02_training_neural_nets.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Training Neural Networks\n",
    "\n",
    "In the previous lesson, we learned to build neural networks and manually set their weights and bias values. However, what we really want is an automated way of *discovering* the right weight and bias values that we need in order for our neural network to make useful predictions for a particular  problem. This process of *discovering* the right parameter values is referred to as *training* a neural network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "The TensorFlow library that forms the basis for most of these lessons uses random numbers for certain operations, for reasons that we will later explain. In order to make the results that you observe match the descriptions given in this lesson, you must run the code below in order to make TensorFlow choose a specific set of values for the random numbers that it employs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from consistency import remove_randomness\n",
    "remove_randomness()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Next, let's grab our necessary imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Training a Neural Network to Predict a Linear Trend\n",
    "\n",
    "Let's start with an extremely simple example - how do we train a neural network to predict the linear trend shown below?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# data for training example\n",
    "m = 1.5\n",
    "b = 0.5\n",
    "x = np.arange(0,1,0.1)\n",
    "y = m * x + b\n",
    "plt.scatter(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We'll start the process from a simple, blank Keras model - since we'll use a lot of these blank models as building blocks, we'll define a function to create them quickly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we'll be creating and testing lots of copies of the same simple model,\n",
    "# so encapsulate its creation in a function.\n",
    "# note that we use non-random initializers for consistency\n",
    "def new_example_model():\n",
    "    return keras.Sequential(\n",
    "        [\n",
    "            keras.layers.Dense(\n",
    "                name=\"output\",\n",
    "                units=1,\n",
    "                input_shape=(1,),\n",
    "                kernel_initializer=tf.keras.initializers.ones,\n",
    "                bias_initializer=tf.keras.initializers.zeros\n",
    "            )\n",
    "        ]\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Let's instantiate one of these blank models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# starting point - untrained model\n",
    "model_training_example = new_example_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "How accurate is this untrained model? Let's check by using it to generate some predicted `y` values for the `x` values in our dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# untrained predictions\n",
    "y_pred_untrained = model_training_example.predict(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We can use the graph below to compare our model's predictions to the true values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred_untrained, color=\"orange\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Clearly, these predictions are not accurate. We need to *train* our model in order to adjust the values of its weights and biases so that it gives accurate predictions for this dataset. As a first step, we'll call the `compile` method to configure our model for training:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prepare model for training\n",
    "model_training_example.compile(\n",
    "    optimizer=\"sgd\",\n",
    "    loss=\"mean_squared_error\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "In the code snippet above, we've passed `sgd` (stochastic gradient descent) as the optimizer argument, indicating the optimization procedure that should be used to train our model. For now, you don't need to worry about the meaning of \"stochastic gradient descent\" - just know that it is one of several methods that TensorFlow can use to find the right weight values. We've also passed the `loss` argument value of `mean_squared_error` - this tells TensorFlow to measure how \"bad\" a given set of weights is by computing the mean squared error of our predictions relative to the true values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Having configured our model, we can start training it using the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 10 samples\n",
      "10/10 [==============================] - 0s 30ms/sample - loss: 0.5462\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7fb4145a19b0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train\n",
    "model_training_example.fit(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "TensorFlow has now spent one *epoch* training our model to improve its predictive power. How good are its predictions now? We can check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check our progress\n",
    "y_pred_one_epoch = model_training_example.predict(x)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred_untrained, color=\"orange\")\n",
    "plt.plot(x, y_pred_one_epoch, color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Unfortunately, this is barely any better. However, we can tell TensorFlow to keep searching for better model parameters in order to improve our predictions. Let's run for 10 more epochs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 10 samples\n",
      "Epoch 1/10\n",
      "10/10 [==============================] - 0s 490us/sample - loss: 0.5201\n",
      "Epoch 2/10\n",
      "10/10 [==============================] - 0s 329us/sample - loss: 0.4953\n",
      "Epoch 3/10\n",
      "10/10 [==============================] - 0s 231us/sample - loss: 0.4716\n",
      "Epoch 4/10\n",
      "10/10 [==============================] - 0s 130us/sample - loss: 0.4491\n",
      "Epoch 5/10\n",
      "10/10 [==============================] - 0s 141us/sample - loss: 0.4277\n",
      "Epoch 6/10\n",
      "10/10 [==============================] - 0s 674us/sample - loss: 0.4073\n",
      "Epoch 7/10\n",
      "10/10 [==============================] - 0s 134us/sample - loss: 0.3879\n",
      "Epoch 8/10\n",
      "10/10 [==============================] - 0s 144us/sample - loss: 0.3694\n",
      "Epoch 9/10\n",
      "10/10 [==============================] - 0s 254us/sample - loss: 0.3518\n",
      "Epoch 10/10\n",
      "10/10 [==============================] - 0s 168us/sample - loss: 0.3350\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7fb4144bd278>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# need to run for more epochs\n",
    "model_training_example.fit(x,y, epochs=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Let's see if these extra epochs made any difference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check our further progress\n",
    "y_pred_ten_epochs = model_training_example.predict(x)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred_untrained, color=\"orange\")\n",
    "plt.plot(x, y_pred_ten_epochs, color=\"green\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We're getting closer! Let's run for more epochs - we'll add the `verbose=0` argument to keep the printed output from overloading our screen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7fb41444d0f0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# need to run for more epochs\n",
    "model_training_example.fit(x,y, epochs=100, verbose=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "As you can see, we now have a model that yields predictions which closely track the real line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y2H8igasCXDXgKlJTUr0u0SQxC3pjGqCkvISn1zxNIBRg3Z51ZLbI5AdjfsBs32wGdBzgdXnGABb0xpyVDXs3EAgGWLx6MSUVJYzuPprHpz3OjGEzaJne0uvyjDmFBb0xEaqsruTlTS/jD/p558t3aJbajOuHXk9eTh5jssbY4KppsizojalHUUkRj618jPxP8ikqKaJ3u948MP4Bbh11K51bdfa6PGPqZUFvEt7ZzAOvqry77V38QT9LNy6lWquZfM5k5k+dz5RzptjgqokrFvQmoZ3pPPCHyw/z1OqnCIQCbNi7gQ4ZHfjhhT9ktm82/Tv0j2ntxkSLBb1JaJHOA79uzzoCwQBPrXmKIxVH8PXw8cT0J7h+6PVkpGec/rLGxBULepPQvm4e+MrqSpZ+thR/0M97296jeWpzZgybQV5OHjlZOTGu1JjGY0FvElpt88BXsQ9p/TeyH76dXUd20TezLw9OeJBbR91Kx5YdParUmMZjQW8S2vF54I9VVlGWsoYjaa9yLOUjpFq5svuV5ObkMvmcyaRIitelGtNoLOhNQhs3uDWXjAzyzPoFlOp20mjLNefcye+v/An92vfzujxjYsKC3iSktbvXnhhcPVp5lDFZY8j13cf1w66nRVoLr8szJqYs6E3CqKiuYMnGJQSCAd7f/j4t0lpww7AbyM3JxdfD53V5xnjGgt7EvR3FO8hfmc9jnzzG7qO76d++P7+/4vfcMuoWOmR08Lo8YzxnQW/ikqry1ta38Af9LNu0jBqtYerAqeTm5DKx/0QbXDUmTERBLyILganAHlUdVst+AR4BrgSOATer6ifuvpuAn7uH/lpVn4xG4SY5HSo7xOLViwkEA2zav4lOLTtx90V3c6fvTvpk9vG6PGOapEiv6BcBjwKL69g/BRjgfl0AzAUuEJEOOIuJ+wAFVorIMlU92JCiTfJZvWs1gWCAp9c+zbHKY1zY80KeuuYprhtynQ2uGlOPiIJeVd8TkT5fc8h0YLGqKvCRiGSKSHfgMuBNVT0AICJvApOB5xpStEkO5VXlvLjxRQLBAB/s+ICMtAxuPO9GcnNyGd19tNflGRM3onWPPgvYEfa4wN1W1/avEJFZwCyA7OzsKJVl4tH24u3MD81nwaoF7Dm6h3M6nMMfJ/6Rm0feTPuM9l6XZ0zcaTKDsaqaD+QD+Hw+9bgcE2M1WsPftvwNf9DPK5+/AsDUgVPJy8ljQr8JNrhqTANEK+gLgV5hj3u62wpxbt+Eb38nSu9p4kB9c8EfLD3Ik6ufJBAM8MWBL+jcsjM/vfin3Hn+nfTO7O1h5cYkjmgF/TLgLhF5HmcwtlhVd4rICuB+ETn++/ZE4J4ovadp4r5uLvje3fYQCAZ4Zu0zlFaVclGvi7h37L1cN+Q6mqc197JsYxJOpO2Vz+FcmXcSkQKcTpp0AFWdByzHaa3cjNNeeYu774CI/AoIui913/GBWZP4Tp8LXqlkb83bfP+VH1OiG2iZ3pKZw2eSm5PLyG4jPazUmMQWadfNDfXsVyCvjn0LgYVnXpqJd8fngq+SPZSkvsaRtDeokWLSqrN4eMrD3DTyJjJbZHpcpTGJr8kMxprEUqM1ZLRdx5dlSyhNCQGQUTOGNlVT6d/mAv7lwgkeV2hM8rCgN1F1oPQAiz5dxNzQXDZXbiY1JZO2Vd+hTfUk0rQLGemp/NvkwV6XaUxSsaA3UbGyaCWBYIBn1z1LWVUZl2Rfwn2X3UdaxYU8/ObWOrtujDGNz4LenLWyqjJeWP8CgWCAjws/pmV6S74//Pvk5uQyotuIE8d95/y+HlZpTBN2dAccWgtZVzbq21jQmzO29eBW5oXm8fiqx9lfup9BHQfxyORHuGnETbRr0c7r8oxp2g5/DjuWOF8HgpDWCr69D1Ibb84mC3oTkRqtYcXmFfiDfpZ/sZwUSWH6udPJ9eVyed/LcSYwNcZ8hSocWn0y3IvXO9s75MCI30Kvaxo15MGC3tRj/7H9PPHpE8wNzWXLwS10bdWVn1/6c2adP4uebXt6XZ4xTZPWwL4P3XBfCke3gqRA50vh/Eeg59XQKnZzelnQm1oFC4MEQgGeX/c8ZVVlfDP7m9x/+f1cM/gamqU287o8Y5qemkrY/Y4T7gUvQdkuSEmHblfAsJ9B1jRo0dmT0izozQmllaX8af2fCAQDBIuCtEpvxc0jbiY3J5fzup7ndXnGND1VpbDrDTfcl0HlIUhtCT2uhF7XOn82837cyoLesOXgFuYG57Lw04UcKD3A4E6D+e8p/833R3yfts3bel2eMU1LRTEULXfCvWg5VB+DZu2h5zQn3LtNhLQMr6s8hQV9kqquqeb1za/jD/p5ffPrpEgK1wy+hlxfLpf1ucwGV40JV7YXCl52wn33X53bNC26Qb+bnHDvMta5TdNEWdAnmX3H9rFw1ULmheax9dBWurfuzi/G/oI7Rt9BVlv7IJMxJxzdAQVLnXDf+74zwNqqLwz8gRPunS50BljjgAV9Ajs+F3zhoWO0bbuNjl3f4cOdr1BeXc7Y3mP53YTfcfW5V5Oe2nSvRIyJqcObTnbKHHAn3W03DIb+3GmDzBwBcfjbrgV9gnppVSE/XRJkf83blDRfzrbKzaTsyGBi3xn8fsrdDO0y1OsSjfGeKhz81B1MXQLFG5ztHcfAyAeg5zXQdqC3NUaBBX0C2nxgM7mv3sPu1NepSTtCek02HSrm0Kp6HId3drSQN8ntlB73JXD0y7Ae99luj3uvel8mnljQJ4jqmmqWf7Ecf9DPin+sAE2lZfVFtKm+kuY1wxCcXzePzxFvTFKpqYTdbzu3ZE70uDeDruNh2M897XGPBQv6OLf36F4eX/U480Lz2Fa8jR5tevCfl/0nr/z9XPYWt/rK8T0ym1bblzGNpuoY7HR73AtfcXrc01o5ve09r3UmEktPjvbhSJcSnAw8AqQCC1T1gdP2/xcwzn3YEuiiqpnuvmpgrbtvu6pOi0bhyUxV+ajgIwKhAC+sf4GK6grG9RnHHyb+gWmDppGems7wtqeu1wqQkZ7K3ZMGeVi5MY2sohiKXnV73F8L63Gf7va4X9Hketxjod6gF5FUwA9cARQAQRFZpqobjh+jqj8MO/6fgVFhL1GqqrYgaBQcqzzGs2ufJRAMsGrXKto0a8Os0bOYkzOHIZ2HnHLs8TnfH1qxyeaCN4mtbE9Yj/vfnNs0Gd2h381Op0wT73GPhUiu6McAm1V1C4CIPA9MBzbUcfwNOIuHmyj5fP/nzA3OZdHqRRwqO8SwLsOYe9VcZg6fSetmret83tWjsizYTWI6ut29374E9v6vM8Dauh8M+hfntkynC+Kmxz0WIgn6LGBH2OMC4ILaDhSR3kBf4K2wzS1EJARUAQ+o6kt1PHcWMAsgOzt2s7o1VdU11fzl87/gD/p5c8ubpKWkcd2Q68j15XJJ9iX2yVWTfIo/O/kBpgPOOsQne9yvhczhcdnjHgvRHoydAfyPqlaHbeutqoUi0g94S0TWquo/Tn+iquYD+QA+n0+jXFfc2HN0Dws+WcD8lfPZXrydnm178qtxv+L20bfTrXU3r8szJnZU4eCqk22Qhzc62zteACN/5/a4D/C2xjgRSdAXAuFNpT3dbbWZAeSFb1DVQvfPLSLyDs79+68EfTJTVT4s+BB/0M+f1/+ZyppKxvcdz8OTHuZbg75FWoo1R5kkUVN9sse9YAkc3ebcgukyFgbkQq+roaWtg3CmIkmQIDBARPriBPwM4MbTDxKRc4H2wIdh29oDx1S1XEQ6ARcDD0aj8ERwtOIoz6x9hkAwwOrdq2nbvC1zfHOYkzOHczud63V5xsRGdYXT416wxBlULdvt9Lh3mwjD7oWsb0GLTl5XGdfqDXpVrRKRu4AVOO2VC1V1vYjcB4RUdZl76AzgeVUNv+0yGJgvIjVACs49+roGcZPGpn2bmBuay6JPF1FcXszwrsOZP3U+/3TeP9Gq2Vd7341JOFXHYOeKsB73YrfH/Sp3HvcpSdPjHgtyai43DT6fT0OhkNdlRFVVTRWvbHqFQCjAX7f8lfSUdL4z9Dvk+nK5qNdFNrhqEl/FISh81blyL3oNqkuhWQdnHvee10K3CUnZ4x4tIrJSVX217bObv41s95HdPPbJY8xfOZ+CwwX0atuL31z+G24bdRtdW3f1ujxjGlfpbig83uP+ltvj3gP63RrW424x1NjsDDcCVeWDHR/gD/p5ccOLVNZUckW/K3h0yqNcNfAqG1w1ie3oNqfHfYfb445C6/4w6F+d2zIdx1iPe4xZ4kTRkYojPLPmGQKhAGt2ryGVVrSqupJhGdeQO2wC08+1Dy+ZBFW8MazHfaWzLXM4DPuF2+N+nvW4e8iCPgo27t3I3NBcnlz9JIfLD9O37VC6Vf8L6RXfJIUWHKiEe5Y40/3YJ1VNQlCFg5+E9bh/5mzveCGMfNC5LdPmHG9rNCdY0J+lqpoqXv7sZQKhAG9tfYtmqc347tDvkuvL5cdPH6OoouyU40srq3loxSYLehO/aqph399Phvux7SCpzn32gXc587i3tJ/vpsiC/gztLNnJY588Rv7KfApLCslul81vx/+WW0fdSpdWXZxjil+t9bk2F7yJO9UVziBqwfF53PdASnPoPhHO+6X1uMcJC/oIqCrvb38ff9DPko1LqKqpYlL/SQSuCnDVgKtITUk95fgemRkU1hLqNhe8iQtVR8N63P/i9ri3Pq3HvY3XVZozYEH/NUrKS3h6zdMEQgHW7VlHZotMfjDmB8z2zWZAx7rn2Lh70iCbC97El4pDTqjvWAI7Xz/Z497rWnce9wmQ2sLrKs1ZsqCvxYa9GwgEAyxevZiSihJGdx/N49MeZ8awGbRMb1nv820ueBMXSneFzeP+FmiV0+Pe/zYn3Dt/03rcE4T9X3RVVlfy0mcvEQgFeOfLd2iW2ozrh15PXk4eY7LGnPEnV20ueNMkHfnyZBvk3g840eN+7o/cHvcc63FPQEkf9EUlReSvzCd/ZT47j+ykd7vePDD+AW4ddSudWyXuYsEmiRRvPNkpc/ATZ1vmcDjvXifc2w2zHvcEl5RBr6q8u+1d/EE/SzcupUZrmHzOZPJz8plyzpSvDK4aE1dUnQ8tHZ/q9/AmZ3unb8Coh5x53Nv097ZGE1NJFfSHyw/z1OqnCIQCbNi7gQ4ZHfjhhT9ktm82/TvYD76JYzXVsO8D98p9aViP+2Uw8AfO4tjW4560kiLo1+1ZRyAY4Kk1T3Gk4gi+Hj6emP4E1w+9nox0a3k0caq63BlE3eH2uJfvPdnjPvw/nR735h29rtI0AQkb9BXVFSzduJRAKMB7296jeWpzZgybQV5OHjlZOV6XZ8zZqToKRa87V+5Ff4HKw06Pe9ZU535798nW426+IiGD/mDpQYYGhrLzyE76ZvblwQkPcsuoW+jU0j7BZ+JQxcHTetzLnCv1Xte5Pe7jrcfdfK2EDPr2Ge25acRNfLP3N5nUf5INrpr4U7rLuR2zY4mzzJ5WQUYW9L/DmTDMetzNGUjYn5TfTvit1yUYc2aObHXvty+BvX/H6XE/Bwb/2FmBqaPPetzNWYko6EVkMvAIzpqxC1T1gdP23ww8hLN4OMCjqrrA3XcT8HN3+69V9cko1P21XlpVaJ9KNU2fKhwO73Ff5WzPHOFMGNbrWmg31HrcTYPVG/Qikgr4gSuAAiAoIstqWeT7T6p612nP7QDcC/gABVa6zz0Ylepr8dKqwlPmmSk8VGpzwZumQxUOhE6Ge8nnzvZOF8Go3zu3ZVr387ZGk3AiuaIfA2xW1S0AIvI8MB04PehrMwl4U1UPuM99E5gMPHd25dbvoRWbTplMDGwueOOxmmpnSb0dS5zpB47tcHrcu46Dc/8VsqZDyx5eV2kSWCRBnwXsCHtcAFxQy3HfFpFLgc+BH6rqjjqeW2vaisgsYBZAdnZ2BGXVrq45320ueBNT1eWw62/O/faCZU6Pe2oL6DYRhv/K7XHv4HWVJklEazD2FeA5VS0XkTuBJ4HLz+QFVDUfyAfw+Xx6toXYXPDGM5VHnPbH4/O4V5VAWpvTetxbe12lSUKRBH0h0CvscU9ODroCoKr7wx4uAB4Me+5lpz33nSnXlTgAAAwzSURBVDMt8kzYXPAmpsoPOKFesMRZrKO6DJp3gt7fdTpluo2H1OZeV2mSXCRBHwQGiEhfnOCeAdwYfoCIdFfVne7DacBG9/sVwP0i0t59PBG4p8FVfw2bC940utKdYT3u7zg97i17Qv9Zbo/7JdbjbpqUen8aVbVKRO7CCe1UYKGqrheR+4CQqi4DfiAi04Aq4ABws/vcAyLyK5x/LADuOz4w25hsLngTdUe2OD3uO5bAvg8BhTYDYPBPnNsyHXzWBmmaLFE969vhjcbn82koFPK6DJPMVKF4w8mpfg9+6mxvP9K5JdPrWmg3xMLdNBkislJVfbXts98vjTlOFfYHnWDfsQRKvgAEOl8Eo/7g9rj39bpKY86YBb1JbjVVp/W4F4CkuT3uP3Lmcc/o7nWVxjSIBb1JPqf0uL8M5fucHvfuk2D4b5x2SOtxNwnEgt4kh8ojsPM1t8f9VafHPb0t9HB73HtMhrRWXldpTKOwoDeJq/wAFL7izuO+AmrK3R73651w73q59bibpGBBbxLLsaKTPe573gGthpa94Jw7w+Zxt/UJTHKxoDfxr+QfzkDqiR53oM1AGPxvbo/7+dYGaZKaBb2JP6pQvP7kVL+HVjvb249yJgzrdS20HWzhbozLgt7EB61xetyPh/uRzTg97hfD6D9Cz6utx92YOljQm6arpgr2vu+G+1IoLXR73C93ph7oOR0yunldpTFNngW9aVqqy2DXX902yGVQvt/tcZ8MvX7r9Lg3a1//6xhjTrCgN96rLIEit8e96FWoOuL0uGd9y53HfZL1uBvTABb0xhvl+8N63N9we9w7Q+8bwnrcm3ldpTEJwYLexM6xwrAe93fdHvdsGDDH6XHvdLH1uBvTCCzoTeMq2XxyHvf9Hznb2g6CIT91rtzbj7Y2SGMamQW9iS5VOLT25AeYDq1xtrcfDcN/7c7jPtjbGo1JMhb0puG0Bvb/X1iP+z9wetwvgdH/5fa49/G6SmOSVkRBLyKTgUdwlhJcoKoPnLb/R8DtOEsJ7gVuVdVt7r5qYK176HZVnRal2o2Xaqpgz3sn53EvLXJ63LuNhyH/BlnTIaOr11UaY4gg6EUkFfADVwAFQFBElqnqhrDDVgE+VT0mInOAB4Hr3X2lqjoyynUbL1SXwc43nWAveBkqDkBqBvSYAj2vcXvcM72u0hhzmkiu6McAm1V1C4CIPA9MB04Evaq+HXb8R8DMaBZpPFRZAkXL3R735W6Pe7vTetxbel2lMeZrRBL0WcCOsMcFwAVfc/xtwGthj1uISAjnts4DqvpSbU8SkVnALIDs7OwIyjKNpmzfyR73XW86Pe4tukCfG52FsbuOsx53Y+JIVAdjRWQm4APGhm3uraqFItIPeEtE1qrqP05/rqrmA/kAPp9Po1mXicCxAtjxkrO83p53nQHWVr1hQK7b436R9bgbE6ciCfpCoFfY457utlOIyATgZ8BYVS0/vl1VC90/t4jIO8Ao4CtBbzxQsvlkp8z+j51tbQfDkHvcHvdR1uNuTAKIJOiDwAAR6YsT8DOAG8MPEJFRwHxgsqruCdveHjimquUi0gm4GGeg1nhB1elr37HUuXI/5DZDdTgfRvzGGVC1HndjEk69Qa+qVSJyF7ACp71yoaquF5H7gJCqLgMeAloDfxbnCvB4G+VgYL6I1AApOPfoN9T6RqZxaA3s+9gJ9h1L4MgWQKDLN2H0w9DraucWjTEmYYlq07sd7vP5NBQKeV1G/KqpPK3HfSekpEPX8c4tmaxp1uNuTIIRkZWq6qttn30yNlGc6HFfAgXLrMfdGHOCBX08qzwMhcudq/aiV6HqqNvjPs3tcZ9oPe7GGAv6uFO2z1l56USPewW06Ap9Zjrh3uUy63E3xpzCgj4e1NnjnueEe6dvWI+7MaZOFvRN1eEvTk71e7zHvd0QGPIfbo/7SOtxN8ZExIK+qTjR4+52ypzocffBiPvdHvdzva3RGBOXLOi9VFuPu6S487g/7Ew90Mrm/THGNIwFfazV2eM+wZl6oOc0ZwIxY4yJEgv6WKi1x72l0+Pe61rocRU0a+d1lcaYBGVB31hq7XHPdK7Ye15jPe7GmJixoI+mOnvcv+dcuXe9zLlNY4wxMWRB31DHCtzZIJeG9bj3gYF3OeHe8ULrcTfGeMqC/mwc/uJkp8z+/3O2tRsKQ3/m3JaxHndjTBNiQR8JVTi02rly37EEitc52zvkwIjfOm2QbQd5W6MxxtTBgr4uWgP7Pjq5AtPRrW6P+zfh/Eeg59XW426MiQsW9OFqKp377DuWOFfvZbucwdNuV8CwnzmzQrbo7HWVxhhzRizoq0ph1xtOuBe+AhUH3R73K90e9yutx90YE9eSM+grD0Phq064Fy2H6mPQrD1kfcsJ924TIS3D6yqNMSYqIgp6EZkMPIKzZuwCVX3gtP3NgcXA+cB+4HpV/dLddw9wG1AN/EBVV0St+jNRthcKXnbaIHf91e1x7wb9bnLncR9rPe7GmIRUb9CLSCrgB64ACoCgiCw7bZHv24CDqnqOiMwAfgdcLyJDgBnAUKAH8FcRGaiq1dH+D6nV0R0np/rd+77b494XBv6zO4/7hc4AqzHGJLBIrujHAJtVdQuAiDwPTAfCg3468Ev3+/8BHhURcbc/r6rlwFYR2ey+3ofRKb8OFcXw1hVwIOg8bjfM6XHvdS1kjrAed2NMUokk6LOAHWGPC4AL6jpGVatEpBjo6G7/6LTnZtX2JiIyC5gFkJ3dwLbFZu2gdT/I/rbzAaa2Axv2esYYE8eazGCsquYD+QA+n08b/IKXPN/glzDGmEQQyQ3qQqBX2OOe7rZajxGRNKAdzqBsJM81xhjTiCIJ+iAwQET6ikgznMHVZacdswy4yf3+OuAtVVV3+wwRaS4ifYEBwP9Fp3RjjDGRqPfWjXvP/S5gBU575UJVXS8i9wEhVV0GPA485Q62HsD5xwD3uBdwBm6rgLyYddwYY4wBQJwL76bF5/NpKBTyugxjjIkbIrJSVX217bMmcmOMSXAW9MYYk+As6I0xJsFZ0BtjTIJrkoOxIrIX2BaFl+oE7IvC68Q7Ow8OOw8n2blwJNJ56K2qtS6Y0SSDPlpEJFTXKHQysfPgsPNwkp0LR7KcB7t1Y4wxCc6C3hhjElyiB32+1wU0EXYeHHYeTrJz4UiK85DQ9+iNMcYk/hW9McYkPQt6Y4xJcAkR9CIyWUQ2ichmEfn3WvY3F5E/ufs/FpE+sa+y8UVwHn4kIhtEZI2I/E1EentRZ2Or7zyEHfdtEVERScj2ukjOg4h81/2ZWC8iz8a6xliJ4O9Gtoi8LSKr3L8fV3pRZ6NR1bj+wpk6+R9AP6AZsBoYctoxucA89/sZwJ+8rtuj8zAOaOl+PydZz4N7XBvgPZylLn1e1+3Rz8MAYBXQ3n3cxeu6PTwX+cAc9/shwJde1x3Nr0S4oj+xeLmqVgDHFy8PNx140v3+f4Dx7uLliaTe86Cqb6vqMffhRzgrfiWaSH4eAH4F/A4oi2VxMRTJebgD8KvqQQBV3RPjGmMlknOhQFv3+3ZAUQzra3SJEPS1LV5++gLkpyxeDhxfvDyRRHIewt0GvNaoFXmj3vMgIqOBXqr6aiwLi7FIfh4GAgNF5AMR+UhEJsesutiK5Fz8EpgpIgXAcuCfY1NabDSZxcFN7IjITMAHjPW6llgTkRTgj8DNHpfSFKTh3L65DOe3u/dE5DxVPeRpVd64AVikqn8QkW/grJg3TFVrvC4sGhLhir4hi5cnkogWYheRCcDPgGmqWh6j2mKpvvPQBhgGvCMiXwIXAssScEA2kp+HAmCZqlaq6lbgc5zgTzSRnIvbgBcAVPVDoAXOhGcJIRGCviGLlyeSes+DiIwC5uOEfKLej/3a86CqxaraSVX7qGofnLGKaaqaaGtXRvL34iWcq3lEpBPOrZwtsSwyRiI5F9uB8QAiMhgn6PfGtMpGFPdB795zP754+UbgBXUXLxeRae5hjwMd3cXLfwTU2XIXryI8Dw8BrYE/i8inInL6D3vci/A8JLwIz8MKYL+IbADeBu5W1UT7TTfSc/Fj4A4RWQ08B9ycSBeDNgWCMcYkuLi/ojfGGPP1LOiNMSbBWdAbY0yCs6A3xpgEZ0FvjDEJzoLeGGMSnAW9McYkuP8Pfu23nGUL6/IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_fifty_epochs = model_training_example.predict(x)\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred_untrained, color=\"orange\")\n",
    "plt.plot(x, y_pred_fifty_epochs, color=\"green\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Understanding the Training Process\n",
    "\n",
    "What exactly is TensorFlow doing when we ask it to train our model? Let's start from a blank model and trace exactly what is happening as we train using the `sgd` optimizer: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a model that we will train step-by-step\n",
    "model_sgd = new_example_model()\n",
    "model_sgd.compile(\n",
    "    optimizer=\"sgd\",\n",
    "    loss=\"mean_squared_error\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We'll follow the progress of the training process using a custom add-on that we'll call a \"training tracker\" - we can obtain this add-on from our custom `training_visualization` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from training_visualization import Tracker"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Let's create a tracker object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "tracker_sgd = Tracker(\"sgd\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We can use this tracker to follow our training process by passing it to the `callbacks` argument of `fit`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 10 samples\n",
      "Epoch 1/10\n",
      "10/10 [==============================] - 0s 34ms/sample - loss: 0.5462\n",
      "Epoch 2/10\n",
      "10/10 [==============================] - 0s 5ms/sample - loss: 0.5201\n",
      "Epoch 3/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4953\n",
      "Epoch 4/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4716\n",
      "Epoch 5/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4491\n",
      "Epoch 6/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4277\n",
      "Epoch 7/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4073\n",
      "Epoch 8/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.3879\n",
      "Epoch 9/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.3694\n",
      "Epoch 10/10\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.3518\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7fb414454518>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_sgd.fit(x,y, epochs=10, callbacks=[tracker_sgd.get_callback()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Having trained our model, we can visualize the results recorded by our tracker using the `visualize_progress` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tracker_sgd.visualize_progress(m_true = m, b_true = b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We can see that the weight and bias values of our model are slowly approaching the true slope and intercept values of our linear trend, but they aren't there yet."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    " Let's try training a different way and see if TensorFlow can approach the true value faster. This time, we'll customize the default `sgd` optimizer by changing the `learning_rate` - using a larger `learning_rate` can help us find the right set of weights faster, but the downside is that it can potentially make the training process unstable and prevent us from finding anything useful at all:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# build new model\n",
    "model_sgd_faster = new_example_model()\n",
    "optimizer_sgd_faster = tf.keras.optimizers.SGD(learning_rate=0.6)\n",
    "model_sgd_faster.compile(\n",
    "    optimizer=optimizer_sgd_faster,\n",
    "    loss=\"mean_squared_error\"\n",
    ")\n",
    "\n",
    "# train - in addition to using a different optimizer, we run for longer\n",
    "tracker_sgd_faster = Tracker(\"sgd-faster\")\n",
    "model_sgd_faster.fit(x,y, epochs=25, callbacks=[tracker_sgd_faster.get_callback()], verbose=0)\n",
    "tracker_sgd_faster.visualize_progress(m_true = m, b_true = b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "As you can see, appropriately choosing the configuration of our training process allows TensorFlow to effectively determine the weight values that should go into our network without us having to specify them manually."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "<span style=\"color:blue;font-weight:bold\">Exercise</span>: Let's experiment with another optimizer and view its impact on the training process. Perform the following actions:\n",
    "\n",
    "* Create a variable named `my_model` and set its value using `new_example_model()` as above\n",
    "* Create a variable called `my_optimizer` and set its value to: `keras.optimizers.Adam(learning_rate=0.02)` \n",
    "* `compile` your model using the optimizer value `my_optimizer` and the loss function `mean_absolute_error` \n",
    "* Create a new tracker object as follows:\n",
    "\n",
    "```\n",
    "my_model_tracker = Tracker(\"my-model\")\n",
    "```\n",
    "\n",
    "* using the `fit` method, train your model for `25` epochs, passing your `my_model_tracker.get_callback()` appropriately as shown above\n",
    "\n",
    "* Call the `visualize_progress` method of your `my_model_tracker` object to view how the training process has proceeded. \n",
    "\n",
    "Be careful not to delete the `remove_randomness()` call at the top of the cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false,
    "tags": [
     "exercise"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 10 samples\n",
      "Epoch 1/25\n",
      "10/10 [==============================] - 0s 43ms/sample - loss: 0.7250\n",
      "Epoch 2/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.6960\n",
      "Epoch 3/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.6670\n",
      "Epoch 4/25\n",
      "10/10 [==============================] - 0s 7ms/sample - loss: 0.6380\n",
      "Epoch 5/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.6090\n",
      "Epoch 6/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.5800\n",
      "Epoch 7/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.5510\n",
      "Epoch 8/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.5220\n",
      "Epoch 9/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4930\n",
      "Epoch 10/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4640\n",
      "Epoch 11/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4350\n",
      "Epoch 12/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.4060\n",
      "Epoch 13/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.3770\n",
      "Epoch 14/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.3480\n",
      "Epoch 15/25\n",
      "10/10 [==============================] - 0s 5ms/sample - loss: 0.3190\n",
      "Epoch 16/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.2900\n",
      "Epoch 17/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.2610\n",
      "Epoch 18/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.2320\n",
      "Epoch 19/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.2030\n",
      "Epoch 20/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.1740\n",
      "Epoch 21/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.1450\n",
      "Epoch 22/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.1160\n",
      "Epoch 23/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.0870\n",
      "Epoch 24/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.0580\n",
      "Epoch 25/25\n",
      "10/10 [==============================] - 0s 4ms/sample - loss: 0.0290\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7fb3fea26940>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remove_randomness()\n",
    "\n",
    "my_model = new_example_model()\n",
    "my_optimizer = keras.optimizers.Adam(learning_rate=0.02)\n",
    "my_model.compile(optimizer=my_optimizer, loss=\"mean_absolute_error\")\n",
    "\n",
    "my_model_tracker = Tracker(\"my-model\")\n",
    "\n",
    "my_model.fit(x,y, callbacks=[my_model_tracker.get_callback()], epochs=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "deletable": false,
    "editable": false,
    "strategicml": {
     "execution_time": 1584779177808,
     "exercise_id": "883ee4e2-d83b-4afe-8e56-d731102394e9",
     "points": 4
    },
    "tags": [
     "test"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"background-color:#e8fcef\n",
       ";color:#333333;padding:10px;border-style:solid;border-width:2px;border-color:#038c33\">\n",
       "<div style=\"font-weight:bold\">Correct!</div>\n",
       "</div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_variable_definition(\"my_model\")\n",
    "assert str(type(my_model)) ==  \"<class 'tensorflow.python.keras.engine.sequential.Sequential'>\", \"Your variable <code>my_model</code> does not contain an object of the right type - did you create it using <code>keras.Seqential()</code>?\"\n",
    "assert abs(my_model.get_weights()[0][0][0] - 1.5) < 0.001, \"Your model does not have the correct final weights - check your training code\"\n",
    "assert abs(my_model.get_weights()[1][0] - 0.5) < 0.001, \"Your model does not have the correct final weights - check your training code\"\n",
    "success()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "In later lessons, you will learn to train a more complicated neural network to make more useful, business-relevant predictions. However, before we can start that material, we must tackle the issue of *overfitting*, which is discussed in the next lesson. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tracker_sgd_faster.visualize_progress(m_true = m, b_true = b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb3fc3f2908>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, my_model.predict(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[1.4999988]], dtype=float32), array([0.49999923], dtype=float32)]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_model.get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": null,
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  },
  "strategicml": {
   "lesson_id": "d70d095f-32cb-4c22-a68f-8f031c2267f7",
   "release": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}