Bidirectional RNN for Digit Classification

    In this tutorial we will learn how to write code for designing a Bidirectional Recurrent Neural Network (BRNN) in TensorFlow for classifying MNIST digits.


    Fig1. Unfolded representation of a sample BRNN structure


    1. Import the required libraries:

    We will start with importing the required libraries to our Python environment.

    In [2]:
    # imports
    import tensorflow as tf
    import numpy as np
    import matplotlib.pyplot as plt
    from tensorflow.contrib import rnn

    1. Load the MNIST data

    For this tutorial we use the MNIST dataset. MNIST is a dataset of handwritten digits. If you are into machine learning, you might have heard of this dataset by now. MNIST is kind of benchmark of datasets for deep learning. One other reason that we use the MNIST is that it is easily accesible through Tensorflow.

    The dataset contains 55,000 examples for training, 5,000 examples for validation and 10,000 examples for testing. The digits have been size-normalized and centered in a fixed-size image (28x28 pixels) with values from 0 to 1. For simplicity, each image has been flattened and converted to a 1-D numpy array of 784 features (28*28).


    If you want to know more about the MNIST dataset you can check Yann Lecun's website.

    1.1. Data dimension

    Here, we specify the dimensions of the images which will be used in several places in the code below. Defining these variables makes it easier (compared with using hard-coded number all throughout the code) to modify them later. Ideally these would be inferred from the data that has been read, but here we just write the numbers.

    To classify images using a recurrent neural network, we consider every image row as a sequence of pixels. Because MNIST image shape is 28x28 pixels, we will then handle 28 sequences of 28 timesteps for every sample.

    In [3]:
    # Data Dimension
    num_input = 28          # MNIST data input (image shape: 28x28)
    timesteps = 28          # Timesteps
    n_classes = 10          # Number of classes, one class per digit

    1.2. Helper functions to load the MNIST data

    In this section, we'll write the function which automatically loads the MNIST data and returns it in our desired shape and format. If you wanna learn more about loading your data, you may read our How to Load Data in TensorFlow tutorial which explains all the available methods to load your own data; no matter how big it is. Here, we'll simply write a function (load_data) which has two mode: train (which loads the training and validation images and their corresponding labels) and test (which loads the test images and their corresponding labels).

    In [4]:
    def load_data(mode='train'):
        Function to (download and) load the MNIST data
        :param mode: train or test
        :return: images and the corresponding labels
        from tensorflow.examples.tutorials.mnist import input_data
        mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)
        if mode == 'train':
            x_train, y_train, x_valid, y_valid = mnist.train.images, mnist.train.labels, \
                                                 mnist.validation.images, mnist.validation.labels
            return x_train, y_train, x_valid, y_valid
        elif mode == 'test':
            x_test, y_test = mnist.test.images, mnist.test.labels
        return x_test, y_test
    def randomize(x, y):
        """ Randomizes the order of data samples and their corresponding labels"""
        permutation = np.random.permutation(y.shape[0])
        shuffled_x = x[permutation, :]
        shuffled_y = y[permutation]
        return shuffled_x, shuffled_y
    def get_next_batch(x, y, start, end):
        x_batch = x[start:end]
        y_batch = y[start:end]
        return x_batch, y_batch

    1.3. Load the data and display the sizes

    Now we can use the defined helper function in "train" mode which loads the train and validation images and their corresponding labels. We'll also display their sizes:

    In [5]:
    x_train, y_train, x_valid, y_valid = load_data(mode='train')
    print("Size of:")
    print("- Training-set:\t\t{}".format(len(y_train)))
    print("- Validation-set:\t{}".format(len(y_valid)))
    Extracting MNIST_data/train-images-idx3-ubyte.gz
    Extracting MNIST_data/train-labels-idx1-ubyte.gz
    Extracting MNIST_data/t10k-images-idx3-ubyte.gz
    Extracting MNIST_data/t10k-labels-idx1-ubyte.gz
    Size of:
    - Training-set:        55000
    - Validation-set:    5000

    2. Hyperparameters

    In [6]:
    learning_rate = 0.001 # The optimization initial learning rate
    epochs = 10           # Total number of training epochs
    batch_size = 100      # Training batch size
    display_freq = 100    # Frequency of displaying the training results

    3. Network configuration

    In [7]:
    num_hidden_units = 128  # Number of hidden units of the RNN

    4. Create network helper functions

    4.1. Helper functions for creating new variables

    In [8]:
    # weight and bais wrappers
    def weight_variable(shape):
        Create a weight variable with appropriate initialization
        :param name: weight name
        :param shape: weight shape
        :return: initialized weight variable
        initer = tf.truncated_normal_initializer(stddev=0.01)
        return tf.get_variable('W',
    def bias_variable(shape):
        Create a bias variable with appropriate initialization
        :param name: bias variable name
        :param shape: bias variable shape
        :return: initialized bias variable
        initial = tf.constant(0., shape=shape, dtype=tf.float32)
        return tf.get_variable('b',

    4.2. Helper-function for creating a Bidirectional RNN

    In [9]:
    def BiRNN(x, weights, biases, timesteps, num_hidden):
        # Prepare data shape to match `rnn` function requirements
        # Current data input shape: (batch_size, timesteps, n_input)
        # Required shape: 'timesteps' tensors list of shape (batch_size, num_input)
        # Unstack to get a list of 'timesteps' tensors of shape (batch_size, num_input)
        x = tf.unstack(x, timesteps, 1)
        # Define lstm cells with tensorflow
        # Forward direction cell
        lstm_fw_cell = rnn.BasicLSTMCell(num_hidden, forget_bias=1.0)
        # Backward direction cell
        lstm_bw_cell = rnn.BasicLSTMCell(num_hidden, forget_bias=1.0)
        # Get BiRNN cell output
        outputs, _, _ = rnn.static_bidirectional_rnn(lstm_fw_cell, lstm_bw_cell, x,
        # Linear activation, using rnn inner loop last output
        return tf.matmul(outputs[-1], weights) + biases

    5. Create the network graph

    5.1. Placeholders for the inputs (x) and corresponding labels (y)

    In [10]:
    # Placeholders for inputs (x) and outputs(y)
    x = tf.placeholder(tf.float32, shape=[None, timesteps, num_input], name='X')
    y = tf.placeholder(tf.float32, shape=[None, n_classes], name='Y')

    5.2. Define the network

    In [11]:
    # create weight matrix initialized randomely from N~(0, 0.01)
    W = weight_variable(shape=[2*num_hidden_units, n_classes])
    # create bias vector initialized as zero
    b = bias_variable(shape=[n_classes])
    output_logits = BiRNN(x, W, b, timesteps, num_hidden_units)
    y_pred = tf.nn.softmax(output_logits)

    5.3. Define the loss function, optimizer, accuracy, and predicted class

    In [12]:
    # Model predictions
    cls_prediction = tf.argmax(output_logits, axis=1, name='predictions')
    # Define the loss function, optimizer, and accuracy
    loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y, logits=output_logits), name='loss')
    optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate, name='Adam-op').minimize(loss)
    correct_prediction = tf.equal(tf.argmax(output_logits, 1), tf.argmax(y, 1), name='correct_pred')
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32), name='accuracy')

    5.4. Initialize all variables

    In [13]:
    # Creating the op for initializing all variables
    init = tf.global_variables_initializer()

    6. Train

    In [14]:
    sess = tf.InteractiveSession()
    global_step = 0
    # Number of training iterations in each epoch
    num_tr_iter = int(len(y_train) / batch_size)
    for epoch in range(epochs):
        print('Training epoch: {}'.format(epoch + 1))
        x_train, y_train = randomize(x_train, y_train)
        for iteration in range(num_tr_iter):
            global_step += 1
            start = iteration * batch_size
            end = (iteration + 1) * batch_size
            x_batch, y_batch = get_next_batch(x_train, y_train, start, end)
            x_batch = x_batch.reshape((batch_size, timesteps, num_input))
            # Run optimization op (backprop)
            feed_dict_batch = {x: x_batch, y: y_batch}
  , feed_dict=feed_dict_batch)
            if iteration % display_freq == 0:
                # Calculate and display the batch loss and accuracy
                loss_batch, acc_batch =[loss, accuracy],
                print("iter {0:3d}:\t Loss={1:.2f},\tTraining Accuracy={2:.01%}".
                      format(iteration, loss_batch, acc_batch))
        # Run validation after every epoch
        feed_dict_valid = {x: x_valid[:1000].reshape((-1, timesteps, num_input)), y: y_valid[:1000]}
        loss_valid, acc_valid =[loss, accuracy], feed_dict=feed_dict_valid)
        print("Epoch: {0}, validation loss: {1:.2f}, validation accuracy: {2:.01%}".
              format(epoch + 1, loss_valid, acc_valid))
    Training epoch: 1
    iter   0:     Loss=2.30,    Training Accuracy=24.0%
    iter 100:     Loss=0.74,    Training Accuracy=77.0%
    iter 200:     Loss=0.51,    Training Accuracy=88.0%
    iter 300:     Loss=0.51,    Training Accuracy=83.0%
    iter 400:     Loss=0.30,    Training Accuracy=88.0%
    iter 500:     Loss=0.21,    Training Accuracy=94.0%
    Epoch: 1, validation loss: 0.23, validation accuracy: 93.5%
    Training epoch: 2
    iter   0:     Loss=0.22,    Training Accuracy=93.0%
    iter 100:     Loss=0.22,    Training Accuracy=94.0%
    iter 200:     Loss=0.15,    Training Accuracy=96.0%
    iter 300:     Loss=0.13,    Training Accuracy=96.0%
    iter 400:     Loss=0.21,    Training Accuracy=96.0%
    iter 500:     Loss=0.12,    Training Accuracy=97.0%
    Epoch: 2, validation loss: 0.14, validation accuracy: 96.0%
    Training epoch: 3
    iter   0:     Loss=0.10,    Training Accuracy=97.0%
    iter 100:     Loss=0.05,    Training Accuracy=99.0%
    iter 200:     Loss=0.10,    Training Accuracy=98.0%
    iter 300:     Loss=0.08,    Training Accuracy=98.0%
    iter 400:     Loss=0.20,    Training Accuracy=93.0%
    iter 500:     Loss=0.06,    Training Accuracy=99.0%
    Epoch: 3, validation loss: 0.10, validation accuracy: 97.0%
    Training epoch: 4
    iter   0:     Loss=0.05,    Training Accuracy=99.0%
    iter 100:     Loss=0.06,    Training Accuracy=99.0%
    iter 200:     Loss=0.07,    Training Accuracy=99.0%
    iter 300:     Loss=0.14,    Training Accuracy=97.0%
    iter 400:     Loss=0.17,    Training Accuracy=97.0%
    iter 500:     Loss=0.09,    Training Accuracy=99.0%
    Epoch: 4, validation loss: 0.09, validation accuracy: 97.6%
    Training epoch: 5
    iter   0:     Loss=0.05,    Training Accuracy=99.0%
    iter 100:     Loss=0.09,    Training Accuracy=98.0%
    iter 200:     Loss=0.19,    Training Accuracy=92.0%
    iter 300:     Loss=0.01,    Training Accuracy=100.0%
    iter 400:     Loss=0.05,    Training Accuracy=98.0%
    iter 500:     Loss=0.06,    Training Accuracy=98.0%
    Epoch: 5, validation loss: 0.08, validation accuracy: 97.7%
    Training epoch: 6
    iter   0:     Loss=0.07,    Training Accuracy=98.0%
    iter 100:     Loss=0.03,    Training Accuracy=99.0%
    iter 200:     Loss=0.04,    Training Accuracy=98.0%
    iter 300:     Loss=0.06,    Training Accuracy=99.0%
    iter 400:     Loss=0.02,    Training Accuracy=99.0%
    iter 500:     Loss=0.06,    Training Accuracy=97.0%
    Epoch: 6, validation loss: 0.08, validation accuracy: 97.8%
    Training epoch: 7
    iter   0:     Loss=0.04,    Training Accuracy=99.0%
    iter 100:     Loss=0.02,    Training Accuracy=100.0%
    iter 200:     Loss=0.04,    Training Accuracy=99.0%
    iter 300:     Loss=0.04,    Training Accuracy=99.0%
    iter 400:     Loss=0.03,    Training Accuracy=99.0%
    iter 500:     Loss=0.06,    Training Accuracy=97.0%
    Epoch: 7, validation loss: 0.09, validation accuracy: 97.8%
    Training epoch: 8
    iter   0:     Loss=0.07,    Training Accuracy=99.0%
    iter 100:     Loss=0.15,    Training Accuracy=98.0%
    iter 200:     Loss=0.11,    Training Accuracy=99.0%
    iter 300:     Loss=0.06,    Training Accuracy=99.0%
    iter 400:     Loss=0.02,    Training Accuracy=100.0%
    iter 500:     Loss=0.01,    Training Accuracy=99.0%
    Epoch: 8, validation loss: 0.06, validation accuracy: 98.5%
    Training epoch: 9
    iter   0:     Loss=0.02,    Training Accuracy=100.0%
    iter 100:     Loss=0.02,    Training Accuracy=100.0%
    iter 200:     Loss=0.03,    Training Accuracy=99.0%
    iter 300:     Loss=0.02,    Training Accuracy=99.0%
    iter 400:     Loss=0.02,    Training Accuracy=100.0%
    iter 500:     Loss=0.01,    Training Accuracy=100.0%
    Epoch: 9, validation loss: 0.06, validation accuracy: 98.4%
    Training epoch: 10
    iter   0:     Loss=0.11,    Training Accuracy=98.0%
    iter 100:     Loss=0.02,    Training Accuracy=99.0%
    iter 200:     Loss=0.02,    Training Accuracy=99.0%
    iter 300:     Loss=0.02,    Training Accuracy=99.0%
    iter 400:     Loss=0.05,    Training Accuracy=99.0%
    iter 500:     Loss=0.01,    Training Accuracy=100.0%
    Epoch: 10, validation loss: 0.07, validation accuracy: 97.7%

    7. Test

    7.1. Helper functions for plotting the results

    In [15]:
    def plot_images(images, cls_true, cls_pred=None, title=None):
        Create figure with 3x3 sub-plots.
        :param images: array of images to be plotted, (9, img_h*img_w)
        :param cls_true: corresponding true labels (9,)
        :param cls_pred: corresponding true labels (9,)
        fig, axes = plt.subplots(3, 3, figsize=(9, 9))
        fig.subplots_adjust(hspace=0.3, wspace=0.3)
        for i, ax in enumerate(axes.flat):
            # Plot image.
            ax.imshow(np.squeeze(images[i]).reshape(28, 28), cmap='binary')
            # Show true and predicted classes.
            if cls_pred is None:
                ax_title = "True: {0}".format(cls_true[i])
                ax_title = "True: {0}, Pred: {1}".format(cls_true[i], cls_pred[i])
            # Remove ticks from the plot.
        if title:
            plt.suptitle(title, size=20)
    def plot_example_errors(images, cls_true, cls_pred, title=None):
        Function for plotting examples of images that have been mis-classified
        :param images: array of all images, (#imgs, img_h*img_w)
        :param cls_true: corresponding true labels, (#imgs,)
        :param cls_pred: corresponding predicted labels, (#imgs,)
        # Negate the boolean array.
        incorrect = np.logical_not(np.equal(cls_pred, cls_true))
        # Get the images from the test-set that have been
        # incorrectly classified.
        incorrect_images = images[incorrect]
        # Get the true and predicted classes for those images.
        cls_pred = cls_pred[incorrect]
        cls_true = cls_true[incorrect]
        # Plot the first 9 images.

    7.2. Run the test and plot some results

    In [16]:
    # Test the network (only on 1000 samples) after training
    x_test, y_test = load_data(mode='test')
    feed_dict_test = {x: x_test[:1000].reshape((-1, timesteps, num_input)), y: y_test[:1000]}
    loss_test, acc_test =[loss, accuracy], feed_dict=feed_dict_test)
    print("Test loss: {0:.2f}, test accuracy: {1:.01%}".format(loss_test, acc_test))
    # Plot some of the correct and misclassified examples
    cls_pred =, feed_dict=feed_dict_test)
    cls_true = np.argmax(y_test, axis=1)
    plot_images(x_test, cls_true, cls_pred, title='Correct Examples')
    plot_example_errors(x_test[:1000], cls_true[:1000], cls_pred, title='Misclassified Examples')
    Extracting MNIST_data/train-images-idx3-ubyte.gz
    Extracting MNIST_data/train-labels-idx1-ubyte.gz
    Extracting MNIST_data/t10k-images-idx3-ubyte.gz
    Extracting MNIST_data/t10k-labels-idx1-ubyte.gz
    Test loss: 0.08, test accuracy: 97.7%

    After we are finished the testing, we will close the session to free the memory.

    In [16]:
    # close the session after you are done with testing

    Thanks for reading! If you have any question or doubt, feel free to leave a comment in our website.

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