# A Guide to TF Layers: Building a Convolutional Neural Network

The TensorFlow @{tf.layers$`layers` module} provides a high-level API that makes
it easy to construct a neural network. It provides methods that facilitate the
creation of dense (fully connected) layers and convolutional layers, adding
activation functions, and applying dropout regularization. In this tutorial,
you'll learn how to use `layers` to build a convolutional neural network model
to recognize the handwritten digits in the MNIST data set.

![handwritten digits 0–9 from the MNIST data set](../images/mnist_0-9.png)

**The [MNIST dataset](http://yann.lecun.com/exdb/mnist/) comprises 60,000
training examples and 10,000 test examples of the handwritten digits 0–9,
formatted as 28x28-pixel monochrome images.**

## Getting Started

Let's set up the skeleton for our TensorFlow program. Create a file called
`cnn_mnist.py`, and add the following code:

```python
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

# Imports
import numpy as np
import tensorflow as tf

from tensorflow.contrib import learn
from tensorflow.contrib.learn.python.learn.estimators import model_fn as model_fn_lib

tf.logging.set_verbosity(tf.logging.INFO)

# Our application logic will be added here

if __name__ == "__main__":
  tf.app.run()
```

As you work through the tutorial, you'll add code to construct, train, and
evaluate the convolutional neural network. The complete, final code can be
[found here](https://www.tensorflow.org/code/tensorflow/examples/tutorials/layers/cnn_mnist.py).

## Intro to Convolutional Neural Networks

Convolutional neural networks (CNNs) are the current state-of-the-art model
architecture for image classification tasks. CNNs apply a series of filters to
the raw pixel data of an image to extract and learn higher-level features, which
the model can then use for classification. CNNs contains three components:

*   **Convolutional layers**, which apply a specified number of convolution
    filters to the image. For each subregion, the layer performs a set of
    mathematical operations to produce a single value in the output feature map.
    Convolutional layers then typically apply a
    [ReLU activation function](https://en.wikipedia.org/wiki/Rectifier_\(neural_networks\)) to
    the output to introduce nonlinearities into the model.

*   **Pooling layers**, which
    [downsample the image data](https://en.wikipedia.org/wiki/Convolutional_neural_network#Pooling_layer)
    extracted by the convolutional layers to reduce the dimensionality of the
    feature map in order to decrease processing time. A commonly used pooling
    algorithm is max pooling, which extracts subregions of the feature map
    (e.g., 2x2-pixel tiles), keeps their maximum value, and discards all other
    values.

*   **Dense (fully connected) layers**, which perform classification on the
    features extracted by the convolutional layers and downsampled by the
    pooling layers. In a dense layer, every node in the layer is connected to
    every node in the preceding layer.

Typically, a CNN is composed of a stack of convolutional modules that perform
feature extraction. Each module consists of a convolutional layer followed by a
pooling layer. The last convolutional module is followed by one or more dense
layers that perform classification. The final dense layer in a CNN contains a
single node for each target class in the model (all the possible classes the
model may predict), with a
[softmax](https://en.wikipedia.org/wiki/Softmax_function) activation function to
generate a value between 0–1 for each node (the sum of all these softmax values
is equal to 1). We can interpret the softmax values for a given image as
relative measurements of how likely it is that the image falls into each target
class.

> Note: For a more comprehensive walkthrough of CNN architecture, see Stanford
> University's <a href="http://cs231n.github.io/convolutional-networks/">
> Convolutional Neural Networks for Visual Recognition course materials</a>.</p>

## Building the CNN MNIST Classifier {#building_the_cnn_mnist_classifier}

Let's build a model to classify the images in the MNIST dataset using the
following CNN architecture:

1.  **Convolutional Layer #1**: Applies 32 5x5 filters (extracting 5x5-pixel
    subregions), with ReLU activation function
2.  **Pooling Layer #1**: Performs max pooling with a 2x2 filter and stride of 2
    (which specifies that pooled regions do not overlap)
3.  **Convolutional Layer #2**: Applies 64 5x5 filters, with ReLU activation
    function
4.  **Pooling Layer #2**: Again, performs max pooling with a 2x2 filter and
    stride of 2
5.  **Dense Layer #1**: 1,024 neurons, with dropout regularization rate of 0.4
    (probability of 0.4 that any given element will be dropped during training)
6.  **Dense Layer #2 (Logits Layer)**: 10 neurons, one for each digit target
    class (0–9).

The `tf.layers` module contains methods to create each of the three layer types
above:

*   `conv2d()`. Constructs a two-dimensional convolutional layer. Takes number
    of filters, filter kernel size, padding, and activation function as
    arguments.
*   `max_pooling2d()`. Constructs a two-dimensional pooling layer using the
    max-pooling algorithm. Takes pooling filter size and stride as arguments.
*   `dense()`. Constructs a dense layer. Takes number of neurons and activation
    function as arguments.

Each of these methods accepts a tensor as input and returns a transformed tensor
as output. This makes it easy to connect one layer to another: just take the
output from one layer-creation method and supply it as input to another.

Open `cnn_mnist.py` and add the following `cnn_model_fn` function, which
conforms to the interface expected by TensorFlow's Estimator API (more on this
later in [Create the Estimator](#create-the-estimator)). `cnn_mnist.py` takes
MNIST feature data, labels, and
@{tf.contrib.learn.ModeKeys$model mode} (`TRAIN`, `EVAL`,
`INFER`) as arguments; configures the CNN; and returns predictions, loss, and a
training operation:

```python
def cnn_model_fn(features, labels, mode):
  """Model function for CNN."""
  # Input Layer
  input_layer = tf.reshape(features, [-1, 28, 28, 1])

  # Convolutional Layer #1
  conv1 = tf.layers.conv2d(
      inputs=input_layer,
      filters=32,
      kernel_size=[5, 5],
      padding="same",
      activation=tf.nn.relu)

  # Pooling Layer #1
  pool1 = tf.layers.max_pooling2d(inputs=conv1, pool_size=[2, 2], strides=2)

  # Convolutional Layer #2 and Pooling Layer #2
  conv2 = tf.layers.conv2d(
      inputs=pool1,
      filters=64,
      kernel_size=[5, 5],
      padding="same",
      activation=tf.nn.relu)
  pool2 = tf.layers.max_pooling2d(inputs=conv2, pool_size=[2, 2], strides=2)

  # Dense Layer
  pool2_flat = tf.reshape(pool2, [-1, 7 * 7 * 64])
  dense = tf.layers.dense(inputs=pool2_flat, units=1024, activation=tf.nn.relu)
  dropout = tf.layers.dropout(
      inputs=dense, rate=0.4, training=mode == learn.ModeKeys.TRAIN)

  # Logits Layer
  logits = tf.layers.dense(inputs=dropout, units=10)

  loss = None
  train_op = None

  # Calculate Loss (for both TRAIN and EVAL modes)
  if mode != learn.ModeKeys.INFER:
    onehot_labels = tf.one_hot(indices=tf.cast(labels, tf.int32), depth=10)
    loss = tf.losses.softmax_cross_entropy(
        onehot_labels=onehot_labels, logits=logits)

  # Configure the Training Op (for TRAIN mode)
  if mode == learn.ModeKeys.TRAIN:
    train_op = tf.contrib.layers.optimize_loss(
        loss=loss,
        global_step=tf.contrib.framework.get_global_step(),
        learning_rate=0.001,
        optimizer="SGD")

  # Generate Predictions
  predictions = {
      "classes": tf.argmax(
          input=logits, axis=1),
      "probabilities": tf.nn.softmax(
          logits, name="softmax_tensor")
  }

  # Return a ModelFnOps object
  return model_fn_lib.ModelFnOps(
      mode=mode, predictions=predictions, loss=loss, train_op=train_op)
```

The following sections (with headings corresponding to each code block above)
dive deeper into the `tf.layers` code used to create each layer, as well as how
to calculate loss, configure the training op, and generate predictions. If
you're already experienced with CNNs and @{$estimators$TensorFlow `Estimator`s},
and find the above code intuitive, you may want to skim these sections or just
skip ahead to ["Training and Evaluating the CNN MNIST
Classifier"](#training-and-evaluating-the-cnn-mnist-classifier).

### Input Layer

The methods in the `layers` module for creating convolutional and pooling layers
for two-dimensional image data expect input tensors to have a shape of
<code>[<em>batch_size</em>, <em>image_width</em>, <em>image_height</em>,
<em>channels</em>]</code>, defined as follows:

*   _`batch_size`_. Size of the subset of examples to use when performing
    gradient descent during training.
*   _`image_width`_. Width of the example images.
*   _`image_height`_. Height of the example images.
*   _`channels`_. Number of color channels in the example images. For color
    images, the number of channels is 3 (red, green, blue). For monochrome
    images, there is just 1 channel (black).

Here, our MNIST dataset is composed of monochrome 28x28 pixel images, so the
desired shape for our input layer is <code>[<em>batch_size</em>, 28, 28,
1]</code>.

To convert our input feature map (`features`) to this shape, we can perform the
following `reshape` operation:

```python
input_layer = tf.reshape(features, [-1, 28, 28, 1])
```

Note that we've indicated `-1` for batch size, which specifies that this
dimension should be dynamically computed based on the number of input values in
`features`, holding the size of all other dimensions constant. This allows us to
treat `batch_size` as a hyperparameter that we can tune. For example, if we feed
examples into our model in batches of 5, `features` will contain 3,920 values
(one value for each pixel in each image), and `input_layer` will have a shape of
`[5, 28, 28, 1]`. Similarly, if we feed examples in batches of 100, `features`
will contain 78,400 values, and `input_layer` will have a shape of `[100, 28,
28, 1]`.

### Convolutional Layer #1

In our first convolutional layer, we want to apply 32 5x5 filters to the input
layer, with a ReLU activation function. We can use the `conv2d()` method in the
`layers` module to create this layer as follows:

```python
conv1 = tf.layers.conv2d(
    inputs=input_layer,
    filters=32,
    kernel_size=[5, 5],
    padding="same",
    activation=tf.nn.relu)
```

The `inputs` argument specifies our input tensor, which must have the shape
<code>[<em>batch_size</em>, <em>image_width</em>, <em>image_height</em>,
<em>channels</em>]</code>. Here, we're connecting our first convolutional layer
to `input_layer`, which has the shape <code>[<em>batch_size</em>, 28, 28,
1]</code>.

> Note: <code>conv2d()</code> will instead accept a shape of
> <code>[<em>channels</em>, <em>batch_size</em>, <em>image_width</em>,
> <em>image_height</em>]</code> when passed the argument
> <code>data_format=channels_first</code>.

The `filters` argument specifies the number of filters to apply (here, 32), and
`kernel_size` specifies the dimensions of the filters as <code>[<em>width</em>,
<em>height</em>]</code> (here, <code>[5, 5]</code>).

<p class="tip"><b>TIP:</b> If filter width and height have the same value, you can instead specify a
single integer for <code>kernel_size</code>—e.g., <code>kernel_size=5</code>.</p>

The `padding` argument specifies one of two enumerated values
(case-insensitive): `valid` (default value) or `same`. To specify that the
output tensor should have the same width and height values as the input tensor,
we set `padding=same` here, which instructs TensorFlow to add 0 values to the
edges of the output tensor to preserve width and height of 28. (Without padding,
a 5x5 convolution over a 28x28 tensor will produce a 24x24 tensor, as there are
24x24 locations to extract a 5x5 tile from a 28x28 grid.)

The `activation` argument specifies the activation function to apply to the
output of the convolution. Here, we specify ReLU activation with
@{tf.nn.relu}.

Our output tensor produced by `conv2d()` has a shape of
<code>[<em>batch_size</em>, 28, 28, 32]</code>: the same width and height
dimensions as the input, but now with 32 channels holding the output from each
of the filters.

### Pooling Layer #1

Next, we connect our first pooling layer to the convolutional layer we just
created. We can use the `max_pooling2d()` method in `layers` to construct a
layer that performs max pooling with a 2x2 filter and stride of 2:

```python
pool1 = tf.layers.max_pooling2d(inputs=conv1, pool_size=[2, 2], strides=2)
```

Again, `inputs` specifies the input tensor, with a shape of
<code>[<em>batch_size</em>, <em>image_width</em>, <em>image_height</em>,
<em>channels</em>]</code>. Here, our input tensor is `conv1`, the output from
the first convolutional layer, which has a shape of <code>[<em>batch_size</em>,
28, 28, 32]</code>.

> Note: As with <code>conv2d()</code>, <code>max_pooling2d()</code> will instead
> accept a shape of <code>[<em>channels</em>, <em>batch_size</em>,
> <em>image_width</em>, <em>image_height</em>]</code> when passed the argument
> <code>data_format=channels_first</code>.

The `pool_size` argument specifies the size of the max pooling filter as
<code>[<em>width</em>, <em>height</em>]</code> (here, `[2, 2]`). If both
dimensions have the same value, you can instead specify a single integer (e.g.,
`pool_size=2`).

The `strides` argument specifies the size of the stride. Here, we set a stride
of 2, which indicates that the subregions extracted by the filter should be
separated by 2 pixels in both the width and height dimensions (for a 2x2 filter,
this means that none of the regions extracted will overlap). If you want to set
different stride values for width and height, you can instead specify a tuple or
list (e.g., `stride=[3,6]`).

Our output tensor produced by `max_pooling2d()` (`pool1`) has a shape of
<code>[<em>batch_size</em>, 14, 14, 1]</code>: the 2x2 filter reduces width and
height by 50%.

### Convolutional Layer #2 and Pooling Layer #2

We can connect a second convolutional and pooling layer to our CNN using
`conv2d()` and `max_pooling2d()` as before. For convolutional layer #2, we
configure 64 5x5 filters with ReLU activation, and for pooling layer #2, we use
the same specs as pooling layer #1 (a 2x2 max pooling filter with stride of 2):

```python
conv2 = tf.layers.conv2d(
    inputs=pool1,
    filters=64,
    kernel_size=[5, 5],
    padding="same",
    activation=tf.nn.relu)

pool2 = tf.layers.max_pooling2d(inputs=conv2, pool_size=[2, 2], strides=2)
```

Note that convolutional layer #2 takes the output tensor of our first pooling
layer (`pool1`) as input, and produces the tensor `h_conv2` as output. `conv2`
has a shape of <code>[<em>batch_size</em>, 14, 14, 64]</code>, the same width
and height as `pool1` (due to `padding="same"`), and 64 channels for the 64
filters applied.

Pooling layer #2 takes `conv2` as input, producing `pool2` as output. `pool2`
has shape <code>[<em>batch_size</em>, 7, 7, 64]</code> (50% reduction of width
and height from `conv2`).

### Dense Layer

Next, we want to add a dense layer (with 1,024 neurons and ReLU activation) to
our CNN to perform classification on the features extracted by the
convolution/pooling layers. Before we connect the layer, however, we'll flatten
our feature map (`pool2`) to shape <code>[<em>batch_size</em>,
<em>features</em>]</code>, so that our tensor has only two dimensions:

```python
pool2_flat = tf.reshape(pool2, [-1, 7 * 7 * 64])
```

In the `reshape()` operation above, the `-1` signifies that the *`batch_size`*
dimension will be dynamically calculated based on the number of examples in our
input data. Each example has 7 (`pool2` width) * 7 (`pool2` height) * 64
(`pool2` channels) features, so we want the `features` dimension to have a value
of 7 * 7 * 64 (3136 in total). The output tensor, `pool2_flat`, has shape
<code>[<em>batch_size</em>, 3136]</code>.

Now, we can use the `dense()` method in `layers` to connect our dense layer as
follows:

```python
dense = tf.layers.dense(inputs=pool2_flat, units=1024, activation=tf.nn.relu)
```

The `inputs` argument specifies the input tensor: our flattened feature map,
`pool2_flat`. The `units` argument specifies the number of neurons in the dense
layer (1,024). The `activation` argument takes the activation function; again,
we'll use `tf.nn.relu` to add ReLU activation.

To help improve the results of our model, we also apply dropout regularization
to our dense layer, using the `dropout` method in `layers`:

```python
dropout = tf.layers.dropout(
    inputs=dense, rate=0.4, training=mode == learn.ModeKeys.TRAIN)
```

Again, `inputs` specifies the input tensor, which is the output tensor from our
dense layer (`dense`).

The `rate` argument specifies the dropout rate; here, we use `0.4`, which means
40% of the elements will be randomly dropped out during training.

The `training` argument takes a boolean specifying whether or not the model is
currently being run in training mode; dropout will only be performed if
`training` is `True`. Here, we check if the `mode` passed to our model function
`cnn_model_fn` is `TRAIN` mode.

Our output tensor `dropout` has shape <code>[<em>batch_size</em>, 1024]</code>.

### Logits Layer

The final layer in our neural network is the logits layer, which will return the
raw values for our predictions. We create a dense layer with 10 neurons (one for
each target class 0–9), with linear activation (the default):

```python
logits = tf.layers.dense(inputs=dropout, units=10)
```

Our final output tensor of the CNN, `logits`, has shape
<code>[<em>batch_size</em>, 10]</code>.

### Calculate Loss {#calculating-loss}

For both training and evaluation, we need to define a
[loss function](https://en.wikipedia.org/wiki/Loss_function)
that measures how closely the model's predictions match the target classes. For
multiclass classification problems like MNIST,
[cross entropy](https://en.wikipedia.org/wiki/Cross_entropy) is typically used
as the loss metric. The following code calculates cross entropy when the model
runs in either `TRAIN` or `EVAL` mode:

```python
loss = None
train_op = None

# Calculate loss for both TRAIN and EVAL modes
if mode != learn.ModeKeys.INFER:
  onehot_labels = tf.one_hot(indices=tf.cast(labels, tf.int32), depth=10)
  loss = tf.losses.softmax_cross_entropy(
      onehot_labels=onehot_labels, logits=logits)
```

Let's take a closer look at what's happening above.

Our `labels` tensor contains a list of predictions for our examples, e.g. `[1,
9, ...]`. In order to calculate cross-entropy, first we need to convert `labels`
to the corresponding
[one-hot encoding](https://www.quora.com/What-is-one-hot-encoding-and-when-is-it-used-in-data-science):

```none
[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
 ...]
```

We use the @{tf.one_hot} function
to perform this conversion. `tf.one_hot()` has two required arguments:

*   `indices`. The locations in the one-hot tensor that will have "on
    values"—i.e., the locations of `1` values in the tensor shown above.
*   `depth`. The depth of the one-hot tensor—i.e., the number of target classes.
    Here, the depth is `10`.

The following code creates the one-hot tensor for our labels, `onehot_labels`:

```python
onehot_labels = tf.one_hot(indices=tf.cast(labels, tf.int32), depth=10)
```

Because `labels` contains a series of values from 0–9, `indices` is just our
`labels` tensor, with values cast to integers. The `depth` is `10` because we
have 10 possible target classes, one for each digit.

Next, we compute cross-entropy of `onehot_labels` and the softmax of the
predictions from our logits layer. `tf.losses.softmax_cross_entropy()` takes
`onehot_labels` and `logits` as arguments, performs softmax activation on
`logits`, calculates cross-entropy, and returns our `loss` as a scalar `Tensor`:

```python
loss = tf.losses.softmax_cross_entropy(
        onehot_labels=onehot_labels, logits=logits)
```

### Configure the Training Op

In the previous section, we defined loss for our CNN as the softmax
cross-entropy of the logits layer and our labels. Let's configure our model to
optimize this loss value during training, using the
@{tf.contrib.layers.optimize_loss}
method in `tf.contrib.layers`. We'll use a learning rate of 0.001 and
[stochastic gradient descent](https://en.wikipedia.org/wiki/Stochastic_gradient_descent)
as the optimization algorithm:

```python
# Configure the Training Op (for TRAIN mode)
if mode == learn.ModeKeys.TRAIN:
    train_op = tf.contrib.layers.optimize_loss(
        loss=loss,
        global_step=tf.contrib.framework.get_global_step(),
        learning_rate=0.001,
        optimizer="SGD")
```

> Note: For a more in-depth look at configuring training ops for Estimator model
> functions, see @{$estimators#defining-the-training-op-for-the-model$"Defining
> the training op for the model"} in the @{$estimators$"Creating Estimations in
> tf.contrib.learn"} tutorial.

### Generate Predictions {#generate_predictions}

The logits layer of our model returns our predictions as raw values in a
<code>[<em>batch_size</em>, 10]</code>-dimensional tensor. Let's convert these
raw values into two different formats that our model function can return:

*   The **predicted class** for each example: a digit from 0–9.
*   The **probabilities** for each possible target class for each example: the
    probability that the example is a 0, is a 1, is a 2, etc.

For a given example, our predicted class is the element in the corresponding row
of the logits tensor with the highest raw value. We can find the index of this
element using the @{tf.argmax}
function:

```python
tf.argmax(input=logits, axis=1)
```

The `input` argument specifies the tensor from which to extract maximum
values—here `logits`. The `axis` argument specifies the axis of the `input`
tensor along which to find the greatest value. Here, we want to find the largest
value along the dimension with index of 1, which corresponds to our predictions
(recall that our logits tensor has shape <code>[<em>batch_size</em>,
10]</code>).

We can derive probabilities from our logits layer by applying softmax activation
using @{tf.nn.softmax}:

```python
tf.nn.softmax(logits, name="softmax_tensor")
```

> Note: We use the `name` argument to explicitly name this operation
> `softmax_tensor`, so we can reference it later. (We'll set up logging for the
> softmax values in ["Set Up a Logging Hook"](#set-up-a-logging-hook).

We compile our predictions in a dict as follows:

```python
predictions = {
    "classes": tf.argmax(
        input=logits, axis=1),
    "probabilities": tf.nn.softmax(
        logits, name="softmax_tensor")
}
```

Finally, now that we've got our `predictions`, `loss`, and `train_op`, we can
return them, along with our `mode` argument, in a
@{tf.contrib.learn.ModelFnOps} object:

```python
# Return a ModelFnOps object
return model_fn_lib.ModelFnOps(
    mode=mode, predictions=predictions, loss=loss, train_op=train_op)
```

## Training and Evaluating the CNN MNIST Classifier {#training_and_evaluating_the_cnn_mnist_classifier}

We've coded our MNIST CNN model function; now we're ready to train and evaluate
it.

### Load Training and Test Data

First, let's load our training and test data. Add a `main()` function to
`cnn_mnist.py` with the following code:

```python
def main(unused_argv):
  # Load training and eval data
  mnist = learn.datasets.load_dataset("mnist")
  train_data = mnist.train.images # Returns np.array
  train_labels = np.asarray(mnist.train.labels, dtype=np.int32)
  eval_data = mnist.test.images # Returns np.array
  eval_labels = np.asarray(mnist.test.labels, dtype=np.int32)
```

We store the training feature data (the raw pixel values for 55,000 images of
hand-drawn digits) and training labels (the corresponding value from 0–9 for
each image) as [numpy
arrays](https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html)
in `train_data` and `train_labels`, respectively. Similarly, we store the
evalulation feature data (10,000 images) and evaluation labels in `eval_data`
and `eval_labels`, respectively.

### Create the Estimator {#create-the-estimator}

Next, let's create an `Estimator` (a TensorFlow class for performing high-level
model training, evaluation, and inference) for our model. Add the following code
to `main()`:

```python
# Create the Estimator
mnist_classifier = learn.Estimator(
      model_fn=cnn_model_fn, model_dir="/tmp/mnist_convnet_model")
```

The `model_fn` argument specifies the model function to use for training,
evaluation, and inference; we pass it the `cnn_model_fn` we created in
["Building the CNN MNIST Classifier."](#building-the-cnn-mnist-classifier) The
`model_dir` argument specifies the directory where model data (checkpoints) will
be saved (here, we specify the temp directory `/tmp/mnist_convnet_model`, but
feel free to change to another directory of your choice).

> Note: For an in-depth walkthrough of the TensorFlow `Estimator` API, see the
> tutorial @{$estimators$"Creating Estimators in tf.contrib.learn."}

### Set Up a Logging Hook {#set_up_a_logging_hook}

Since CNNs can take a while to train, let's set up some logging so we can track
progress during training. We can use TensorFlow's @{tf.train.SessionRunHook} to create a
@{tf.train.LoggingTensorHook}
that will log the probability values from the softmax layer of our CNN. Add the
following to `main()`:

```python
# Set up logging for predictions
  tensors_to_log = {"probabilities": "softmax_tensor"}
  logging_hook = tf.train.LoggingTensorHook(
      tensors=tensors_to_log, every_n_iter=50)
```

We store a dict of the tensors we want to log in `tensors_to_log`. Each key is a
label of our choice that will be printed in the log output, and the
corresponding label is the name of a `Tensor` in the TensorFlow graph. Here, our
`probabilities` can be found in `softmax_tensor`, the name we gave our softmax
operation earlier when we generated the probabilities in `cnn_model_fn`.

> Note: If you don't explicitly assign a name to an operation via the `name`
> argument, TensorFlow will assign a default name. A couple easy ways to
> discover the names applied to operations are to visualize your graph on
> @{$graph_viz$TensorBoard}) or to enable the @{$debugger$TensorFlow Debugger
> (tfdbg)}.

Next, we create the `LoggingTensorHook`, passing `tensors_to_log` to the
`tensors` argument. We set `every_n_iter=50`, which specifies that probabilities
should be logged after every 50 steps of training.

### Train the Model

Now we're ready to train our model, which we can do by calling `fit()` on
`mnist_classifier`. Add the following to `main()`:

```python
# Train the model
mnist_classifier.fit(
    x=train_data,
    y=train_labels,
    batch_size=100,
    steps=20000,
    monitors=[logging_hook])
```

In the `fit` call, we pass the training feature data and labels to `x` and `y`,
respectively. We set a `batch_size` of `100` (which means that the model will
train on minibatches of 100 examples at each step), and `steps` of `20000`
(which means the model will train for 20,000 steps total). We pass our
`logging_hook` to the `monitors` argument, so that it will be triggered during
training.

### Evaluate the Model

Once training is complete, we want to evaluate our model to determine its
accuracy on the MNIST test set. To set up the accuracy metric for our model, we
need to create a metrics dict with a @{tf.contrib.learn.MetricSpec}
that calculates accuracy. Add the following to `main()`:

```python
# Configure the accuracy metric for evaluation
metrics = {
    "accuracy":
        learn.MetricSpec(
            metric_fn=tf.metrics.accuracy, prediction_key="classes"),
}
```

We create our `MetricSpec`s with the following two arguments:

*   `metric_fn`. The function that calculates and returns the value of our
    metric. Here, we can use the predefined `accuracy` function in the
    @{tf.metrics} module.
*   `prediction_key`. The key of the tensor that contains the predictions
    returned by the model function. Here, because we're building a
    classification model, the prediction key is `"classes"`, which we specified
    back in ["Generate Predictions."](#generate_predictions)

Now that we've set up our `metrics` dict, we can evaluate the model. Add the
following code, which performs evaluation and prints the results:

```python
# Evaluate the model and print results
eval_results = mnist_classifier.evaluate(
    x=eval_data, y=eval_labels, metrics=metrics)
print(eval_results)
```

We pass our evaluation feature data and labels to `evaluate()` in the `x` and
`y` arguments, respectively. The `metrics` argument takes the metrics dict we
just defined.

### Run the Model

We've coded the CNN model function, `Estimator`, and the training/evaluation
logic; now let's see the results. Run `cnn_mnist.py`.

> Note: Training CNNs is quite computationally intensive. Estimated completion
> time of `cnn_mnist.py` will vary depending on your processor, but will likely
> be upwards of 1 hour on CPU. To train more quickly, you can decrease the
> number of `steps` passed to `fit()`, but note that this will affect accuracy.

As the model trains, you'll see log output like the following:

```python
INFO:tensorflow:loss = 2.36026, step = 1
INFO:tensorflow:probabilities = [[ 0.07722801  0.08618255  0.09256398, ...]]
...
INFO:tensorflow:loss = 2.13119, step = 101
INFO:tensorflow:global_step/sec: 5.44132
...
INFO:tensorflow:Loss for final step: 0.553216.

INFO:tensorflow:Restored model from /tmp/mnist_convnet_model
INFO:tensorflow:Eval steps [0,inf) for training step 20000.
INFO:tensorflow:Input iterator is exhausted.
INFO:tensorflow:Saving evaluation summary for step 20000: accuracy = 0.9733, loss = 0.0902271
{'loss': 0.090227105, 'global_step': 20000, 'accuracy': 0.97329998}
```

Here, we've achieved an accuracy of 97.3% on our test data set.

## Additional Resources

To learn more about TensorFlow Estimators and CNNs in TensorFlow, see the
following resources:

*   @{$estimators$Creating Estimators in tf.contrib.learn}. An
    introduction to the TensorFlow Estimator API, which walks through
    configuring an Estimator, writing a model function, calculating loss, and
    defining a training op.
*   @{$pros#build-a-multilayer-convolutional-network$Deep MNIST for Experts: Building a Multilayer CNN}. Walks
    through how to build a MNIST CNN classification model *without layers* using
    lower-level TensorFlow operations.
