本文在調參記錄17的基礎上，將殘差模塊的數量增加到27個。其實之前也這樣做過，現在的區(qū)別在于，自適應參數化ReLU激活函數中第一個全連接層中的神經元個數設置成了特征通道數量的1/16。同樣是在Cifar10數據集上進行測試。

自適應參數化ReLU激活函數的基本原理如下：

自適應參數化ReLU激活函數

Keras代碼如下：

#!/usr/bin/env python3# -*- coding: utf-8 -*-"""Created on Tue Apr 14 04:17:45 2020Implemented using TensorFlow 1.0.1 and Keras 2.2.1Minghang Zhao, Shisheng Zhong, Xuyun Fu, Baoping Tang, Shaojiang Dong, Michael Pecht,Deep Residual Networks with Adaptively Parametric Rectifier Linear Units for Fault Diagnosis, IEEE Transactions on Industrial Electronics, 2020, DOI: 10.1109/TIE.2020.2972458 @author: Minghang Zhao"""from __future__ import print_functionimport kerasimport numpy as npfrom keras.datasets import cifar10from keras.layers import Dense, Conv2D, BatchNormalization, Activation, Minimumfrom keras.layers import AveragePooling2D, Input, GlobalAveragePooling2D, Concatenate, Reshapefrom keras.regularizers import l2from keras import backend as Kfrom keras.models import Modelfrom keras import optimizersfrom keras.preprocessing.image import ImageDataGeneratorfrom keras.callbacks import LearningRateSchedulerK.set_learning_phase(1)# The data, split between train and test sets(x_train, y_train), (x_test, y_test) = cifar10.load_data()# Noised datax_train = x_train.astype('float32') / 255.x_test = x_test.astype('float32') / 255.x_test = x_test-np.mean(x_train)x_train = x_train-np.mean(x_train)print('x_train shape:', x_train.shape)print(x_train.shape[0], 'train samples')print(x_test.shape[0], 'test samples')# convert class vectors to binary class matricesy_train = keras.utils.to_categorical(y_train, 10)y_test = keras.utils.to_categorical(y_test, 10)# Schedule the learning rate, multiply 0.1 every 1500 epochesdef scheduler(epoch): if epoch % 1500 == 0 and epoch != 0: lr = K.get_value(model.optimizer.lr) K.set_value(model.optimizer.lr, lr * 0.1) print("lr changed to {}".format(lr * 0.1)) return K.get_value(model.optimizer.lr)# An adaptively parametric rectifier linear unit (APReLU)def aprelu(inputs): # get the number of channels channels = inputs.get_shape().as_list()[-1] # get a zero feature map zeros_input = keras.layers.subtract([inputs, inputs]) # get a feature map with only positive features pos_input = Activation('relu')(inputs) # get a feature map with only negative features neg_input = Minimum()([inputs,zeros_input]) # define a network to obtain the scaling coefficients scales_p = GlobalAveragePooling2D()(pos_input) scales_n = GlobalAveragePooling2D()(neg_input) scales = Concatenate()([scales_n, scales_p]) scales = Dense(channels//16, activation='linear', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(scales) scales = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(scales) scales = Activation('relu')(scales) scales = Dense(channels, activation='linear', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(scales) scales = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(scales) scales = Activation('sigmoid')(scales) scales = Reshape((1,1,channels))(scales) # apply a paramtetric relu neg_part = keras.layers.multiply([scales, neg_input]) return keras.layers.add([pos_input, neg_part])# Residual Blockdef residual_block(incoming, nb_blocks, out_channels, downsample=False, downsample_strides=2): residual = incoming in_channels = incoming.get_shape().as_list()[-1] for i in range(nb_blocks): identity = residual if not downsample: downsample_strides = 1 residual = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(residual) residual = aprelu(residual) residual = Conv2D(out_channels, 3, strides=(downsample_strides, downsample_strides), padding='same', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(residual) residual = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(residual) residual = aprelu(residual) residual = Conv2D(out_channels, 3, padding='same', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(residual) # Downsampling if downsample_strides > 1: identity = AveragePooling2D(pool_size=(1,1), strides=(2,2))(identity) # Zero_padding to match channels if in_channels != out_channels: zeros_identity = keras.layers.subtract([identity, identity]) identity = keras.layers.concatenate([identity, zeros_identity]) in_channels = out_channels residual = keras.layers.add([residual, identity]) return residual# define and train a modelinputs = Input(shape=(32, 32, 3))net = Conv2D(16, 3, padding='same', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(inputs)net = residual_block(net, 9, 32, downsample=False)net = residual_block(net, 1, 32, downsample=True)net = residual_block(net, 8, 32, downsample=False)net = residual_block(net, 1, 64, downsample=True)net = residual_block(net, 8, 64, downsample=False)net = BatchNormalization(momentum=0.9, gamma_regularizer=l2(1e-4))(net)net = aprelu(net)net = GlobalAveragePooling2D()(net)outputs = Dense(10, activation='softmax', kernel_initializer='he_normal', kernel_regularizer=l2(1e-4))(net)model = Model(inputs=inputs, outputs=outputs)sgd = optimizers.SGD(lr=0.1, decay=0., momentum=0.9, nesterov=True)model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])# data augmentationdatagen = ImageDataGenerator( # randomly rotate images in the range (deg 0 to 180) rotation_range=30, # Range for random zoom zoom_range = 0.2, # shear angle in counter-clockwise direction in degrees shear_range = 30, # randomly flip images horizontal_flip=True, # randomly shift images horizontally width_shift_range=0.125, # randomly shift images vertically height_shift_range=0.125)reduce_lr = LearningRateScheduler(scheduler)# fit the model on the batches generated by datagen.flow().model.fit_generator(datagen.flow(x_train, y_train, batch_size=100), validation_data=(x_test, y_test), epochs=5000, verbose=1, callbacks=[reduce_lr], workers=4)# get resultsK.set_learning_phase(0)DRSN_train_score = model.evaluate(x_train, y_train, batch_size=100, verbose=0)print('Train loss:', DRSN_train_score[0])print('Train accuracy:', DRSN_train_score[1])DRSN_test_score = model.evaluate(x_test, y_test, batch_size=100, verbose=0)print('Test loss:', DRSN_test_score[0])print('Test accuracy:', DRSN_test_score[1])

結果如下：

Train loss: 0.04765264599025249Train accuracy: 0.9993600006103516Test loss: 0.2855186524987221Test accuracy: 0.9428000026941299

測試準確率第一次突破了94%。

其實，在訓練的后半階段還是出現了過擬合，說明還要針對性地調整超參數。

同時，似乎沒必要訓練5000個epoch。因為epoch再多，loss也不怎么下降。

Minghang Zhao, Shisheng Zhong, Xuyun Fu, Baoping Tang, Shaojiang Dong, Michael Pecht, Deep Residual Networks with Adaptively Parametric Rectifier Linear Units for Fault Diagnosis, IEEE Transactions on Industrial Electronics, 2020, DOI: 10.1109/TIE.2020.2972458

https://ieeexplore.ieee.org/document/8998530

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