The TensorFlow `tf$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. The complete code for this tutorial can be found here.

**The MNIST dataset comprises 60,000 training examples and 10,000 test examples of the handwritten digits 0–9, formatted as 28x28-pixel monochrome images.**

Let’s set up the skeleton for our TensorFlow program by adding the following code to import the necessary libraries and change the logging verbosity:

```
library(tensorflow)
library(tfestimators)
tf$logging$set_verbosity(tf$logging$INFO)
```

As you work through the tutorial, you’ll add code to construct, train, and evaluate the convolutional neural network.

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 to the output to introduce nonlinearities into the model.**Pooling layers**, which downsample the image data 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 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 Convolutional Neural Networks for Visual Recognition course materials.

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

**Convolutional Layer #1**: Applies 32 5x5 filters (extracting 5x5-pixel subregions), with ReLU activation function**Pooling Layer #1**: Performs max pooling with a 2x2 filter and stride of 2 (which specifies that pooled regions do not overlap)**Convolutional Layer #2**: Applies 64 5x5 filters, with ReLU activation function**Pooling Layer #2**: Again, performs max pooling with a 2x2 filter and stride of 2**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)**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.

The following `cnn_model_fn`

function conforms to the interface expected by TensorFlow’s Estimator API (more on this later in Create the Estimator). This example takes MNIST feature data, labels, and `mode_keys()`

(e.g. `"train"`

, `"eval"`

, `"infer"`

) as arguments; configures the CNN; and returns predictions, loss, and a training operation:

```
cnn_model_fn <- function(features, labels, mode, params, config) {
# Input Layer
# Reshape X to 4-D tensor: [batch_size, width, height, channels]
# MNIST images are 28x28 pixels, and have one color channel
input_layer <- tf$reshape(features$x, c(-1L, 28L, 28L, 1L))
# Convolutional Layer #1
# Computes 32 features using a 5x5 filter with ReLU activation.
# Padding is added to preserve width and height.
# Input Tensor Shape: [batch_size, 28, 28, 1]
# Output Tensor Shape: [batch_size, 28, 28, 32]
conv1 <- tf$layers$conv2d(
inputs = input_layer,
filters = 32L,
kernel_size = c(5L, 5L),
padding = "same",
activation = tf$nn$relu)
# Pooling Layer #1
# First max pooling layer with a 2x2 filter and stride of 2
# Input Tensor Shape: [batch_size, 28, 28, 32]
# Output Tensor Shape: [batch_size, 14, 14, 32]
pool1 <- tf$layers$max_pooling2d(inputs = conv1, pool_size = c(2L, 2L), strides = 2L)
# Convolutional Layer #2
# Computes 64 features using a 5x5 filter.
# Padding is added to preserve width and height.
# Input Tensor Shape: [batch_size, 14, 14, 32]
# Output Tensor Shape: [batch_size, 14, 14, 64]
conv2 <- tf$layers$conv2d(
inputs = pool1,
filters = 64L,
kernel_size = c(5L, 5L),
padding = "same",
activation = tf$nn$relu)
# Pooling Layer #2
# Second max pooling layer with a 2x2 filter and stride of 2
# Input Tensor Shape: [batch_size, 14, 14, 64]
# Output Tensor Shape: [batch_size, 7, 7, 64]
pool2 <- tf$layers$max_pooling2d(inputs = conv2, pool_size = c(2L, 2L), strides = 2L)
# Flatten tensor into a batch of vectors
# Input Tensor Shape: [batch_size, 7, 7, 64]
# Output Tensor Shape: [batch_size, 7 * 7 * 64]
pool2_flat <- tf$reshape(pool2, c(-1L, 7L * 7L * 64L))
# Dense Layer
# Densely connected layer with 1024 neurons
# Input Tensor Shape: [batch_size, 7 * 7 * 64]
# Output Tensor Shape: [batch_size, 1024]
dense <- tf$layers$dense(inputs = pool2_flat, units = 1024L, activation = tf$nn$relu)
# Add dropout operation; 0.6 probability that element will be kept
dropout <- tf$layers$dropout(
inputs = dense, rate = 0.4, training = (mode == "train"))
# Logits layer
# Input Tensor Shape: [batch_size, 1024]
# Output Tensor Shape: [batch_size, 10]
logits <- tf$layers$dense(inputs = dropout, units = 10L)
# Generate Predictions (for prediction mode)
predicted_classes <- tf$argmax(input = logits, axis = 1L, name = "predicted_classes")
if (mode == "infer") {
predictions <- list(
classes = predicted_classes,
probabilities = tf$nn$softmax(logits, name = "softmax_tensor")
)
return(estimator_spec(mode = mode, predictions = predictions))
}
# Calculate Loss (for both "train" and "eval" modes)
onehot_labels <- tf$one_hot(indices = tf$cast(labels, tf$int32), depth = 10L)
loss <- tf$losses$softmax_cross_entropy(
onehot_labels = onehot_labels, logits = logits)
# Configure the Training Op (for "train" mode)
if (mode == "train") {
optimizer <- tf$train$GradientDescentOptimizer(learning_rate = 0.001)
train_op <- optimizer$minimize(
loss = loss,
global_step = tf$train$get_global_step())
return(estimator_spec(mode = mode, loss = loss, train_op = train_op))
}
# Add evaluation metrics (for EVAL mode)
eval_metric_ops <- list(accuracy = tf$metrics$accuracy(
labels = labels, predictions = predicted_classes))
return(estimator_spec(
mode = mode, loss = loss, eval_metric_ops = eval_metric_ops))
}
```

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 creatings estimators in tfestimators, 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”.

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 `[`

, defined as follows:*batch_size*, *image_width*, *image_height*, *channels*]

. Size of the subset of examples to use when performing gradient descent during training.`batch_size`

. Width of the example images.`image_width`

. Height of the example images.`image_height`

. 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).`channels`

Here, our MNIST dataset is composed of monochrome 28x28 pixel images, so the desired shape for our input layer is `[`

.*batch_size*, 28, 28, 1]

To convert our input feature map (`features`

) to this shape, we can perform the following `reshape`

operation:

`input_layer <- tf$reshape(features$x, c(-1L, 28L, 28L, 1L))`

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$x`

, 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$x`

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$x`

will contain 78,400 values, and `input_layer`

will have a shape of `[100, 28, 28, 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:

```
conv1 <- tf$layers$conv2d(
inputs = input_layer,
filters = 32L,
kernel_size = c(5L, 5L),
padding = "same",
activation = tf$nn$relu)
```

The `inputs`

argument specifies our input tensor, which must have the shape `[`

. Here, we’re connecting our first convolutional layer to *batch_size*, *image_width*, *image_height*, *channels*]`input_layer`

, which has the shape `[`

.*batch_size*, 28, 28, 1]

Note:

`conv2d()`

will instead accept a shape of`[`

when passed the argumentchannels,batch_size,image_width,image_height]`data_format=channels_first`

.

The `filters`

argument specifies the number of filters to apply (here, 32), and `kernel_size`

specifies the dimensions of the filters as `[`

(here, *width*, *height*]`[5, 5]`

).

**TIP:** If filter width and height have the same value, you can instead specify a single integer for `kernel_size`

—e.g., `kernel_size=5`

.

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 `[`

: the same width and height dimensions as the input, but now with 32 channels holding the output from each of the filters.*batch_size*, 28, 28, 32]

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:

`pool1 <- tf$layers$max_pooling2d(inputs = conv1, pool_size = c(2L, 2L), strides = 2L)`

Again, `inputs`

specifies the input tensor, with a shape of `[`

. Here, our input tensor is *batch_size*, *image_width*, *image_height*, *channels*]`conv1`

, the output from the first convolutional layer, which has a shape of `[`

.*batch_size*, 28, 28, 32]

Note: As with

`conv2d()`

,`max_pooling2d()`

will instead accept a shape of`[`

when passed the argumentchannels,batch_size,image_width,image_height]`data_format=channels_first`

.

The `pool_size`

argument specifies the size of the max pooling filter as `[`

(here, *width*, *height*]`[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 = c(3, 6)`

).

Our output tensor produced by `max_pooling2d()`

(`pool1`

) has a shape of `[`

: the 2x2 filter reduces width and height by 50% each.*batch_size*, 14, 14, 32]

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):

```
conv2 <- tf$layers$conv2d(
inputs = pool1,
filters = 64L,
kernel_size = c(5L, 5L),
padding = "same",
activation = tf$nn$relu)
pool2 <- tf$layers$max_pooling2d(inputs = conv2, pool_size = c(2L, 2L), strides = 2L)
```

Note that convolutional layer #2 takes the output tensor of our first pooling layer (`pool1`

) as input, and produces the tensor `conv2`

as output. `conv2`

has a shape of `[`

, the same width and height as *batch_size*, 14, 14, 64]`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 `[`

(50% reduction of width and height from *batch_size*, 7, 7, 64]`conv2`

).

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 `[`

, so that our tensor has only two dimensions:*batch_size*, *features*]

`pool2_flat <- tf$reshape(pool2, c(-1L, 7L * 7L * 64L))`

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 `[`*batch_size*, 3136]

.Now, we can use the `dense()`

method in `layers`

to connect our dense layer as follows:

`dense <- tf$layers$dense(inputs = pool2_flat, units = 1024L, 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`

:

```
dropout <- tf$layers$dropout(
inputs = dense, rate = 0.4, training = (mode == "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 `[`

.*batch_size*, 1024]

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):

`logits <- tf$layers$dense(inputs = dropout, units = 10L)`

Our final output tensor of the CNN, `logits`

, has shape `[`

.*batch_size*, 10]

The logits layer of our model returns our predictions as raw values in a `[`

-dimensional tensor. Let’s convert these raw values into two different formats that our model function can return:*batch_size*, 10]

- 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:

`tf$argmax(input = logits, axis = 1L)`

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 `[`

).*batch_size*, 10]

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

`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 compile our predictions in a dict, and return an `estimator_spec`

object:

```
predicted_classes <- tf$argmax(input = logits, axis = 1L)
if (mode == "infer") {
predictions <- list(
classes = predicted_classes,
probabilities = tf$nn$softmax(logits, name = "softmax_tensor")
)
return(estimator_spec(mode = mode, predictions = predictions))
}
```

For both training and evaluation, we need to define a loss function that measures how closely the model’s predictions match the target classes. For multiclass classification problems like MNIST, 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:

```
onehot_labels <- tf$one_hot(indices = tf$cast(labels, tf$int32), depth = 10L)
loss <- tf$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:

```
[[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`

:

`onehot_labels <- tf$one_hot(indices = tf$cast(labels, tf$int32), depth = 10L)`

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`

:

```
loss <- tf$losses$softmax_cross_entropy(
onehot_labels = onehot_labels, logits = logits)
```

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. We’ll use a learning rate of 0.001 and stochastic gradient descent as the optimization algorithm:

```
if (mode == "train") {
optimizer <- tf$train$GradientDescentOptimizer(learning_rate = 0.001)
train_op <- optimizer$minimize(
loss = loss,
global_step = tf$train$get_global_step())
return(estimator_spec(mode = mode, loss = loss, train_op = train_op))
}
```

To add accuracy metric in our model, we define `eval_metric_ops`

dict in EVAL mode as follows:

```
eval_metric_ops <- list(accuracy = tf$metrics$accuracy(
labels = labels, predictions = predicted_classes))
return(estimator_spec(
mode = mode, loss = loss, eval_metric_ops = eval_metric_ops))
```

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

First, let’s load our training and test data:

```
np <- import("numpy", convert = FALSE)
# Load training and eval data
mnist <- tf$contrib$learn$datasets$load_dataset("mnist")
train_data <- np$asmatrix(mnist$train$images, dtype = np$float32)
train_labels <- np$asarray(mnist$train$labels, dtype = np$int32)
eval_data <- np$asmatrix(mnist$test$images, dtype = np$float32)
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 in `train_data`

and `train_labels`

, respectively. Similarly, we store the evaluation feature data (10,000 images) and evaluation labels in `eval_data`

and `eval_labels`

, respectively.

Next, let’s create an `estimator`

(a TensorFlow class for performing high-level model training, evaluation, and inference) for our model.

```
# Create the Estimator
mnist_classifier <- 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 prediction; we pass it the `cnn_model_fn`

we created in “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 for custom estimator.

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 `SessionRunHook`

to create a `hook_logging_tensor`

that will log the predicted classes from the `argmax`

operation.

```
# Set up logging for predicted classes
tensors_to_log <- list(predicted_classes = "predicted_classes")
logging_hook <- hook_logging_tensor(
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 `predicted classes`

can be found in `predicted_classes`

, the name we gave our argmax operation earlier when we generated the predicted classes in `cnn_model_fn`

.

Next, we create the `hook_logging_tensor`

, 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.

Now we’re ready to train our model, which we can do by creating `train_input_fn`

ans calling `train()`

on `mnist_classifier`

.

```
# Train the model
train_input_fn <- function(features_as_named_list) {
tf$estimator$inputs$numpy_input_fn(
x = list(x = train_data),
y = train_labels,
batch_size = 100L,
num_epochs = NULL,
shuffle = TRUE)
}
train(
mnist_classifier,
input_fn = train_input_fn,
steps = 20,
hooks = logging_hook)
```

In the `numpy_input_fn`

call, we pass the training feature data and labels to `x`

(as a dict) 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). `num_epochs = NULL`

means that the model will train until the specified number of steps is reached. We also set `shuffle = TRUE`

to shuffle the training data. In the `train`

call, we set `steps = 2`

(which means the model will train for 10 steps total).

Once training is complete, we want to evaluate our model to determine its accuracy on the MNIST test set. We call the `evaluate`

method, which evaluates the metrics we specified in `eval_metric_ops`

argument in the `model_fn`

.

```
# Evaluate the model and print results
eval_input_fn <- function(features_as_named_list) {
tf$estimator$inputs$numpy_input_fn(
x = list(x = eval_data),
y = eval_labels,
batch_size = 100L,
num_epochs = NULL,
shuffle = TRUE)
}
evaluate(
mnist_classifier,
input_fn = eval_input_fn,
steps = 10,
hooks = logging_hook)
```

To create `eval_input_fn`

, we set `num_epochs = 1`

, so that the model evaluates the metrics over one epoch of data and returns the result. We also set `shuffle = FALSE`

to iterate through the data sequentially.

We pass our `logging_hook`

to the `hooks`

argument, so that it will be triggered during evaluation.

We’ve coded the CNN model function, `Estimator`

, and the training/evaluation logic; now let’s see the results.

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

```
INFO:tensorflow:Create CheckpointSaverHook.
INFO:tensorflow:Restoring parameters from /tmp/mnist_convnet_model/model.ckpt-5
INFO:tensorflow:Saving checkpoints for 6 into /tmp/mnist_convnet_model/model.ckpt.
INFO:tensorflow:loss = 2.29727, step = 6
INFO:tensorflow:Saving checkpoints for 7 into /tmp/mnist_convnet_model/model.ckpt.
INFO:tensorflow:Loss for final step: 2.30916.
```

You’ll see log output like the following during model evaluation with the `predicted_classes`

that we included in the `logging_hook`

:

```
INFO:tensorflow:Starting evaluation at 2017-07-04-17:05:28
INFO:tensorflow:Restoring parameters from /tmp/mnist_convnet_model/model.ckpt-19
INFO:tensorflow:predicted_classes = [6 9 1 9 9 1 9 1 9 6 1 9 9 9 9 1 9 9 9 3 1 1 1 9 6 1 9 9 9 9 9 9 1 1 9 9 9
9 9 9 9 1 9 9 1 4 4 1 9 1 9 9 1 9 9 9 9 9 9 1 6 9 9 1 9 6 9 9 9 9 9 9 1 9
9 3 9 9 9 9 1 9 9 9 3 9 1 9 9 9 9 9 9 9 9 9 1 9 9 9]
INFO:tensorflow:Evaluation [1/10]
INFO:tensorflow:Evaluation [2/10]
INFO:tensorflow:predicted_classes = [9 9 1 9 1 9 9 9 9 9 9 9 9 9 9 9 9 9 1 4 1 9 9 9 1 9 9 9 9 9 1 9 4 9 1 1 9
9 1 1 9 9 1 9 9 9 9 1 9 9 9 9 4 9 9 9 9 4 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 1 9 9 9 9 9 9 9 9 1 1 9 9 9 9 1 9 9 9 9 9 9 9 9 9] (0.204 sec)
INFO:tensorflow:Evaluation [3/10]
INFO:tensorflow:Evaluation [4/10]
...
```