'll call them $\\hat{y_1}$ and $\\hat{y_2}$ for the outputs of $h_1$ and $h_2$, respectively.\n",
    "4. The outputs of the hidden layer, $\\hat{y_1}$ and $\\hat{y_2}$, are then used as the *inputs* to the perceptron $o$ in the output layer.\n",
    "5. The perceptron in the output layer, $o$, essentially acts as an AND gate to the outputs of the hidden layer, forming a *combined* boundary for classification based on the boundaries drawn by both $h_1$ and $h_2$.\n",
    "\n",
    "In essence, perceptrons $h_1$ and $h_2$ both draw a decision boundary line like normal based on the data in the input layer.\n",
    "<br>\n",
    "The decision boundaries are then brought together in the output layer to form one unified solution.\n",
    "<br></br>\n",
    "The process of passing data into the input layer, through the hidden layers, and out of the output layer is known as **forward propagation** (the data propagates *forward* through the model).\n",
    "<br></br>\n",
    "**Let's try implementing this with sklearn!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 541
    },
    "id": "jYKSB993GV-s",
    "outputId": "33823ebb-1826-4ac7-9b60-4e919bb0b1b0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([[ 1.68881792, -1.45309046],\n",
      "       [ 1.68900732, -1.45245966]]), array([[-2.06978946],\n",
      "       [-2.53494834]])]\n",
      "[array([-1.68921254,  1.45229639]), array([1.48000545])]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neural_network import MLPClassifier\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.lines import Line2D\n",
    "import numpy as np\n",
    "\n",
    "#----------------------------------------------#\n",
    "\n",
    "# XOR Data\n",
    "\n",
    "X = np.array(\n",
    "        [[0, 0],\n",
    "         [0, 1],\n",
    "         [1, 0],\n",
    "         [1, 1]])\n",
    "\n",
    "y = np.array([0, 1, 1, 0])\n",
    "\n",
    "#----------------------------------------------#\n",
    "\n",
    "# Create MLP with 2 neurons in the hidden layer\n",
    "model = MLPClassifier(hidden_layer_sizes=(2,), alpha=0.02, max_iter=8000, random_state=6)\n",
    "\n",
    "# Fit the MLP to the data\n",
    "model.fit(X, y)\n",
    "\n",
    "#----------------------------------------------#\n",
    "\n",
    "# Plotting\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Generate a grid over the input space to plot the color of the\n",
    "# classification at that grid point\n",
    "x_min, x_max = -0.5, 1.5\n",
    "y_min, y_max = -0.5, 1.5\n",
    "\n",
    "# Find model predictions over grid of entire plot\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, .02),\n",
    "                     np.arange(y_min, y_max, .02))\n",
    "predictions = model.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "predictions = predictions.reshape(xx.shape)\n",
    "\n",
    "# Create a contour plot of the decision boundary\n",
    "ax.contourf(xx, yy, predictions, cmap=plt.cm.Spectral_r, alpha=0.5)\n",
    "\n",
    "# Plot the data points\n",
    "ax.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral_r, edgecolors='k')\n",
    "\n",
    "# Adjust the plot\n",
    "legend_elements = [Line2D([0], [0], linestyle='', marker='o', color='w', markerfacecolor='tab:blue', markersize=10, label='Class 0'),\n",
    "                   Line2D([0], [0], linestyle='', marker='o', color='w', markerfacecolor='tab:red', markersize=10, label='Class 1')]\n",
    "ax.legend(handles=legend_elements, loc='upper left')\n",
    "ax.set_title('XOR With MLP')\n",
    "ax.set_xlabel('x1')\n",
    "ax.set_ylabel('x2')\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# Display the plot\n",
    "plt.show()\n",
    "\n",
    "weights = model.coefs_\n",
    "bias = model.intercepts_\n",
    "\n",
    "print(weights)\n",
    "print(bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LDMS2EklSN7Y"
   },
   "source": [
    "Run the code below to plot XOR with noise. Noise may be added to classification problems to make the data more difficult to classify."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 504,
     "referenced_widgets": [
      "dc0b6fc30541407994542e645e0cbed1",
      "ad067c21b1b243809ed2140546c95357",
      "adc115a5dcd14bf8823dc8715242718d",
      "b2dbdfc083014159a80441680c1281a9",
      "d2d5e957586d457a86923218897a1970",
      "60db48f81752454c90690bd11d0f7b90",
      "f9ab1dc54e53436ab6c465f5f60247dc"
     ]
    },
    "id": "n3u8HHcxWfEt",
    "outputId": "bcd36520-277c-4690-9705-968a1bf07bc1"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dc0b6fc30541407994542e645e0cbed1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='noise', max=0.5, step=0.01), Output()), _dom_classes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "\n",
    "def plot_with_noise(noise):\n",
    "  # Generate random XOR values\n",
    "  A = np.random.choice([0, 1], size=100).astype(float)\n",
    "  B = np.random.choice([0, 1], size=100).astype(float)\n",
    "  Y = np.logical_xor(A, B)\n",
    "\n",
    "  # Add noise to points\n",
    "  A_noise = np.random.uniform(-noise, noise, 100)\n",
    "  B_noise = np.random.uniform(-noise, noise, 100)\n",
    "  A += A_noise\n",
    "  B += B_noise\n",
    "\n",
    "  # Create a plot\n",
    "  fig, ax = plt.subplots()\n",
    "\n",
    "  # Sort data by class\n",
    "  classes = {False: [], True: []}\n",
    "  data = zip((zip(A, B)), Y)\n",
    "  for x_i, y_i in data:\n",
    "    classes[y_i].append(x_i)\n",
    "\n",
    "  # Plot data points\n",
    "  ax.scatter(*np.array(classes[False]).T, color='tab:blue', label='Class 0 (false)')\n",
    "  ax.scatter(*np.array(classes[True]).T, color='tab:red', label='Class 1 (true)')\n",
    "\n",
    "  # Adjust plot\n",
    "  ax.set_title('XOR')\n",
    "  ax.set_xlabel('x1')\n",
    "  ax.set_ylabel('x2')\n",
    "  ax.set_xlim([-0.5, 1.5])\n",
    "  ax.set_ylim([-0.5, 1.5])\n",
    "  ax.set_aspect('equal')\n",
    "  ax.legend(loc='upper right')\n",
    "  ax.grid()\n",
    "\n",
    "  # Display plot\n",
    "  plt.show()\n",
    "\n",
    "# Controls noise slider\n",
    "_ = interact(plot_with_noise, noise=FloatSlider(value=0, min=0, max=0.5, step=0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qnDtkJr9qVK6"
   },
   "source": [
    "### Advanced - Updating Weights and Biases\n",
    "\n",
    "Updating the parameters for each perceptron in an MLP is a more complicated process than for a single perceptron.  \n",
    "\n",
    "However, it follows the same basic principle: **Calculate the gradients of loss with respect to each parameter, then update using the update rule**.\n",
    "\n",
    "What complicates things, though, is the forward propagating nature of the model.\n",
    "\n",
    "To compute gradients based on loss (only after an output is calculated), you have to trace your steps *backwards* through the model, calculating gradients in *reverse order*.\n",
    "<br></br>\n",
    "The process of calculating gradients *backwards* from the output layer to the first hidden layer is known as ***backpropagation***.\n",
    "<br></br>\n",
    "Though the concepts surrounding backpropagation are too advanced for this course, you can check out the video below to get an idea of what it means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 322
    },
    "id": "xHNGWgtftWVK",
    "outputId": "968b765e-e047-468f-99be-53798468de57"
   },
   "outputs": [
    {
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",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/Ilg3gGewQ5U\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f0e6225b340>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title **3Blue1Brown Video - Backpropagation**\n",
    "\n",
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('Ilg3gGewQ5U')"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  },
  "language_info": {
   "name": "python"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "60db48f81752454c90690bd11d0f7b90": {
     "model_module": "@jupyter-widgets/controls",
     "model_module_version": "1.5.0",
     "model_name": "SliderStyleModel",
     "state": {
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "SliderStyleModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/base",
      "_view_module_version": "1.2.0",
      "_view_name": "StyleView",
      "description_width": "",
      "handle_color": null
     }
    },
    "ad067c21b1b243809ed2140546c95357": {
     "model_module": "@jupyter-widgets/controls",
     "model_module_version": "1.5.0",
     "model_name": "FloatSliderModel",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/controls",
      "_model_module_version": "1.5.0",
      "_model_name": "FloatSliderModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/controls",
      "_view_module_version": "1.5.0",
      "_view_name": "FloatSliderView",
      "continuous_update": true,
      "description": "noise",
      "description_tooltip": null,
      "disabled": false,
      "layout": "IPY_MODEL_d2d5e957586d457a86923218897a1970",
      "max": 0.5,
      "min": 0,
      "orientation": "horizontal",
      "readout": true,
      "readout_format": ".2f",
      "step": 0.01,
      "style": "IPY_MODEL_60db48f81752454c90690bd11d0f7b90",
      "value": 0
     }
    },
    "adc115a5dcd14bf8823dc8715242718d": {
     "model_module": "@jupyter-widgets/output",
     "model_module_version": "1.0.0",
     "model_name": "OutputModel",
     "state": {
      "_dom_classes": [],
      "_model_module": "@jupyter-widgets/output",
      "_model_module_version": "1.0.0",
      "_model_name": "OutputModel",
      "_view_count": null,
      "_view_module": "@jupyter-widgets/output",
      "_view_module_version": "1.0.0",
      "_view_name": "OutputView",
      "layout": "IPY_MODEL_f9ab1dc54e53436ab6c465f5f60247dc",
      "msg_id": "",
      "outputs": [
       {
        "data": {
         "image/png": 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