{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Improving the Performance of the MNIST Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import keras\n",
    "plt.rcParams[\"figure.figsize\"] = (4,3)  # default figure size: 4x3 inches"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.datasets import mnist\n",
    "from keras.utils import to_categorical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# return images of type float32 in the range 0-1\n",
    "def load_normalized_mnist_data():\n",
    "    (train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
    "    # scale the pixel values to the range 0-1\n",
    "    train_images = train_images.astype('float32') / 255\n",
    "    test_images = test_images.astype('float32') / 255\n",
    "    return (train_images, train_labels), (test_images, test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "(train_images,train_labels), (test_images,test_labels) = load_normalized_mnist_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# create the one-hot target vectors\n",
    "train_targets, test_targets = to_categorical(train_labels), to_categorical(test_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 10)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_targets.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def show_random_images():\n",
    "    images = test_images\n",
    "    labels = test_labels\n",
    "    plt.figure(figsize=(12,12))  # (width, height) in inches\n",
    "    rows, columns = 5, 6\n",
    "    for i in range(1, columns*rows+1):\n",
    "        n = random.randrange(len(images))\n",
    "        plt.subplot(rows, columns, i)\n",
    "        plt.title(f\"{labels[n]}\")\n",
    "        plt.axis('off')\n",
    "        plt.imshow(images[n], cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x1200 with 30 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_random_images()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the Classification Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "<img src=\"http://science.slc.edu/jmarshall/bioai/images/mnist-network-with-flatten.png\" width=\"55%\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Flatten, Dense, Input\n",
    "from keras.optimizers import SGD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def build_network():\n",
    "    network = Sequential()\n",
    "    network.add(Input(shape=(28,28)))\n",
    "    network.add(Flatten())\n",
    "    network.add(Dense(30, activation='sigmoid', name='hidden'))\n",
    "    network.add(Dense(10, activation='sigmoid', name='output'))\n",
    "    network.compile(loss='mean_squared_error',\n",
    "                    optimizer=SGD(learning_rate=0.01, momentum=0.9), # defaults: 0.01, 0\n",
    "                    metrics=['accuracy'])\n",
    "    return network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "network = build_network()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">Model: \"sequential_1\"</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1mModel: \"sequential_1\"\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Layer (type)                    </span>┃<span style=\"font-weight: bold\"> Output Shape           </span>┃<span style=\"font-weight: bold\">       Param # </span>┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ flatten_1 (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Flatten</span>)             │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">784</span>)            │             <span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ hidden (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                  │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">30</span>)             │        <span style=\"color: #00af00; text-decoration-color: #00af00\">23,550</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ output (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                  │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">10</span>)             │           <span style=\"color: #00af00; text-decoration-color: #00af00\">310</span> │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mLayer (type)                   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mOutput Shape          \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m      Param #\u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ flatten_1 (\u001b[38;5;33mFlatten\u001b[0m)             │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m784\u001b[0m)            │             \u001b[38;5;34m0\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ hidden (\u001b[38;5;33mDense\u001b[0m)                  │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m30\u001b[0m)             │        \u001b[38;5;34m23,550\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ output (\u001b[38;5;33mDense\u001b[0m)                  │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m10\u001b[0m)             │           \u001b[38;5;34m310\u001b[0m │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Total params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">23,860</span> (93.20 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Total params: \u001b[0m\u001b[38;5;34m23,860\u001b[0m (93.20 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">23,860</span> (93.20 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Trainable params: \u001b[0m\u001b[38;5;34m23,860\u001b[0m (93.20 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Non-trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> (0.00 B)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Non-trainable params: \u001b[0m\u001b[38;5;34m0\u001b[0m (0.00 B)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "network.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train and Evaluate the Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "\u001b[1m   1/1875\u001b[0m \u001b[37m━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[1m9:17\u001b[0m 298ms/step - accuracy: 0.0625 - loss: 0.2692"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2026-04-06 16:11:12.025444: I tensorflow/core/grappler/optimizers/custom_graph_optimizer_registry.cc:117] Plugin optimizer for device_type GPU is enabled.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 3ms/step - accuracy: 0.3778 - loss: 0.0908\n",
      "Epoch 2/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 3ms/step - accuracy: 0.5725 - loss: 0.0753\n",
      "Epoch 3/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 3ms/step - accuracy: 0.6967 - loss: 0.0628\n",
      "Epoch 4/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 3ms/step - accuracy: 0.7599 - loss: 0.0530\n",
      "Epoch 5/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 3ms/step - accuracy: 0.8002 - loss: 0.0460\n"
     ]
    }
   ],
   "source": [
    "history = network.fit(train_images, train_targets, epochs=5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 3ms/step - accuracy: 0.8155 - loss: 0.0431\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.04311462119221687, 0.8154833316802979]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.evaluate(train_images, train_targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 3ms/step - accuracy: 0.8229 - loss: 0.0424\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.042420439422130585, 0.8228999972343445]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.evaluate(test_images, test_targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def plot_history(history):\n",
    "    loss_values = history.history['loss']\n",
    "    accuracy_values = history.history['accuracy']\n",
    "    epoch_nums = range(1, len(loss_values)+1)\n",
    "    plt.figure(figsize=(12,4)) # width, height in inches\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(epoch_nums, loss_values, 'r')\n",
    "    plt.title(\"Training loss\")\n",
    "    plt.xlabel(\"Epochs\")\n",
    "    plt.ylabel(\"Loss\")\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(epoch_nums, accuracy_values, 'b')\n",
    "    plt.title(\"Training accuracy\")\n",
    "    plt.xlabel(\"Epochs\")\n",
    "    plt.ylabel(\"Accuracy\")\n",
    "    plt.ylim(0, 1)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_history(history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def show_wrong_images():\n",
    "    outputs = network.predict(test_images)\n",
    "    predictions = [np.argmax(output) for output in outputs]\n",
    "    wrong = [i for i in range(10000) if predictions[i] != test_labels[i]]\n",
    "    print(f\"Misclassified {len(wrong)} test images out of {len(test_images)}\")\n",
    "    plt.figure(figsize=(12,12))  # (width, height) in inches\n",
    "    rows, columns = 5, 6\n",
    "    for i in range(1, columns*rows+1):\n",
    "        w = random.choice(wrong)\n",
    "        img = test_images[w]\n",
    "        correct_label = test_labels[w]\n",
    "        prediction = predictions[w]\n",
    "        plt.subplot(rows, columns, i)\n",
    "        plt.title(f'\"{prediction}\"  (correct: {correct_label})')\n",
    "        plt.axis('off')\n",
    "        plt.imshow(img, cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 1ms/step\n",
      "Misclassified 1771 test images out of 10000\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x1200 with 30 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_wrong_images()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "### Activation Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Sigmoid\n",
    "\n",
    "$\\sigma(x) = \\dfrac{1}{1 + e^{-x}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + math.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "[sigmoid(x) for x in [0, 1, 2, -3, -4, 5]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_values = np.arange(-5, 5, 0.1)\n",
    "plt.plot(x_values, [sigmoid(x) for x in x_values])\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(0, 1)\n",
    "plt.title(\"Sigmoid Unit\")\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Activation\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Linear\n",
    "\n",
    "Linear($x$) = $x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def linear(x):\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "[linear(x) for x in [0, 1, 2, -3, -4, 5]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_values = np.arange(-2, 2, 0.1)\n",
    "plt.plot(x_values, [linear(x) for x in x_values])\n",
    "plt.xlim(-2, 2)\n",
    "plt.ylim(-2, 2)\n",
    "plt.title(\"Linear Unit\")\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Activation\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### ReLU (Rectified Linear Unit)\n",
    "\n",
    "ReLU($x$) = $max(x, 0)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def ReLU(x):\n",
    "    return max(x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "[ReLU(x) for x in [0, 1, 2, -3, -4, 5]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_values = np.arange(-2, 2, 0.1)\n",
    "plt.plot(x_values, [ReLU(x) for x in x_values])\n",
    "plt.xlim(-2, 2)\n",
    "plt.ylim(-0.5, 2)\n",
    "plt.title(\"Rectified Linear Unit (ReLU)\")\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Activation\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "$ \\mathbf{x} = [x_1, x_2, x_3, \\ldots , x_n]$\n",
    "\n",
    "Softmax($\\mathbf{x}$) $= {\\large \\dfrac{e^{x_i}}{{\\LARGE \\Sigma_{i}} ~ e^{x_i} }}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def softmax(x_values):\n",
    "    powers = [math.exp(x) for x in x_values]\n",
    "    total = sum(powers)\n",
    "    return [ex/total for ex in powers]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "softmax([1,1,1,1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sum(softmax([1,1,1,1,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "softmax([0, 1, 2, -3, -4, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum (softmax([0, 1, 2, -3, -4, 5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "softmax([6,5,5,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sum(softmax([6,5,5,5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The softmax output values always sum to 1.0, so the output can be interpreted as a **probability distribution**.  The name \"softmax\" is short for \"soft argmax\".  The greater the difference between the maximum value in the input vector and the other values, the more closely the output of softmax approximates a one-hot vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "softmax([30,10,7,100,40,25,3,9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sum(softmax([30,10,7,100,40,25,3,9]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sum([30,10,7,100,40,25,3,9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "softmax([2.5, -1, 3.2, 0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "[Interactive demo of softmax](http://neuralnetworksanddeeplearning.com/chap3.html#eqtn78) &nbsp; (from Michael Nielsen's book [*Neural Networks and Deep Learning*](http://neuralnetworksanddeeplearning.com))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "### Types of Learning Tasks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Binary classification\n",
    "* Example: Detecting sunglasses: yes / no\n",
    "* Single output unit\n",
    "* Output-layer activation function: <font color=\"blue\">**sigmoid**</font>\n",
    "* Example target values: 0, 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Multiclass classification\n",
    "* Example: Classifying poses: left / forward / up / right\n",
    "* Multiple output units\n",
    "* Output-layer activation function: <font color=\"blue\">**softmax**</font>\n",
    "* Example target vectors: [1, 0, 0, 0], &nbsp; [0, 0, 1, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Regression (predicting arbitrary values)\n",
    "* Example: Predicting housing prices\n",
    "* Single or multiple output units\n",
    "* Output-layer activation function: <font color=\"blue\">**linear**</font>\n",
    "* Example target values: 0.5, 3.8, -12.6, 516.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "### Loss Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Mean-squared-error (single output unit)\n",
    "\n",
    "$C = \\dfrac{1}{n}\n",
    "\\displaystyle\\sum\\limits_{\\textit{patterns}} \\,\n",
    "\\tfrac{1}{2}\\,(y - a)^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Example:\n",
    "\n",
    "<img src=\"http://science.slc.edu/jmarshall/bioai/images/dataset1.png\" width=\"40%\">\n",
    "\n",
    "${\\scriptsize = \\dfrac{1}{8} \\bigg( \\frac{1}{2}(0 - 0.80)^2 + \\frac{1}{2}(0 - 0.77)^2 +\n",
    "\\frac{1}{2}(0 - 0.82)^2 + \\frac{1}{2}(1 - 0.60)^2 + \\frac{1}{2}(0 - 0.53)^2 + \\frac{1}{2}(1 - 0.59)^2 + \\frac{1}{2}(1 - 0.73)^2 + \\frac{1}{2}(1 - 0.81)^2 \\bigg)}$\n",
    "\n",
    "${\\scriptsize = 0.164}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Mean-squared-error (multiple output units)\n",
    "\n",
    "$C = \\dfrac{1}{n}\n",
    "\\displaystyle\\sum\\limits_{\\textit{patterns}} \\,\n",
    "\\displaystyle\\sum\\limits_{i} \\,\n",
    "\\tfrac{1}{2}\\,({y_i} - {a_i})^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Example:\n",
    "\n",
    "<img src=\"http://science.slc.edu/jmarshall/bioai/images/dataset2.png\" width=\"60%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Mean-squared-error with sigmoid units can cause problems\n",
    "\n",
    "Learning task: &nbsp; input $x$ **= 1** $\\,\\rightarrow\\,$ output $y$ **= 0**\n",
    "\n",
    "<img src=\"http://neuralnetworksanddeeplearning.com/images/tikz28.png\" width=\"30%\">\n",
    "\n",
    "[Demo of learning with mean-squared-error](http://neuralnetworksanddeeplearning.com/chap3.html) &nbsp; (from Michael Nielsen's book [*Neural Networks and Deep Learning*](http://neuralnetworksanddeeplearning.com))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "$\\Delta w_{ij} = -\\eta \\dfrac{\\partial C}{\\partial w_{ij}}$\n",
    "\n",
    "$\\dfrac{\\partial C}{\\partial w_{ij}} = (a_i - y_i)\\,a_i\\,(1 - a_i)\\,a_j~~~$ using the **mean-squared error** cost function $C$\n",
    "\n",
    "$\\dfrac{\\partial C}{\\partial w} = (a - y)\\,a\\,(1 - a)\\,x~~~$ for the above example neuron with a single weight\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The term $(a - y)$ represents the neuron's actual error, that is, how far off the neuron's output $a$ is from the correct answer $y$.  But when $a$ is close to 0 or close to 1, the term $a\\,(1 - a)$ is close to 0, which makes the error term $(a - y)$ essentially irrelevant because it gets multiplied by a number close to 0.  Consequently, $\\frac{\\partial C}{\\partial w}$ is close to 0, which makes the weight change $\\Delta w$ close to 0, meaning that **learning is very slow!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Binary cross-entropy (single output unit)\n",
    "\n",
    "$C ~=~ -\\dfrac{1}{n}\n",
    "\\displaystyle\\sum\\limits_{\\textit{patterns}} \\left[y \\ln a + (1-y ) \\ln (1-a) \\right]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_values = np.arange(0.005, 1.6, 0.001)\n",
    "plt.plot(x_values, np.log(x_values))\n",
    "plt.xlim(-0.01, 1.75)\n",
    "plt.ylim(-5, 1)\n",
    "plt.title(\"Natural logarithm function ln(x)\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"ln(x)\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Example:\n",
    "\n",
    "<img src=\"http://science.slc.edu/jmarshall/bioai/images/dataset1.png\" width=\"40%\">\n",
    "\n",
    "${\\scriptsize = -\\dfrac{1}{8} \\bigg( \\ln(1 - 0.80) + \\ln(1 - 0.77) + \\ln(1 - 0.82) +\n",
    "\\ln(0.60) + \\ln(1 - 0.53) + \\ln(0.59) + \\ln(0.73) + \\ln(0.81) \\bigg)}$\n",
    "\n",
    "${\\scriptsize = 0.889}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Cross-entropy avoids learning slowdown with sigmoid output units\n",
    "\n",
    "Learning task: &nbsp; input $x$ = **1** $\\,\\rightarrow\\,$ output $y$ = **0**\n",
    "\n",
    "<img src=\"http://neuralnetworksanddeeplearning.com/images/tikz28.png\" width=\"30%\">\n",
    "\n",
    "[Demo of learning with cross-entropy](http://neuralnetworksanddeeplearning.com/chap3.html#eqtn62) &nbsp; (from Michael Nielsen's book [*Neural Networks and Deep Learning*](http://neuralnetworksanddeeplearning.com))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "$\\Delta w_{ij} = -\\eta \\dfrac{\\partial C}{\\partial w_{ij}}$\n",
    "\n",
    "$\\dfrac{\\partial C}{\\partial w_{ij}} = (a_i - y_i)\\,a_j~~~$ using the **cross-entropy** cost function $C$\n",
    "\n",
    "$\\dfrac{\\partial C}{\\partial w} = (a - y)\\,x~~~$ for the above example neuron with a single weight"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "This time, the error term $(a - y)$ influences $\\frac{\\partial C}{\\partial w}$ **independently** of the value of the neuron's output $a$.  The larger the error, the larger the weight change $\\Delta w$ will be.  So there is **no more learning slowdown** when the neuron's output is far off from the correct answer!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Categorical cross-entropy (multiple output units)\n",
    "\n",
    "$C ~=~ -\\dfrac{1}{n}\n",
    "\\displaystyle\\sum\\limits_{\\textit{patterns}} \\,\n",
    "\\displaystyle\\sum\\limits_{i} \\,\n",
    "\\left[ {y_i} \\ln {a_i} + (1-{y_i})\\ln (1-{a_i}) \\right]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Problem type|Output-layer activation function|Loss function\n",
    "--|:--:|--\n",
    "Binary classification | sigmoid | binary_crossentropy\n",
    "Multi-category classification | softmax | categorical_crossentropy\n",
    "Predicting arbitrary values | linear | mean_squared_error\n",
    "Predicting values between 0 and 1 | sigmoid | mean_squared_error *or* binary_crossentropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### The Problem of Vanishing Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Sigmoid Units in a Deep Network\n",
    "\n",
    "$w_i$ = weight into the $i^{\\text{th}}$ neuron\n",
    "\n",
    "$b_i$ = bias of the $i^{\\text{th}}$ neuron\n",
    "\n",
    "$z_i$ = sum of inputs into the $i^{\\text{th}}$ neuron = $w_i \\cdot a_{i-1} + b_i$\n",
    "\n",
    "$a_i$ = output activation of the $i^{\\text{th}}$ neuron = $\\sigma(z_i) = \\dfrac{1}{1 + e^{-z_i}}$\n",
    "\n",
    "<img src=\"http://science.slc.edu/jmarshall/bioai/images/simple-deep-network.png\" width=\"55%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Update rule for bias $b_1$: &nbsp;&nbsp; $\\Delta b_1 = -\\eta \\dfrac{\\partial C}{\\partial b_1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "$\\dfrac{\\partial C}{\\partial b_1}$ is the influence of bias $b_1$ on the total cost $C$, which we can express as a \"cascade of influences\" using the chain rule:\n",
    "\n",
    "$\\dfrac{\\partial C}{\\partial b_1} =\n",
    "\\dfrac{\\partial z_1}{\\partial b_1} \\times\n",
    "\\dfrac{\\partial a_1}{\\partial z_1} \\times\n",
    "\\dfrac{\\partial z_2}{\\partial a_1} \\times\n",
    "\\dfrac{\\partial a_2}{\\partial z_2} \\times\n",
    "\\dfrac{\\partial z_3}{\\partial a_2} \\times\n",
    "\\dfrac{\\partial a_3}{\\partial z_3} \\times\n",
    "\\dfrac{\\partial z_4}{\\partial a_3} \\times\n",
    "\\dfrac{\\partial a_4}{\\partial z_4} \\times\n",
    "\\dfrac{\\partial C}{\\partial a_4}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "$~~~~~~~= 1 ~\\times \\sigma'(z_1) \\times w_2 \\times \\sigma'(z_2) \\times w_3 \\times \\sigma'(z_3)\n",
    "\\times w_4 \\times \\sigma'(z_4) \\times \\dfrac{\\partial C}{\\partial a_4}$\n",
    "\n",
    "where $\\sigma'(z_i)$ is the derivative of the sigmoid function $\\dfrac{1}{1 + e^{-z_i}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The derivative $\\sigma'(z_i)$ equals $a_i(1 - a_i)$, as we saw when we went through the [derivation of backpropagation](http://science.slc.edu/jmarshall/bioai/notes/backprop-algorithm-derivation.pdf) in class. Consequently, hidden units with activations close to 0 or 1 will make this factor small, and multiplying many such factors together will **dramatically reduce the gradient values** in earlier layers of the network, which means that **learning will be very slow**, regardless of which cost function we use."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Rectified Linear Units\n",
    "\n",
    "One proposed solution that has been empirically shown to help reduce the problem of vanishing gradients in practice is to have the hidden layers use the **ReLU activation function** instead of the sigmoid function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_values = np.arange(-2, 2, 0.1)\n",
    "plt.plot(x_values, [ReLU(x) for x in x_values])\n",
    "plt.xlim(-2, 2)\n",
    "plt.ylim(-0.5, 2)\n",
    "plt.title(\"Rectified Linear Unit (ReLU)\")\n",
    "plt.xlabel(\"Input\")\n",
    "plt.ylabel(\"Activation\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The derivative of the ReLU function is simply 1 when its input is greater than zero, which avoids the problematic factors $a_i\\,(1 - a_i)$ that arise from the derivative of the sigmoid function.  Of course, if the input to the ReLU unit is negative, then the derivative is precisely zero, and the gradient information will vanish completely.  But as long as the input remains positive, larger values will not cause the gradient to diminish at all.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### The Improved Version of the Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def build_network():\n",
    "    network = Sequential()\n",
    "    network.add(Input(shape=(28,28)))\n",
    "    network.add(Flatten())\n",
    "    network.add(Dense(30, activation='relu', name='hidden'))\n",
    "    network.add(Dense(10, activation='softmax', name='output'))\n",
    "    network.compile(loss='categorical_crossentropy', optimizer='nadam', metrics=['accuracy'])\n",
    "    return network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "network = build_network()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dtype: float32\n",
      "Min: 0.0\n",
      "Max: 1.0\n"
     ]
    }
   ],
   "source": [
    "print(\"Dtype:\", train_images.dtype)\n",
    "print(\"Min:\", train_images.min())\n",
    "print(\"Max:\", train_images.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m16s\u001b[0m 8ms/step - accuracy: 0.8846 - loss: 0.4102\n",
      "Epoch 2/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m16s\u001b[0m 8ms/step - accuracy: 0.9175 - loss: 0.2975\n",
      "Epoch 3/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m16s\u001b[0m 8ms/step - accuracy: 0.9200 - loss: 0.2901\n",
      "Epoch 4/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m16s\u001b[0m 8ms/step - accuracy: 0.9209 - loss: 0.2869\n",
      "Epoch 5/5\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m16s\u001b[0m 8ms/step - accuracy: 0.9210 - loss: 0.2873\n"
     ]
    }
   ],
   "source": [
    "history = network.fit(train_images, train_targets, epochs=5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m11s\u001b[0m 6ms/step - accuracy: 0.9257 - loss: 0.2734\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.27343985438346863, 0.9256500005722046]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.evaluate(train_images, train_targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m2s\u001b[0m 6ms/step - accuracy: 0.9208 - loss: 0.2920\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.2919723093509674, 0.920799970626831]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.evaluate(test_images, test_targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_history(history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}