11_training_deep_neural_nets.ipynb

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    "# Chapter 11 Training Deep Neural Nets\n",
    "\n",
    "There are three problems with training deep neural nets that we will cover in this chapter: the vanishing/exploding gradient problem, slow training with a large network, and overfitting. \n",
    "\n",
    "## Vanishing/Exploding Gradients\n",
    "\n",
    "When using the backpropagation algorithm, the gradient for each weight and bias is calculated backwards beginning from the output layer. In particular, the gradient of the bias at a particular layer (the reasoning for the gradient of a weight remains the same since the weight gradient is a product of two terms, one of which is the gradient of the bias at its layer) can be calculated as the gradient of a future layer multiplied by the product of the weight and derivative of the activation function of the intermediate layers. This means that the earlier a layer is, the more terms appear in this product. Furthermore, initializing with a 0-centered normal with a standard deviation of 1 means the weights are usually smaller than 1, and the derivative of the sigmoid activation function reaches a maximum of 1/4. Because the terms are quite small, so are the gradients, which are called *vanishing gradients*. The earlier a layer appears, the smaller its gradient is, and small gradients cause the network to learn slowly. It is also possible that the weights and derivative become large in later layers or with a different activation function, in which case the gradients are referred to as *exploding gradients* and make learning very erratic. \n",
    "\n",
    "We can also see that the sigmoid function has a very small derivative once the input becomes very positive or very negative, exacerbating the problem. We can deal with these by changing the way we initialize the weights or by changing the activation function.  \n",
    "\n",
    "### Xavier and He Initialization\n",
    "\n",
    "When using the logistic activation function, we can use a strategy called *Xavier intialization* which samples weights from either a 0-centered normal where the standard deviation is function of the number of inputs and outputs or a uniform distribution where the limits are are a function of the same parameters. *He initialization* also defines these distributions with different functions but the same parameters when using the ReLU activation function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "from tensorflow_graph_in_jupyter import show_graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "(X_train, y_train), (X_test, y_test) = tf.keras.datasets.mnist.load_data()\n",
    "X_train = X_train.astype(np.float32).reshape(-1, 28*28) / 255.0\n",
    "X_test = X_test.astype(np.float32).reshape(-1, 28*28) / 255.0\n",
    "y_train = y_train.astype(np.int32)\n",
    "y_test = y_test.astype(np.int32)\n",
    "X_valid, X_train = X_train[:5000], X_train[5000:]\n",
    "y_valid, y_train = y_train[:5000], y_train[5000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "n_inputs = 28 * 28  \n",
    "n_hidden1 = 300\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name=\"X\")\n",
    "\n",
    "# Use Xavier intialization with uniform distribution\n",
    "xavier_initializer = tf.contrib.layers.variance_scaling_initializer(factor=1.0, \n",
    "                                                                    mode='FAN_AVG', \n",
    "                                                                    uniform=True)\n",
    "hidden1 = tf.layers.dense(X, n_hidden1, activation=tf.nn.relu, \n",
    "                         kernel_initializer=xavier_initializer, name='hidden1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonsaturating Activation Functions\n",
    "\n",
    "While the ReLU function doesn't saturate no matter how large its positive input is, it's derivative becomes 0 for any negative input. The gradient obviously doesn't change at this point, so this neuron is unlikely to change given further training. One alternative is the leaky ReLU, which has a small slope (the hyperparameter alpha which should be less than 1, usually 0.01) instead of a constant 0 for negative inputs. The leaky ReLU function is defined as as max(alpha\\*z, z). There is also randomized leaky ReLU, which randomly picks alpha during training and fixes an average during training, and can be used as a method of regularization. Finally, parametric leaky ReLU treats alpha as a variable like the weights or biases than can be optimized by backpropagation, but this activatoin function is more prone to overfitting. \n",
    "\n",
    "We can also use the exponential linear unit (ELU), which is defined as z for positive z, and alpha\\*(e^z - 1) for negative z. This function turned out to perform better and train faster than other activation functions. While the gradient is more costly computationally, the convergence rate more than compensates for this slowdown during training. However, we will see this computational slowdown during training. \n",
    "\n",
    "The scaled exponential linear unit (SELU) activation function performs normalization like batch normalization, discussed below, inside the activation function. However, this only works with feed forward neural networks and doesn't allow for the use of techniques such as l1 or l2 regularization and dropout. When these conditions are met, it generally performs better than other activation functions. Remember to scale and normalize the initial inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Leaky ReLU and ELU functions\n",
    "tf.reset_default_graph()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name='X')\n",
    "\n",
    "hidden1 = tf.layers.dense(X, n_hidden1, activation=tf.nn.leaky_relu, name='hidden1')\n",
    "hidden2 = tf.layers.dense(hidden1, n_hidden1, activation=tf.nn.elu, name='hidden2')"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Batch Normalization\n",
    "\n",
    "While the above methods are good for dealing with gradient instability, the problem might reappear as we update the weights and biases during training. Batch normalization can prevent this by normalizing the inputs to your activation function, leading to less extreme values for your inputs and thus decreased chances of saturation. More generally, it is meant to deal with the problem of layers having to deal with varying input distributions as the network's parameters are updated. It does this by calculating the batch mean and standard deviation, using these values to center and normalize the inputs, and calculating the linear output using gamma\\*X + beta, where gamma (scaling) and beta (offset) are learned during training. This technique is so effective it even allows the use of saturating activation functions such as the sigmoid function, makes networks less sensitive to weight/bias initalization, allows for higher learning rates, and acts like a form of regularization. There is, however, a computational cost.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import partial\n",
    "\n",
    "n_hidden2 = 100\n",
    "n_outputs = 10\n",
    "\n",
    "tf.reset_default_graph()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name='X')\n",
    "# Boolean for whether using training data\n",
    "training = tf.placeholder_with_default(False, shape=(), name='training')\n",
    "he_initializer = tf.contrib.layers.variance_scaling_initializer()\n",
    "\n",
    "batch_norm_layer = partial(tf.layers.batch_normalization, \n",
    "                          training=training, momentum=0.9)\n",
    "dense_layer = partial(tf.layers.dense, \n",
    "                     kernel_initializer = he_initializer)\n",
    "\n",
    "# Hidden layer\n",
    "hidden1 = dense_layer(X, n_hidden1, name='hidden1')\n",
    "# Batch normalization, inherits parameters from partial\n",
    "bn1 = batch_norm_layer(hidden1)\n",
    "# ELU activation function\n",
    "bn1_act = tf.nn.elu(bn1)\n",
    "hidden2 = dense_layer(bn1_act, n_hidden2, name='hidden2')\n",
    "bn2_act = tf.nn.elu(batch_norm_layer(hidden2))\n",
    "logits_before_bn = dense_layer(bn2_act, n_outputs, name='outputs')\n",
    "logits = batch_norm_layer(logits_before_bn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reusing Pretrained Layers\n",
    "\n",
    "*Transfer learning* is the process of using layers from pretrained models in your current network, generally the older layers since these are the ones that have learned to identify lower level details such as lines, edges, and so on. Let's look at the MNIST model we trained and saved in the last chapter.\n",
    "\n",
    "### Reusing a TensorFlow Model\n",
    "\n",
    "We can load this graph and look at all of its operations by its name or using TensorBoard."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
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     "text": [
      "X\n",
      "y\n",
      "hidden1/kernel/Initializer/random_uniform/shape\n",
      "hidden1/kernel/Initializer/random_uniform/min\n",
      "hidden1/kernel/Initializer/random_uniform/max\n",
      "hidden1/kernel/Initializer/random_uniform/RandomUniform\n",
      "hidden1/kernel/Initializer/random_uniform/sub\n",
      "hidden1/kernel/Initializer/random_uniform/mul\n",
      "hidden1/kernel/Initializer/random_uniform\n",
      "hidden1/kernel\n",
      "hidden1/kernel/Assign\n",
      "hidden1/kernel/read\n",
      "hidden1/bias/Initializer/zeros\n",
      "hidden1/bias\n",
      "hidden1/bias/Assign\n",
      "hidden1/bias/read\n",
      "dnn/hidden1/MatMul\n",
      "dnn/hidden1/BiasAdd\n",
      "dnn/hidden1/Relu\n",
      "hidden2/kernel/Initializer/random_uniform/shape\n",
      "hidden2/kernel/Initializer/random_uniform/min\n",
      "hidden2/kernel/Initializer/random_uniform/max\n",
      "hidden2/kernel/Initializer/random_uniform/RandomUniform\n",
      "hidden2/kernel/Initializer/random_uniform/sub\n",
      "hidden2/kernel/Initializer/random_uniform/mul\n",
      "hidden2/kernel/Initializer/random_uniform\n",
      "hidden2/kernel\n",
      "hidden2/kernel/Assign\n",
      "hidden2/kernel/read\n",
      "hidden2/bias/Initializer/zeros\n",
      "hidden2/bias\n",
      "hidden2/bias/Assign\n",
      "hidden2/bias/read\n",
      "dnn/hidden2/MatMul\n",
      "dnn/hidden2/BiasAdd\n",
      "dnn/hidden2/Relu\n",
      "outputs/kernel/Initializer/random_uniform/shape\n",
      "outputs/kernel/Initializer/random_uniform/min\n",
      "outputs/kernel/Initializer/random_uniform/max\n",
      "outputs/kernel/Initializer/random_uniform/RandomUniform\n",
      "outputs/kernel/Initializer/random_uniform/sub\n",
      "outputs/kernel/Initializer/random_uniform/mul\n",
      "outputs/kernel/Initializer/random_uniform\n",
      "outputs/kernel\n",
      "outputs/kernel/Assign\n",
      "outputs/kernel/read\n",
      "outputs/bias/Initializer/zeros\n",
      "outputs/bias\n",
      "outputs/bias/Assign\n",
      "outputs/bias/read\n",
      "dnn/outputs/MatMul\n",
      "dnn/outputs/BiasAdd\n",
      "dnn/Softmax\n",
      "loss/SparseSoftmaxCrossEntropyWithLogits/Shape\n",
      "loss/SparseSoftmaxCrossEntropyWithLogits/SparseSoftmaxCrossEntropyWithLogits\n",
      "loss/Const\n",
      "loss/loss\n",
      "train/gradients/Shape\n",
      "train/gradients/grad_ys_0\n",
      "train/gradients/Fill\n",
      "train/gradients/loss/loss_grad/Reshape/shape\n",
      "train/gradients/loss/loss_grad/Reshape\n",
      "train/gradients/loss/loss_grad/Shape\n",
      "train/gradients/loss/loss_grad/Tile\n",
      "train/gradients/loss/loss_grad/Shape_1\n",
      "train/gradients/loss/loss_grad/Shape_2\n",
      "train/gradients/loss/loss_grad/Const\n",
      "train/gradients/loss/loss_grad/Prod\n",
      "train/gradients/loss/loss_grad/Const_1\n",
      "train/gradients/loss/loss_grad/Prod_1\n",
      "train/gradients/loss/loss_grad/Maximum/y\n",
      "train/gradients/loss/loss_grad/Maximum\n",
      "train/gradients/loss/loss_grad/floordiv\n",
      "train/gradients/loss/loss_grad/Cast\n",
      "train/gradients/loss/loss_grad/truediv\n",
      "train/gradients/zeros_like\n",
      "train/gradients/loss/SparseSoftmaxCrossEntropyWithLogits/SparseSoftmaxCrossEntropyWithLogits_grad/PreventGradient\n",
      "train/gradients/loss/SparseSoftmaxCrossEntropyWithLogits/SparseSoftmaxCrossEntropyWithLogits_grad/ExpandDims/dim\n",
      "train/gradients/loss/SparseSoftmaxCrossEntropyWithLogits/SparseSoftmaxCrossEntropyWithLogits_grad/ExpandDims\n",
      "train/gradients/loss/SparseSoftmaxCrossEntropyWithLogits/SparseSoftmaxCrossEntropyWithLogits_grad/mul\n",
      "train/gradients/dnn/outputs/BiasAdd_grad/BiasAddGrad\n",
      "train/gradients/dnn/outputs/BiasAdd_grad/tuple/group_deps\n",
      "train/gradients/dnn/outputs/BiasAdd_grad/tuple/control_dependency\n",
      "train/gradients/dnn/outputs/BiasAdd_grad/tuple/control_dependency_1\n",
      "train/gradients/dnn/outputs/MatMul_grad/MatMul\n",
      "train/gradients/dnn/outputs/MatMul_grad/MatMul_1\n",
      "train/gradients/dnn/outputs/MatMul_grad/tuple/group_deps\n",
      "train/gradients/dnn/outputs/MatMul_grad/tuple/control_dependency\n",
      "train/gradients/dnn/outputs/MatMul_grad/tuple/control_dependency_1\n",
      "train/gradients/dnn/hidden2/Relu_grad/ReluGrad\n",
      "train/gradients/dnn/hidden2/BiasAdd_grad/BiasAddGrad\n",
      "train/gradients/dnn/hidden2/BiasAdd_grad/tuple/group_deps\n",
      "train/gradients/dnn/hidden2/BiasAdd_grad/tuple/control_dependency\n",
      "train/gradients/dnn/hidden2/BiasAdd_grad/tuple/control_dependency_1\n",
      "train/gradients/dnn/hidden2/MatMul_grad/MatMul\n",
      "train/gradients/dnn/hidden2/MatMul_grad/MatMul_1\n",
      "train/gradients/dnn/hidden2/MatMul_grad/tuple/group_deps\n",
      "train/gradients/dnn/hidden2/MatMul_grad/tuple/control_dependency\n",
      "train/gradients/dnn/hidden2/MatMul_grad/tuple/control_dependency_1\n",
      "train/gradients/dnn/hidden1/Relu_grad/ReluGrad\n",
      "train/gradients/dnn/hidden1/BiasAdd_grad/BiasAddGrad\n",
      "train/gradients/dnn/hidden1/BiasAdd_grad/tuple/group_deps\n",
      "train/gradients/dnn/hidden1/BiasAdd_grad/tuple/control_dependency\n",
      "train/gradients/dnn/hidden1/BiasAdd_grad/tuple/control_dependency_1\n",
      "train/gradients/dnn/hidden1/MatMul_grad/MatMul\n",
      "train/gradients/dnn/hidden1/MatMul_grad/MatMul_1\n",
      "train/gradients/dnn/hidden1/MatMul_grad/tuple/group_deps\n",
      "train/gradients/dnn/hidden1/MatMul_grad/tuple/control_dependency\n",
      "train/gradients/dnn/hidden1/MatMul_grad/tuple/control_dependency_1\n",
      "train/GradientDescent/learning_rate\n",
      "train/GradientDescent/update_hidden1/kernel/ApplyGradientDescent\n",
      "train/GradientDescent/update_hidden1/bias/ApplyGradientDescent\n",
      "train/GradientDescent/update_hidden2/kernel/ApplyGradientDescent\n",
      "train/GradientDescent/update_hidden2/bias/ApplyGradientDescent\n",
      "train/GradientDescent/update_outputs/kernel/ApplyGradientDescent\n",
      "train/GradientDescent/update_outputs/bias/ApplyGradientDescent\n",
      "train/GradientDescent\n",
      "eval/in_top_k/InTopKV2/k\n",
      "eval/in_top_k/InTopKV2\n",
      "eval/Cast\n",
      "eval/Const\n",
      "eval/Mean\n",
      "init\n",
      "save/Const\n",
      "save/SaveV2/tensor_names\n",
      "save/SaveV2/shape_and_slices\n",
      "save/SaveV2\n",
      "save/control_dependency\n",
      "save/RestoreV2/tensor_names\n",
      "save/RestoreV2/shape_and_slices\n",
      "save/RestoreV2\n",
      "save/Assign\n",
      "save/Assign_1\n",
      "save/Assign_2\n",
      "save/Assign_3\n",
      "save/Assign_4\n",
      "save/Assign_5\n",
      "save/restore_all\n"
     ]
    }
   ],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "saver = tf.train.import_meta_graph('models/final_mnist_model.ckpt.meta')\n",
    "\n",
    "for op in tf.get_default_graph().get_operations():\n",
    "    print(op.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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       "          }\n",
       "        </script>\n",
       "        <link rel=&quot;import&quot; href=&quot;https://tensorboard.appspot.com/tf-graph-basic.build.html&quot; onload=load()>\n",
       "        <div style=&quot;height:600px&quot;>\n",
       "          <tf-graph-basic id=&quot;graph0.7421398502123514&quot;></tf-graph-basic>\n",
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     "metadata": {},
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    }
   ],
   "source": [
    "show_graph(tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to load tensors or operations, we can either do this individually or all at once if the user has made a collection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Tensor names include index\n",
    "X = tf.get_default_graph().get_tensor_by_name('X:0')\n",
    "y = tf.get_default_graph().get_tensor_by_name('y:0')\n",
    "\n",
    "loss = tf.get_default_graph().get_operation_by_name('loss/loss')\n",
    "\n",
    "# Create and use collection\n",
    "for op in (X, y, loss):\n",
    "    tf.add_to_collection('collection_name', op)\n",
    "    \n",
    "X, y, loss  = tf.get_collection('collection_name')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's say we wanted just the first layer from our MNIST model, and wanted to add two layers on top of that. There are (at least) two ways we can do this. One is to use import_meta_graph() to load the whole graph, grab the components we want while ignoring the rest, and building the new components into this same graph. Then we can save this graph and restore it within our session before training it. Let's add a third layer to your MNIST model, for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
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   }\\n  }\\n  attr {\\n    key: &quot;validate_shape&quot;\\n    value {\\n      b: true\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/restore_all_1&quot;\\n  op: &quot;NoOp&quot;\\n  input: &quot;^save/Assign_10&quot;\\n  input: &quot;^save/Assign_11&quot;\\n  input: &quot;^save/Assign_12&quot;\\n  input: &quot;^save/Assign_13&quot;\\n  input: &quot;^save/Assign_14&quot;\\n  input: &quot;^save/Assign_15&quot;\\n  input: &quot;^save/Assign_6&quot;\\n  input: &quot;^save/Assign_7&quot;\\n  input: &quot;^save/Assign_8&quot;\\n  input: &quot;^save/Assign_9&quot;\\n}\\n';\n",
       "          }\n",
       "        </script>\n",
       "        <link rel=&quot;import&quot; href=&quot;https://tensorboard.appspot.com/tf-graph-basic.build.html&quot; onload=load()>\n",
       "        <div style=&quot;height:600px&quot;>\n",
       "          <tf-graph-basic id=&quot;graph0.4303556542427942&quot;></tf-graph-basic>\n",
       "        </div>\n",
       "    \"></iframe>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "n_hidden3 = 50\n",
    "n_outputs = 10\n",
    "\n",
    "# Load entire graph\n",
    "saver = tf.train.import_meta_graph('models/final_mnist_model.ckpt.meta')\n",
    "\n",
    "X = tf.get_default_graph().get_tensor_by_name('X:0')\n",
    "y = tf.get_default_graph().get_tensor_by_name('y:0')\n",
    "\n",
    "# Grab last hidden layer from graph\n",
    "hidden2 = tf.get_default_graph().get_tensor_by_name('dnn/hidden2/Relu:0')\n",
    "\n",
    "# Build new hidden and output layer\n",
    "new_hidden3 = tf.layers.dense(hidden2, n_hidden3, activation=tf.nn.relu, name='new_hidden3')\n",
    "new_logits = tf.layers.dense(new_hidden3, n_outputs, name='new_outputs')\n",
    "\n",
    "# Define all components that depend on new layers\n",
    "with tf.name_scope('new_loss'):\n",
    "    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=new_logits)\n",
    "    loss = tf.reduce_mean(xentropy, name='loss')\n",
    "    \n",
    "with tf.name_scope('new_eval'):\n",
    "    correct = tf.nn.in_top_k(new_logits, y, 1)\n",
    "    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32), name='accuracy')\n",
    "    \n",
    "with tf.name_scope('new_train'):\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate)\n",
    "    training_op = optimizer.minimize(loss)\n",
    "    \n",
    "init = tf.global_variables_initializer()\n",
    "# Create new saver for saving model (old saver for restoration)\n",
    "new_saver = tf.train.Saver()\n",
    "\n",
    "show_graph(tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in TensorBoard that the old loss, eval, and training scopes are still in the graph. Now let's train it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./final_mnist_model.ckpt\n",
      "Epoch 0 Validation accuracy: 0.9621999859809875\n",
      "Epoch 5 Validation accuracy: 0.9746000170707703\n",
      "Epoch 10 Validation accuracy: 0.9771999716758728\n",
      "Epoch 15 Validation accuracy: 0.9783999919891357\n",
      "Epoch 20 Validation accuracy: 0.9797999858856201\n",
      "Epoch 25 Validation accuracy: 0.9805999994277954\n",
      "Epoch 30 Validation accuracy: 0.9800000190734863\n",
      "Epoch 35 Validation accuracy: 0.9797999858856201\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 40\n",
    "batch_size = 50\n",
    "\n",
    "def shuffle_batch(X, y, batch_size):\n",
    "    random_idx = np.random.permutation(len(X))\n",
    "    n_batches = len(X) // batch_size\n",
    "    for batch_idx in np.array_split(random_idx, n_batches):\n",
    "        X_batch, y_batch = X[batch_idx], y[batch_idx]\n",
    "        yield X_batch, y_batch\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    saver.restore(sess, 'models/final_mnist_model.ckpt')\n",
    "    \n",
    "    for epoch in np.arange(n_epochs):\n",
    "        for X_batch, y_batch in shuffle_batch(X_train, y_train, batch_size):\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        if epoch % 5 == 0:\n",
    "            accuracy_valid = accuracy.eval(feed_dict={X: X_valid, y: y_valid})\n",
    "            print(f'Epoch {epoch} Validation accuracy: {accuracy_valid}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another method is to construct the graph in its entirety explicitly, and then restore the variables that we want to use with the get_collection method during execution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "n_inputs = 28*28\n",
    "n_hidden1 = 300  # resued layer\n",
    "n_hidden2 = 100  # new layer\n",
    "n_hidden3 = 50   # new layer\n",
    "n_outputs = 10   # new layer\n",
    "learning_rate = 0.01\n",
    "\n",
    "relu_layer = partial(tf.layers.dense, activation=tf.nn.relu)\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name='X')\n",
    "y = tf.placeholder(tf.int32, shape=(None), name='y')\n",
    "\n",
    "with tf.name_scope('dnn'):\n",
    "    hidden1 = relu_layer(X, n_hidden1, name='hidden1')            # old layer\n",
    "    hidden2 = relu_layer(hidden1, n_hidden2, name='hidden2')      # new layer\n",
    "    hidden3 = relu_layer(hidden2, n_hidden3, name='hidden3')      # new layer\n",
    "    logits = tf.layers.dense(hidden3, n_outputs, name='outputs')  # new layer\n",
    "    \n",
    "with tf.name_scope('loss'):\n",
    "    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)\n",
    "    loss = tf.reduce_mean(xentropy, name='loss')\n",
    "    \n",
    "with tf.name_scope('eval'):\n",
    "    correct = tf.nn.in_top_k(logits, y, 1)\n",
    "    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32), name='accuracy') \n",
    "    \n",
    "with tf.name_scope('train'):\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate)\n",
    "    training_op = optimizer.minimize(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./final_mnist_model.ckpt\n",
      "Epoch 0 Validation accuracy: 0.9419999718666077\n",
      "Epoch 5 Validation accuracy: 0.9702000021934509\n",
      "Epoch 10 Validation accuracy: 0.975600004196167\n",
      "Epoch 15 Validation accuracy: 0.9778000116348267\n",
      "Epoch 20 Validation accuracy: 0.979200005531311\n",
      "Epoch 25 Validation accuracy: 0.9779999852180481\n",
      "Epoch 30 Validation accuracy: 0.9801999926567078\n",
      "Epoch 35 Validation accuracy: 0.980400025844574\n"
     ]
    }
   ],
   "source": [
    "# Only grab variables within hidden layers\n",
    "reuse_vars = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES,\n",
    "                              scope='hidden1')\n",
    "restore_saver = tf.train.Saver(reuse_vars)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    # Load variables with hidden layers\n",
    "    restore_saver.restore(sess, 'models/final_mnist_model.ckpt')\n",
    "    \n",
    "    for epoch in np.arange(n_epochs):\n",
    "        for X_batch, y_batch in shuffle_batch(X_train, y_train, batch_size):\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        if epoch % 5 == 0:\n",
    "            validation_accuracy = accuracy.eval(feed_dict={X: X_valid, y: y_valid})\n",
    "            print(f'Epoch {epoch} Validation accuracy: {validation_accuracy}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Freezing the Lower Layers\n",
    "\n",
    "If we want to freeze the lower layers (as mentioned above, these layers detect lower-level features), we can change the train name scope we've been using to only change the variables of certain layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "n_inputs = 28*28\n",
    "n_hidden1 = 300  # resued layer\n",
    "n_hidden2 = 100  # new layer\n",
    "n_hidden3 = 50   # new layer\n",
    "n_outputs = 10   # new layer\n",
    "learning_rate = 0.01\n",
    "\n",
    "relu_layer = partial(tf.layers.dense, activation=tf.nn.relu)\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name='X')\n",
    "y = tf.placeholder(tf.int32, shape=(None), name='y')\n",
    "\n",
    "with tf.name_scope('dnn'):\n",
    "    hidden1 = relu_layer(X, n_hidden1, name='hidden1')            # old layer\n",
    "    hidden2 = relu_layer(hidden1, n_hidden2, name='hidden2')      # new layer\n",
    "    hidden3 = relu_layer(hidden2, n_hidden3, name='hidden3')      # new layer\n",
    "    logits = tf.layers.dense(hidden3, n_outputs, name='outputs')  # new layer\n",
    "    \n",
    "with tf.name_scope('loss'):\n",
    "    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)\n",
    "    loss = tf.reduce_mean(xentropy, name='loss')\n",
    "\n",
    "with tf.name_scope('train'):\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate)\n",
    "    train_vars = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES,\n",
    "                                  scope='hidden[34]|outputs')\n",
    "    training_op = optimizer.minimize(loss, var_list=train_vars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Caching the Frozen Layers\n",
    "\n",
    "We can also just store the output of the topmost frozen layer instead of having to actually travel through those layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "n_inputs = 28*28\n",
    "n_hidden1 = 300  # resued layer\n",
    "n_hidden2 = 100  # new layer\n",
    "n_hidden3 = 50   # new layer\n",
    "n_outputs = 10   # new layer\n",
    "learning_rate = 0.01\n",
    "\n",
    "relu_layer = partial(tf.layers.dense, activation=tf.nn.relu)\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name='X')\n",
    "y = tf.placeholder(tf.int32, shape=(None), name='y')\n",
    "\n",
    "with tf.name_scope('dnn'):\n",
    "    hidden1 = relu_layer(X, n_hidden1, name='hidden1')            # old layer\n",
    "    hidden2 = relu_layer(hidden1, n_hidden2, name='hidden2')      # new layer\n",
    "    hidden2_stop = tf.stop_gradient(hidden2)                      # cache output\n",
    "    hidden3 = relu_layer(hidden2_stop, n_hidden3, name='hidden3') # new layer\n",
    "    logits = tf.layers.dense(hidden3, n_outputs, name='outputs')  # new layer\n",
    "    \n",
    "with tf.name_scope('loss'):\n",
    "    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)\n",
    "    loss = tf.reduce_mean(xentropy, name='loss')\n",
    "    \n",
    "with tf.name_scope('eval'):\n",
    "    correct = tf.nn.in_top_k(logits, y, 1)\n",
    "    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32), name='accuracy') \n",
    "    \n",
    "with tf.name_scope('train'):\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate)\n",
    "    training_op = optimizer.minimize(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from ./final_mnist_model.ckpt\n",
      "0 Validation accuracy: 0.8399999737739563\n",
      "1 Validation accuracy: 0.8838000297546387\n",
      "2 Validation accuracy: 0.9007999897003174\n",
      "3 Validation accuracy: 0.9103999733924866\n",
      "4 Validation accuracy: 0.9182000160217285\n",
      "5 Validation accuracy: 0.9218000173568726\n",
      "6 Validation accuracy: 0.9247999787330627\n",
      "7 Validation accuracy: 0.928600013256073\n",
      "8 Validation accuracy: 0.9308000206947327\n",
      "9 Validation accuracy: 0.9337999820709229\n",
      "10 Validation accuracy: 0.9337999820709229\n",
      "11 Validation accuracy: 0.9366000294685364\n",
      "12 Validation accuracy: 0.9359999895095825\n",
      "13 Validation accuracy: 0.9362000226974487\n",
      "14 Validation accuracy: 0.9383999705314636\n",
      "15 Validation accuracy: 0.9395999908447266\n",
      "16 Validation accuracy: 0.9404000043869019\n",
      "17 Validation accuracy: 0.9404000043869019\n",
      "18 Validation accuracy: 0.9404000043869019\n",
      "19 Validation accuracy: 0.9401999711990356\n",
      "20 Validation accuracy: 0.9413999915122986\n",
      "21 Validation accuracy: 0.9412000179290771\n",
      "22 Validation accuracy: 0.9412000179290771\n",
      "23 Validation accuracy: 0.9430000185966492\n",
      "24 Validation accuracy: 0.9435999989509583\n",
      "25 Validation accuracy: 0.9430000185966492\n",
      "26 Validation accuracy: 0.9437999725341797\n",
      "27 Validation accuracy: 0.9423999786376953\n",
      "28 Validation accuracy: 0.9441999793052673\n",
      "29 Validation accuracy: 0.9452000260353088\n",
      "30 Validation accuracy: 0.9449999928474426\n",
      "31 Validation accuracy: 0.9455999732017517\n",
      "32 Validation accuracy: 0.946399986743927\n",
      "33 Validation accuracy: 0.9448000192642212\n",
      "34 Validation accuracy: 0.9458000063896179\n",
      "35 Validation accuracy: 0.9458000063896179\n",
      "36 Validation accuracy: 0.9477999806404114\n",
      "37 Validation accuracy: 0.9472000002861023\n",
      "38 Validation accuracy: 0.9473999738693237\n",
      "39 Validation accuracy: 0.9459999799728394\n"
     ]
    }
   ],
   "source": [
    "reuse_vars = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES,\n",
    "                              scope='hidden1')\n",
    "restore_saver = tf.train.Saver(reuse_vars)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "n_batches = len(X_train) // batch_size\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    restore_saver.restore(sess, 'models/final_mnist_model.ckpt')\n",
    "    \n",
    "    # Get output of 2nd hidden layer\n",
    "    h2_cache = sess.run(hidden2, feed_dict={X: X_train})\n",
    "    # Run validation data through first two layers\n",
    "    h2_cache_valid = sess.run(hidden2, feed_dict={X: X_valid})\n",
    "    \n",
    "    for epoch in np.arange(n_epochs):\n",
    "        random_indices = np.random.permutation(len(X_train))\n",
    "        # Random batches of output of 2nd hidden layer\n",
    "        hidden2_batches = np.array_split(h2_cache[random_indices], n_batches)\n",
    "        y_batches = np.array_split(y_train[random_indices], n_batches)\n",
    "        for hidden2_batch, y_batch in zip(hidden2_batches, y_batches):\n",
    "            # Use output of 2nd hidden layer as training data\n",
    "            sess.run(training_op, feed_dict={hidden2: hidden2_batch, y: y_batch})\n",
    "        \n",
    "        accuracy_val = accuracy.eval(feed_dict={hidden2: h2_cache_valid, y: y_valid})\n",
    "        print(f\"{epoch} Validation accuracy: {accuracy_val}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Faster Optimizers\n",
    "\n",
    "We also have the choice between optimizers such as momentum optimization, Nesterov Accelerated gradient, AdaGrad, RMSProp, and Adam optimization, although Adam is almost always the best choice.\n",
    "\n",
    "### Learning Rate Scheduling\n",
    "\n",
    "There are multiple methods for how we should change the learning rate when training our model, called the *learning rate schedule*. We'd like to start with a high learning rate and reduce it once we start getting closer to the minimum. TensorFlow has [multiple options](https://github.com/tensorflow/tensorflow/blob/r1.13/tensorflow/python/training/learning_rate_decay.py) for which type of learning rate decay you'd like to use, but let's go with exponential decay with momentum optimization. Keep in mind that AdaGrad, RMSProp, and Adam have their own mechanisms for updating the learning rate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "n_inputs = 28 * 28 \n",
    "n_hidden1 = 300\n",
    "n_hidden2 = 50\n",
    "n_outputs = 10\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name=\"X\")\n",
    "y = tf.placeholder(tf.int32, shape=(None), name=\"y\")\n",
    "\n",
    "with tf.name_scope(\"dnn\"):\n",
    "    hidden1 = tf.layers.dense(X, n_hidden1, activation=tf.nn.relu, name=\"hidden1\")\n",
    "    hidden2 = tf.layers.dense(hidden1, n_hidden2, activation=tf.nn.relu, name=\"hidden2\")\n",
    "    logits = tf.layers.dense(hidden2, n_outputs, name=\"outputs\")\n",
    "\n",
    "with tf.name_scope(\"loss\"):\n",
    "    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)\n",
    "    loss = tf.reduce_mean(xentropy, name=\"loss\")\n",
    "\n",
    "with tf.name_scope('train'):\n",
    "    initial_learning_rate = 0.1\n",
    "    decay_steps = 10000\n",
    "    decay_rate = 1/10\n",
    "    global_step = tf.Variable(0, trainable=False, name='global_step')\n",
    "    # decayed_learning_rate = initial_learning_rate * decay_rate^(global_step / decay_steps)\n",
    "    learning_rate = tf.train.exponential_decay(initial_learning_rate, global_step, \n",
    "                                               decay_steps, decay_rate)\n",
    "    optimizer = tf.train.MomentumOptimizer(learning_rate, momentum=0.9)\n",
    "    # Global_step increments by one each times variables are updated\n",
    "    training_op = optimizer.minimize(loss, global_step=global_step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Avoiding Overfitting through Regularization\n",
    "\n",
    "### Early Stopping\n",
    "\n",
    "One simple strategy to deal with overfitting is to record the validation accuracy at set intervals (number of steps or epochs), and stop training once we're confident that validation accuracy will continue to drop (it's possible that a temporary dip will give way to eventual improvement).\n",
    "\n",
    "### $\\\\l_1$ and $\\\\l_2$ Regularization\n",
    "\n",
    "We can pass TensorFlow's regularizers as parameters to our layers and make sure to include these in our loss function to use l1 and l2 regularization in our network. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "scale=0.001\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name=\"X\")\n",
    "y = tf.placeholder(tf.int32, shape=(None), name=\"y\")\n",
    "\n",
    "regularized_dense_layer = partial(tf.layers.dense, activation=tf.nn.relu,\n",
    "                                 kernel_regularizer=tf.contrib.layers.l1_regularizer(scale))\n",
    "\n",
    "with tf.name_scope('dnn'):\n",
    "    hidden1 = regularized_dense_layer(X, n_hidden1, name='hidden1')\n",
    "    hidden2 = regularized_dense_layer(hidden1, n_hidden2, name='hidden2')\n",
    "    logits = regularized_dense_layer(hidden2, n_outputs, activation=None, \n",
    "                                    name='outputs')\n",
    "    \n",
    "with tf.name_scope('loss'):\n",
    "    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)\n",
    "    base_loss = tf.reduce_mean(xentropy, name='avg_xentropy')\n",
    "    # Regularized losses stored in keys\n",
    "    reg_losses = tf.get_collection(tf.GraphKeys.REGULARIZATION_LOSSES)\n",
    "    loss = tf.add_n([base_loss] + reg_losses, name='loss')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dropout\n",
    "\n",
    "Dropout will temporarily remove neurons at every training step, with each neuron having a probability p (the dropout rate hyperparameter) of being removed. Because the neurons receive only a fraction of the number of inputs and the weights will be adjusted to this smaller number, we have to mutliply the final weights by the keep probability (1-p). We can implement this in TensorFlow by defining a tf.layers.dropout layer after defining the input and each hidden layer. We have to pass the layer we're trying to \"dropout\", the dropout rate, and whether we're currently training (initialized as False and becomes True once we execute our training operation). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs), name='X')\n",
    "y = tf.placeholder(tf.int32, shape=(None), name='y')\n",
    "training = tf.placeholder_with_default(False, shape=(), name='training')\n",
    "\n",
    "dropout_rate = 0.5\n",
    "# Dropout input\n",
    "X_drop = tf.layers.dropout(X, dropout_rate, training)\n",
    "\n",
    "with tf.name_scope('dnn'):\n",
    "    hidden1 = tf.layers.dense(X_drop, n_hidden1, activation=tf.nn.relu\n",
    "                             name='hidden1')\n",
    "    hidden1_drop = tf.layers.dropout(hidden1, dropout_rate, training)\n",
    "    hidden2 = tf.layers.dense(hidden1_drop, n_hidden2, activation=tf.nn.relu\n",
    "                             name='hidden2')\n",
    "    hidden2_drop = tf.layers.dropout(hidden2, dropout_rate, training)\n",
    "    logits = tf.layers.dense(hidden2_drop, n_outputs, name='outputs')"
   ]
  }
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