mnist_net2net.py

'''This is an implementation of Net2Net experiment with MNIST in
'Net2Net: Accelerating Learning via Knowledge Transfer'
by Tianqi Chen, Ian Goodfellow, and Jonathon Shlens

arXiv:1511.05641v4 [cs.LG] 23 Apr 2016
http://arxiv.org/abs/1511.05641

Notes
- What:
  + Net2Net is a group of methods to transfer knowledge from a teacher neural
    net to a student net,so that the student net can be trained faster than
    from scratch.
  + The paper discussed two specific methods of Net2Net, i.e. Net2WiderNet
    and Net2DeeperNet.
  + Net2WiderNet replaces a model with an equivalent wider model that has
    more units in each hidden layer.
  + Net2DeeperNet replaces a model with an equivalent deeper model.
  + Both are based on the idea of 'function-preserving transformations of
    neural nets'.
- Why:
  + Enable fast exploration of multiple neural nets in experimentation and
    design process,by creating a series of wider and deeper models with
    transferable knowledge.
  + Enable 'lifelong learning system' by gradually adjusting model complexity
    to data availability,and reusing transferable knowledge.

Experiments
- Teacher model: a basic CNN model trained on MNIST for 3 epochs.
- Net2WiderNet experiment:
  + Student model has a wider Conv2D layer and a wider FC layer.
  + Comparison of 'random-padding' vs 'net2wider' weight initialization.
  + With both methods, student model should immediately perform as well as
    teacher model, but 'net2wider' is slightly better.
- Net2DeeperNet experiment:
  + Student model has an extra Conv2D layer and an extra FC layer.
  + Comparison of 'random-init' vs 'net2deeper' weight initialization.
  + Starting performance of 'net2deeper' is better than 'random-init'.
- Hyper-parameters:
  + SGD with momentum=0.9 is used for training teacher and student models.
  + Learning rate adjustment: it's suggested to reduce learning rate
    to 1/10 for student model.
  + Addition of noise in 'net2wider' is used to break weight symmetry
    and thus enable full capacity of student models. It is optional
    when a Dropout layer is used.

Results
- Tested with 'Theano' backend and 'channels_first' image_data_format.
- Running on GPU GeForce GTX 980M
- Performance Comparisons - validation loss values during first 3 epochs:
(1) teacher_model:             0.075    0.041    0.041
(2) wider_random_pad:          0.036    0.034    0.032
(3) wider_net2wider:           0.032    0.030    0.030
(4) deeper_random_init:        0.061    0.043    0.041
(5) deeper_net2deeper:         0.032    0.031    0.029
'''

from __future__ import print_function
from six.moves import xrange
import numpy as np
import keras
from keras.models import Sequential
from keras.layers import Conv2D, MaxPooling2D, Dense, Flatten
from keras.optimizers import SGD
from keras.datasets import mnist

if keras.backend.image_data_format() == 'channels_first':
    input_shape = (1, 28, 28)  # image shape
else:
    input_shape = (28, 28, 1)  # image shape
num_class = 10  # number of class


# load and pre-process data
def preprocess_input(x):
    return x.reshape((-1, ) + input_shape) / 255.


def preprocess_output(y):
    return keras.utils.to_categorical(y)

(train_x, train_y), (validation_x, validation_y) = mnist.load_data()
train_x, validation_x = map(preprocess_input, [train_x, validation_x])
train_y, validation_y = map(preprocess_output, [train_y, validation_y])
print('Loading MNIST data...')
print('train_x shape:', train_x.shape, 'train_y shape:', train_y.shape)
print('validation_x shape:', validation_x.shape,
      'validation_y shape', validation_y.shape)


# knowledge transfer algorithms
def wider2net_conv2d(teacher_w1, teacher_b1, teacher_w2, new_width, init):
    '''Get initial weights for a wider conv2d layer with a bigger filters,
    by 'random-padding' or 'net2wider'.

    # Arguments
        teacher_w1: `weight` of conv2d layer to become wider,
          of shape (filters1, num_channel1, kh1, kw1)
        teacher_b1: `bias` of conv2d layer to become wider,
          of shape (filters1, )
        teacher_w2: `weight` of next connected conv2d layer,
          of shape (filters2, num_channel2, kh2, kw2)
        new_width: new `filters` for the wider conv2d layer
        init: initialization algorithm for new weights,
          either 'random-pad' or 'net2wider'
    '''
    assert teacher_w1.shape[0] == teacher_w2.shape[1], (
        'successive layers from teacher model should have compatible shapes')
    assert teacher_w1.shape[0] == teacher_b1.shape[0], (
        'weight and bias from same layer should have compatible shapes')
    assert new_width > teacher_w1.shape[0], (
        'new width (filters) should be bigger than the existing one')

    n = new_width - teacher_w1.shape[0]
    if init == 'random-pad':
        new_w1 = np.random.normal(0, 0.1, size=(n, ) + teacher_w1.shape[1:])
        new_b1 = np.ones(n) * 0.1
        new_w2 = np.random.normal(0, 0.1, size=(
            teacher_w2.shape[0], n) + teacher_w2.shape[2:])
    elif init == 'net2wider':
        index = np.random.randint(teacher_w1.shape[0], size=n)
        factors = np.bincount(index)[index] + 1.
        new_w1 = teacher_w1[index, :, :, :]
        new_b1 = teacher_b1[index]
        new_w2 = teacher_w2[:, index, :, :] / factors.reshape((1, -1, 1, 1))
    else:
        raise ValueError('Unsupported weight initializer: %s' % init)

    student_w1 = np.concatenate((teacher_w1, new_w1), axis=0)
    if init == 'random-pad':
        student_w2 = np.concatenate((teacher_w2, new_w2), axis=1)
    elif init == 'net2wider':
        # add small noise to break symmetry, so that student model will have
        # full capacity later
        noise = np.random.normal(0, 5e-2 * new_w2.std(), size=new_w2.shape)
        student_w2 = np.concatenate((teacher_w2, new_w2 + noise), axis=1)
        student_w2[:, index, :, :] = new_w2
    student_b1 = np.concatenate((teacher_b1, new_b1), axis=0)

    return student_w1, student_b1, student_w2


def wider2net_fc(teacher_w1, teacher_b1, teacher_w2, new_width, init):
    '''Get initial weights for a wider fully connected (dense) layer
       with a bigger nout, by 'random-padding' or 'net2wider'.

    # Arguments
        teacher_w1: `weight` of fc layer to become wider,
          of shape (nin1, nout1)
        teacher_b1: `bias` of fc layer to become wider,
          of shape (nout1, )
        teacher_w2: `weight` of next connected fc layer,
          of shape (nin2, nout2)
        new_width: new `nout` for the wider fc layer
        init: initialization algorithm for new weights,
          either 'random-pad' or 'net2wider'
    '''
    assert teacher_w1.shape[1] == teacher_w2.shape[0], (
        'successive layers from teacher model should have compatible shapes')
    assert teacher_w1.shape[1] == teacher_b1.shape[0], (
        'weight and bias from same layer should have compatible shapes')
    assert new_width > teacher_w1.shape[1], (
        'new width (nout) should be bigger than the existing one')

    n = new_width - teacher_w1.shape[1]
    if init == 'random-pad':
        new_w1 = np.random.normal(0, 0.1, size=(teacher_w1.shape[0], n))
        new_b1 = np.ones(n) * 0.1
        new_w2 = np.random.normal(0, 0.1, size=(n, teacher_w2.shape[1]))
    elif init == 'net2wider':
        index = np.random.randint(teacher_w1.shape[1], size=n)
        factors = np.bincount(index)[index] + 1.
        new_w1 = teacher_w1[:, index]
        new_b1 = teacher_b1[index]
        new_w2 = teacher_w2[index, :] / factors[:, np.newaxis]
    else:
        raise ValueError('Unsupported weight initializer: %s' % init)

    student_w1 = np.concatenate((teacher_w1, new_w1), axis=1)
    if init == 'random-pad':
        student_w2 = np.concatenate((teacher_w2, new_w2), axis=0)
    elif init == 'net2wider':
        # add small noise to break symmetry, so that student model will have
        # full capacity later
        noise = np.random.normal(0, 5e-2 * new_w2.std(), size=new_w2.shape)
        student_w2 = np.concatenate((teacher_w2, new_w2 + noise), axis=0)
        student_w2[index, :] = new_w2
    student_b1 = np.concatenate((teacher_b1, new_b1), axis=0)

    return student_w1, student_b1, student_w2


def deeper2net_conv2d(teacher_w):
    '''Get initial weights for a deeper conv2d layer by net2deeper'.

    # Arguments
        teacher_w: `weight` of previous conv2d layer,
          of shape (filters, num_channel, kh, kw)
    '''
    filters, num_channel, kh, kw = teacher_w.shape
    student_w = np.zeros((filters, filters, kh, kw))
    for i in xrange(filters):
        student_w[i, i, (kh - 1) / 2, (kw - 1) / 2] = 1.
    student_b = np.zeros(filters)
    return student_w, student_b


def copy_weights(teacher_model, student_model, layer_names):
    '''Copy weights from teacher_model to student_model,
     for layers with names listed in layer_names
    '''
    for name in layer_names:
        weights = teacher_model.get_layer(name=name).get_weights()
        student_model.get_layer(name=name).set_weights(weights)


# methods to construct teacher_model and student_models
def make_teacher_model(train_data, validation_data, epochs=3):
    '''Train a simple CNN as teacher model.
    '''
    model = Sequential()
    model.add(Conv2D(64, 3, input_shape=input_shape,
                     padding='same', name='conv1'))
    model.add(MaxPooling2D(2, name='pool1'))
    model.add(Conv2D(64, 3, padding='same', name='conv2'))
    model.add(MaxPooling2D(2, name='pool2'))
    model.add(Flatten(name='flatten'))
    model.add(Dense(64, activation='relu', name='fc1'))
    model.add(Dense(num_class, activation='softmax', name='fc2'))
    model.compile(loss='categorical_crossentropy',
                  optimizer=SGD(lr=0.01, momentum=0.9),
                  metrics=['accuracy'])

    train_x, train_y = train_data
    history = model.fit(train_x, train_y,
                        epochs=epochs,
                        validation_data=validation_data)
    return model, history


def make_wider_student_model(teacher_model, train_data,
                             validation_data, init, epochs=3):
    '''Train a wider student model based on teacher_model,
       with either 'random-pad' (baseline) or 'net2wider'
    '''
    new_conv1_width = 128
    new_fc1_width = 128

    model = Sequential()
    # a wider conv1 compared to teacher_model
    model.add(Conv2D(new_conv1_width, 3, input_shape=input_shape,
                     padding='same', name='conv1'))
    model.add(MaxPooling2D(2, name='pool1'))
    model.add(Conv2D(64, 3, padding='same', name='conv2'))
    model.add(MaxPooling2D(2, name='pool2'))
    model.add(Flatten(name='flatten'))
    # a wider fc1 compared to teacher model
    model.add(Dense(new_fc1_width, activation='relu', name='fc1'))
    model.add(Dense(num_class, activation='softmax', name='fc2'))

    # The weights for other layers need to be copied from teacher_model
    # to student_model, except for widened layers
    # and their immediate downstreams, which will be initialized separately.
    # For this example there are no other layers that need to be copied.

    w_conv1, b_conv1 = teacher_model.get_layer('conv1').get_weights()
    w_conv2, b_conv2 = teacher_model.get_layer('conv2').get_weights()
    new_w_conv1, new_b_conv1, new_w_conv2 = wider2net_conv2d(
        w_conv1, b_conv1, w_conv2, new_conv1_width, init)
    model.get_layer('conv1').set_weights([new_w_conv1, new_b_conv1])
    model.get_layer('conv2').set_weights([new_w_conv2, b_conv2])

    w_fc1, b_fc1 = teacher_model.get_layer('fc1').get_weights()
    w_fc2, b_fc2 = teacher_model.get_layer('fc2').get_weights()
    new_w_fc1, new_b_fc1, new_w_fc2 = wider2net_fc(
        w_fc1, b_fc1, w_fc2, new_fc1_width, init)
    model.get_layer('fc1').set_weights([new_w_fc1, new_b_fc1])
    model.get_layer('fc2').set_weights([new_w_fc2, b_fc2])

    model.compile(loss='categorical_crossentropy',
                  optimizer=SGD(lr=0.001, momentum=0.9),
                  metrics=['accuracy'])

    train_x, train_y = train_data
    history = model.fit(train_x, train_y,
                        epochs=epochs,
                        validation_data=validation_data)
    return model, history


def make_deeper_student_model(teacher_model, train_data,
                              validation_data, init, epochs=3):
    '''Train a deeper student model based on teacher_model,
       with either 'random-init' (baseline) or 'net2deeper'
    '''
    model = Sequential()
    model.add(Conv2D(64, 3, input_shape=input_shape,
                     padding='same', name='conv1'))
    model.add(MaxPooling2D(2, name='pool1'))
    model.add(Conv2D(64, 3, padding='same', name='conv2'))
    # add another conv2d layer to make original conv2 deeper
    if init == 'net2deeper':
        prev_w, _ = model.get_layer('conv2').get_weights()
        new_weights = deeper2net_conv2d(prev_w)
        model.add(Conv2D(64, 3, padding='same',
                         name='conv2-deeper', weights=new_weights))
    elif init == 'random-init':
        model.add(Conv2D(64, 3, padding='same', name='conv2-deeper'))
    else:
        raise ValueError('Unsupported weight initializer: %s' % init)
    model.add(MaxPooling2D(2, name='pool2'))
    model.add(Flatten(name='flatten'))
    model.add(Dense(64, activation='relu', name='fc1'))
    # add another fc layer to make original fc1 deeper
    if init == 'net2deeper':
        # net2deeper for fc layer with relu, is just an identity initializer
        model.add(Dense(64, kernel_initializer='identity',
                        activation='relu', name='fc1-deeper'))
    elif init == 'random-init':
        model.add(Dense(64, activation='relu', name='fc1-deeper'))
    else:
        raise ValueError('Unsupported weight initializer: %s' % init)
    model.add(Dense(num_class, activation='softmax', name='fc2'))

    # copy weights for other layers
    copy_weights(teacher_model, model, layer_names=[
                 'conv1', 'conv2', 'fc1', 'fc2'])

    model.compile(loss='categorical_crossentropy',
                  optimizer=SGD(lr=0.001, momentum=0.9),
                  metrics=['accuracy'])

    train_x, train_y = train_data
    history = model.fit(train_x, train_y,
                        epochs=epochs,
                        validation_data=validation_data)
    return model, history


# experiments setup
def net2wider_experiment():
    '''Benchmark performances of
    (1) a teacher model,
    (2) a wider student model with `random_pad` initializer
    (3) a wider student model with `Net2WiderNet` initializer
    '''
    train_data = (train_x, train_y)
    validation_data = (validation_x, validation_y)
    print('\nExperiment of Net2WiderNet ...')
    print('\nbuilding teacher model ...')
    teacher_model, _ = make_teacher_model(train_data,
                                          validation_data,
                                          epochs=3)

    print('\nbuilding wider student model by random padding ...')
    make_wider_student_model(teacher_model, train_data,
                             validation_data, 'random-pad',
                             epochs=3)
    print('\nbuilding wider student model by net2wider ...')
    make_wider_student_model(teacher_model, train_data,
                             validation_data, 'net2wider',
                             epochs=3)


def net2deeper_experiment():
    '''Benchmark performances of
    (1) a teacher model,
    (2) a deeper student model with `random_init` initializer
    (3) a deeper student model with `Net2DeeperNet` initializer
    '''
    train_data = (train_x, train_y)
    validation_data = (validation_x, validation_y)
    print('\nExperiment of Net2DeeperNet ...')
    print('\nbuilding teacher model ...')
    teacher_model, _ = make_teacher_model(train_data,
                                          validation_data,
                                          epochs=3)

    print('\nbuilding deeper student model by random init ...')
    make_deeper_student_model(teacher_model, train_data,
                              validation_data, 'random-init',
                              epochs=3)
    print('\nbuilding deeper student model by net2deeper ...')
    make_deeper_student_model(teacher_model, train_data,
                              validation_data, 'net2deeper',
                              epochs=3)

# run the experiments
net2wider_experiment()
net2deeper_experiment()