'''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 ''' 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()