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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, after 1 epoch, student model should 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.
+ After 1 epoch, 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 TF backend and 'channels_last' image_data_format.
- Running on GPU GeForce GTX Titan X Maxwell
- Performance Comparisons - validation loss values during first 3 epochs:
Teacher model ...
(0) teacher_model: 0.0537 0.0354 0.0356
Experiment of Net2WiderNet ...
(1) wider_random_pad: 0.0320 0.0317 0.0289
(2) wider_net2wider: 0.0271 0.0274 0.0270
Experiment of Net2DeeperNet ...
(3) deeper_random_init: 0.0682 0.0506 0.0468
(4) deeper_net2deeper: 0.0292 0.0294 0.0286
```python
from __future__ import print_function
import numpy as np
import keras
from keras import backend as K
from keras.models import Sequential
from keras.layers import Conv2D, MaxPooling2D, Dense, Flatten
from keras.optimizers import SGD
from keras.datasets import mnist
if K.image_data_format() == 'channels_first':
input_shape = (1, 28, 28) # image shape
else:
input_shape = (28, 28, 1) # image shape
num_classes = 10 # number of classes
epochs = 3
# load and pre-process data
def preprocess_input(x):
return x.astype('float32').reshape((-1,) + input_shape) / 255
def preprocess_output(y):
return keras.utils.to_categorical(y)
(x_train, y_train), (x_test, y_test) = mnist.load_data()
x_train, x_test = map(preprocess_input, [x_train, x_test])
y_train, y_test = map(preprocess_output, [y_train, y_test])
print('Loading MNIST data...')
print('x_train shape:', x_train.shape, 'y_train shape:', y_train.shape)
print('x_test shape:', x_test.shape, 'y_test shape', y_test.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[3] == teacher_b1.shape[0], (
'weight and bias from same layer should have compatible shapes')
assert new_width > teacher_w1.shape[3], (
'new width (filters) should be bigger than the existing one')
n = new_width - teacher_w1.shape[3]
if init == 'random-pad':
new_w1 = np.random.normal(0, 0.1, size=teacher_w1.shape[:3] + (n,))
new_b1 = np.ones(n) * 0.1
new_w2 = np.random.normal(
0, 0.1,
size=teacher_w2.shape[:2] + (n, teacher_w2.shape[3]))
elif init == 'net2wider':
index = np.random.randint(teacher_w1.shape[3], 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=3)
if init == 'random-pad':
student_w2 = np.concatenate((teacher_w2, new_w2), axis=2)
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=2)
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 (kh, kw, num_channel, filters)
'''
kh, kw, num_channel, filters = teacher_w.shape
student_w = np.zeros_like(teacher_w)
for i in range(filters):
student_w[(kh - 1) // 2, (kw - 1) // 2, i, i] = 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(x_train, y_train,
x_test, y_test,
epochs):
'''Train and benchmark performance of a simple CNN.
(0) 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_classes, activation='softmax', name='fc2'))
model.compile(loss='categorical_crossentropy',
optimizer=SGD(learning_rate=0.01, momentum=0.9),
metrics=['accuracy'])
model.fit(x_train, y_train,
epochs=epochs,
validation_data=(x_test, y_test))
return model
def make_wider_student_model(teacher_model,
x_train, y_train,
x_test, y_test,
init, epochs):
'''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_classes, 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(learning_rate=0.001, momentum=0.9),
metrics=['accuracy'])
model.fit(x_train, y_train,
epochs=epochs,
validation_data=(x_test, y_test))
def make_deeper_student_model(teacher_model,
x_train, y_train,
x_test, y_test,
init, epochs):
'''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_classes, 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(learning_rate=0.001, momentum=0.9),
metrics=['accuracy'])
model.fit(x_train, y_train,
epochs=epochs,
validation_data=(x_test, y_test))
# experiments setup
def net2wider_experiment():
'''Benchmark performances of
(1) a wider student model with `random_pad` initializer
(2) a wider student model with `Net2WiderNet` initializer
'''
print('\nExperiment of Net2WiderNet ...')
print('\n(1) building wider student model by random padding ...')
make_wider_student_model(teacher_model,
x_train, y_train,
x_test, y_test,
init='random-pad',
epochs=epochs)
print('\n(2) building wider student model by net2wider ...')
make_wider_student_model(teacher_model,
x_train, y_train,
x_test, y_test,
init='net2wider',
epochs=epochs)
def net2deeper_experiment():
'''Benchmark performances of
(3) a deeper student model with `random_init` initializer
(4) a deeper student model with `Net2DeeperNet` initializer
'''
print('\nExperiment of Net2DeeperNet ...')
print('\n(3) building deeper student model by random init ...')
make_deeper_student_model(teacher_model,
x_train, y_train,
x_test, y_test,
init='random-init',
epochs=epochs)
print('\n(4) building deeper student model by net2deeper ...')
make_deeper_student_model(teacher_model,
x_train, y_train,
x_test, y_test,
init='net2deeper',
epochs=epochs)
print('\n(0) building teacher model ...')
teacher_model = make_teacher_model(x_train, y_train,
x_test, y_test,
epochs=epochs)
# run the experiments
net2wider_experiment()
net2deeper_experiment()
```
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