[Lecture Notes] Beyond The Simplest Neural Network Ever — Part 1

In the previous posts, we discussed the basic components of the most simple neural network. With the 5 lines of code in mind, we extend the model to the next level. Watch the video first.

Now about the dataset.

We start from the usual setup.

from __future__ import absolute_import, division, print_function, unicode_literals
try:
  # %tensorflow_version only exists in Colab.
  %tensorflow_version 2.x
except Exception:
  pass
import tensorflow as tf

In order to understand the following code, we need to know the concept of tuple in Python.

fashion_mnist = tf.keras.datasets.fashion_mnist

(x_train, y_train), (x_test, y_test) = fashion_mnist.load_data()

Loading the dataset returns four NumPy arrays:

• Thex_train and y_train arrays are the training set—the data the model uses to learn.
• The model is tested against the test set, the x_test, and y_test arrays.

The images are 28x28 NumPy arrays, with pixel values ranging from 0 to 255. The labels are an array of integers, ranging from 0 to 9.

The data must be preprocessed before training the network. If you inspect the first image in the training set, you will see that the pixel values fall in the range of 0 to 255. Scale these values to a range of 0 to 1 before feeding them to the neural network model. To do so, divide the values by 255. It’s important that the training set and the testing set be preprocessed in the same way:

x_train = x_train/255.0
x_test = x_test/255.0

Building the neural network requires configuring the layers of the model, then compiling the model. The basic building block of a neural network is the layer. Layers extract representations from the data fed into them. Hopefully, these representations are meaningful for the problem at hand.

Most of the deep learning models consist of chaining together simple layers. Most layers, such as tf.keras.layers.Dense, have parameters that are learned during training.

model = tf.keras.Sequential([
    tf.keras.layers.Flatten(input_shape=(28, 28)),
    tf.keras.layers.Dense(128, activation='relu'),
    tf.keras.layers.Dense(10, activation='softmax')
])

The first layer in this network, tf.keras.layers.Flatten, transforms the format of the images from a two-dimensional array (of 28 by 28 pixels) to a one-dimensional array (of 28 * 28 = 784 pixels). Think of this layer as unstacking rows of pixels in the image and lining them up. This layer has no parameters to learn; it only reformats the data.

After the pixels are flattened, the network consists of a sequence of two tf.keras.layers.Dense layers. These are densely connected or fully-connected, neural layers. The first Dense layer has 128 nodes (or neurons). The second (and last) layer is a 10-node softmax layer that returns an array of 10 probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the 10 classes.

Before the model is ready for training, it needs a few more settings. These are added during the model’s compile step:

• Loss function — This measures how accurate the model is during training. You want to minimize this function to “steer” the model in the right direction.
• Optimizer — This is how the model is updated based on the data it sees and its loss function.
• Metrics — Used to monitor the training and testing steps. The following example uses accuracy, the fraction of the images that are correctly classified.

model.compile(optimizer='adam',
              loss='sparse_categorical_crossentropy',
              metrics=['accuracy'])

Training the neural network model requires the following steps:

1. Feed the training data to the model. In this example, the training data is in the x_train and y_train arrays.
2. The model learns to associate images and labels.
3. You ask the model to make predictions about a test set — in this example, the x_test array. Verify that the predictions match the labels from the y_test array.

To start training, call the model.fit method—so-called because it "fits" the model to the training data:

model.fit(x_train, y_train, epochs=10)
Train on 60000 samples
Epoch 1/10
60000/60000 [==============================] - 7s 121us/sample - loss: 3.4261 - accuracy: 0.6770
Epoch 2/10
60000/60000 [==============================] - 6s 101us/sample - loss: 0.7029 - accuracy: 0.7423
Epoch 3/10
60000/60000 [==============================] - 6s 97us/sample - loss: 0.6023 - accuracy: 0.7899
Epoch 4/10
60000/60000 [==============================] - 6s 97us/sample - loss: 0.5445 - accuracy: 0.8100
Epoch 5/10
60000/60000 [==============================] - 6s 101us/sample - loss: 0.5316 - accuracy: 0.8210
Epoch 6/10
60000/60000 [==============================] - 6s 102us/sample - loss: 0.5199 - accuracy: 0.8268
Epoch 7/10
60000/60000 [==============================] - 6s 101us/sample - loss: 0.4983 - accuracy: 0.8334
Epoch 8/10
60000/60000 [==============================] - 6s 101us/sample - loss: 0.4879 - accuracy: 0.8373
Epoch 9/10
60000/60000 [==============================] - 6s 103us/sample - loss: 0.4817 - accuracy: 0.8407
Epoch 10/10
60000/60000 [==============================] - 6s 99us/sample - loss: 0.4818 - accuracy: 0.8408
<tensorflow.python.keras.callbacks.History at 0x7f9abc8087b8>

As the model trains, the loss and accuracy metrics are displayed. This model reaches an accuracy of about 0.88 (or 88%) on the training data.

Next, compare how the model performs on the test dataset.

test_loss, test_acc = model.evaluate(x_test,  y_test, verbose=2)
print('\nTest accuracy:', test_acc)
10000/1 - 1s - loss: 0.2934 - accuracy: 0.8830
Test accuracy: 0.883

It turns out that the accuracy on the test dataset is a little less than the accuracy on the training dataset. This gap between training accuracy and test accuracy represents overfitting. Overfitting is when a machine learning model performs worse on new, previously unseen inputs than on the training data.

With the model trained, you can use it to make predictions about some images.

predictions = model.predict(x_test)

Here, the model has predicted the label for each image in the testing set. Let’s take a look at the first prediction:

predictions[0]
array([1.06123218e-06, 8.76374884e-09, 4.13958730e-07, 9.93547733e-09,
       2.39135318e-07, 2.61428091e-03, 2.91701099e-07, 6.94991834e-03,
       1.02351805e-07, 9.90433693e-01], dtype=float32)

A prediction is an array of 10 numbers. They represent the model’s “confidence” that the image corresponds to each of the 10 different articles of clothing. You can see which label has the highest confidence value:

np.argmax(predictions[0])
9

So, the model is most confident that this image is an ankle boot, or class_names[9]. Examining the test label shows that this classification is correct:

y_test[0]
9

Graph this to look at the full set of 10 class predictions.

def plot_image(i, predictions_array, true_label, img):
  predictions_array, true_label, img = predictions_array, true_label[i], img[i]
  plt.grid(False)
  plt.xticks([])
  plt.yticks([])
  plt.imshow(img, cmap=plt.cm.binary)
  predicted_label = np.argmax(predictions_array)
  if predicted_label == true_label:
    color = 'blue'
  else:
    color = 'red'
  plt.xlabel("{} {:2.0f}% ({})".format(class_names[predicted_label],
                                100*np.max(predictions_array),
                                class_names[true_label]),
                                color=color)
def plot_value_array(i, predictions_array, true_label):
  predictions_array, true_label = predictions_array, true_label[i]
  plt.grid(False)
  plt.xticks(range(10))
  plt.yticks([])
  thisplot = plt.bar(range(10), predictions_array, color="#777777")
  plt.ylim([0, 1])
  predicted_label = np.argmax(predictions_array)
  thisplot[predicted_label].set_color('red')
  thisplot[true_label].set_color('blue')

Let’s look at the 0th image, predictions, and prediction array. Correct prediction labels are blue and incorrect prediction labels are red. The number gives the percentage (out of 100) for the predicted label.

i = 0
plt.figure(figsize=(6,3))
plt.subplot(1,2,1)
plot_image(i, predictions[i], test_labels, test_images)
plt.subplot(1,2,2)
plot_value_array(i, predictions[i],  test_labels)
plt.show()

i = 12
plt.figure(figsize=(6,3))
plt.subplot(1,2,1)
plot_image(i, predictions[i], test_labels, test_images)
plt.subplot(1,2,2)
plot_value_array(i, predictions[i],  test_labels)
plt.show()

Let’s plot several images with their predictions. Note that the model can be wrong even when very confident.

# Plot the first X test images, their predicted labels, and the true labels.
# Color correct predictions in blue and incorrect predictions in red.
num_rows = 5
num_cols = 3
num_images = num_rows*num_cols
plt.figure(figsize=(2*2*num_cols, 2*num_rows))
for i in range(num_images):
  plt.subplot(num_rows, 2*num_cols, 2*i+1)
  plot_image(i, predictions[i], test_labels, test_images)
  plt.subplot(num_rows, 2*num_cols, 2*i+2)
  plot_value_array(i, predictions[i], test_labels)
plt.tight_layout()
plt.show()

Finally, use the trained model to make a prediction about a single image.

# Grab an image from the test dataset.
img = test_images[1]
print(img.shape)
(28, 28)

tf.keras models are optimized to make predictions on a batch, or collection, of examples at once. Accordingly, even though you're using a single image, you need to add it to a list:

# Add the image to a batch where it's the only member.
img = (np.expand_dims(img,0))
print(img.shape)
(1, 28, 28)

Now predict the correct label for this image:

predictions_single = model.predict(img)
print(predictions_single)