Welcome to Convolutional Neural Networks’s second article! In this article,I will:
- Implement helper functions that I will use when implementing a TensorFlow model
- Implement a fully functioning ConvNet using TensorFlow
After this article you will be able to:
- Build and train a ConvNet in TensorFlow for a classification problem
I assume here that you are already familiar with TensorFlow. If you are not, please refer the TensorFlow Tutorial .
In the previous article, I built helper functions using numpy to understand the mechanics behind convolutional neural networks. Most practical applications of deep learning today are built using programming frameworks, which have many built-in functions you can simply call.
As usual, I will start by loading in the packages.
Run the next cell to load the “SIGNS” dataset you are going to use.
# Loading the data (signs)
As a reminder, the SIGNS dataset is a collection of 6 signs representing numbers from 0 to 5.
The next cell will show you an example of a labelled image in the dataset. Feel free to change the value of
index below and re-run to see different examples.
# Example of a picture
y = 2
In previous article, I had built a fully-connected network for this dataset. But since this is an image dataset, it is more natural to apply a ConvNet to it.
To get started, let’s examine the shapes of out data.
X_train = X_train_orig/255.
number of training examples = 1080 number of test examples = 120 X_train shape: (1080, 64, 64, 3) Y_train shape: (1080, 6) X_test shape: (120, 64, 64, 3) Y_test shape: (120, 6)
TensorFlow requires that we create placeholders for the input data that will be fed into the model when running the session.
I implemented the function below to create placeholders for the input image X and the output Y. We should not define the number of training examples for the moment. To do so, we could use “None” as the batch size, it will give you the flexibility to choose it later. Hence X should be of dimension [None, n_H0, n_W0, n_C0] and Y should be of dimension [None, n_y]. Hint.
I will initialize weights/filters $W1$ and $W2$ using
tf.contrib.layers.xavier_initializer(seed = 0). You don’t need to worry about bias variables as you will soon see that TensorFlow functions take care of the bias. Note also that we will only initialize the weights/filters for the conv2d functions. TensorFlow initializes the layers for the fully connected part automatically. We will talk more about that later in this assignment.
I implemented initialize_parameters(). The dimensions for each group of filters are provided below. Reminder - to initialize a parameter $W$ of shape [1,2,3,4] in Tensorflow, use:
W = tf.get_variable("W", [1,2,3,4], initializer = ...)
In TensorFlow, there are built-in functions that carry out the convolution steps for us.
tf.nn.conv2d(X,W1, strides = [1,s,s,1], padding = ‘SAME’): given an input $X$ and a group of filters $W1$, this function convolves $W1$’s filters on X. The third input ([1,f,f,1]) represents the strides for each dimension of the input (m, n_H_prev, n_W_prev, n_C_prev). You can read the full documentation here
tf.nn.max_pool(A, ksize = [1,f,f,1], strides = [1,s,s,1], padding = ‘SAME’): given an input A, this function uses a window of size (f, f) and strides of size (s, s) to carry out max pooling over each window. You can read the full documentation here
tf.nn.relu(Z1): computes the elementwise ReLU of Z1 (which can be any shape). You can read the full documentation here.
tf.contrib.layers.flatten(P): given an input P, this function flattens each example into a 1D vector it while maintaining the batch-size. It returns a flattened tensor with shape [batch_size, k]. You can read the full documentation here.
tf.contrib.layers.fully_connected(F, num_outputs): given a the flattened input F, it returns the output computed using a fully connected layer. You can read the full documentation here.
In the last function above (
tf.contrib.layers.fully_connected), the fully connected layer automatically initializes weights in the graph and keeps on training them as we train the model. Hence, we did not need to initialize those weights when initializing the parameters.
I implemented the
forward_propagation function below to build the following model:
CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTED. I will use the functions above.
In detail, we will use the following parameters for all the steps:
- Conv2D: stride 1, padding is “SAME”
- Max pool: Use an 8 by 8 filter size and an 8 by 8 stride, padding is “SAME”
- Conv2D: stride 1, padding is “SAME”
- Max pool: Use a 4 by 4 filter size and a 4 by 4 stride, padding is “SAME”
- Flatten the previous output.
- FULLYCONNECTED (FC) layer: Apply a fully connected layer without an non-linear activation function. Do not call the softmax here. This will result in 6 neurons in the output layer, which then get passed later to a softmax. In TensorFlow, the softmax and cost function are lumped together into a single function, which you’ll call in a different function when computing the cost.
def forward_propagation(X, parameters):
I will implement the compute cost function below. You might find these two functions helpful:
- tf.nn.softmax_cross_entropy_with_logits(logits = Z3, labels = Y): computes the softmax entropy loss. This function both computes the softmax activation function as well as the resulting loss. You can check the full documentation here.
- tf.reduce_mean: computes the mean of elements across dimensions of a tensor. Use this to sum the losses over all the examples to get the overall cost. You can check the full documentation here.
Finally I will merge the helper functions I implemented above to build a model. I will train it on the SIGNS dataset.
I have implemented
random_mini_batches() in the Optimization programming article. Remember that this function returns a list of mini-batches.
The model below should:
- create placeholders
- initialize parameters
- forward propagate
- compute the cost
- create an optimizer
Finally I will create a session and run a for loop for num_epochs, get the mini-batches, and then for each mini-batch you will optimize the function. Hint for initializing the variables
Run the following cell to train our model for 100 epochs.:
_, _, parameters = model(X_train, Y_train, X_test, Y_test)
Cost after epoch 0: 1.920183 Cost after epoch 5: 1.885439 Cost after epoch 10: 1.849110 Cost after epoch 15: 1.730203 Cost after epoch 20: 1.503597 Cost after epoch 25: 1.264177 Cost after epoch 30: 1.095219 Cost after epoch 35: 0.985675 Cost after epoch 40: 0.902660 Cost after epoch 45: 0.831738 Cost after epoch 50: 0.776374 Cost after epoch 55: 0.730666 Cost after epoch 60: 0.678335 Cost after epoch 65: 0.643941 Cost after epoch 70: 0.621297 Cost after epoch 75: 0.594998 Cost after epoch 80: 0.568649 Cost after epoch 85: 0.539469 Cost after epoch 90: 0.514542 Cost after epoch 95: 0.490415
Tensor("Mean_1:0", shape=(), dtype=float32) Train Accuracy: 0.860185 Test Accuracy: 0.75