自适应参数化ReLU是一种动态ReLU（Dynamic ReLU）激活函数，在2019年5月3日投稿至IEEE Transactions on Industrial Electronics，2020年1月24日录用，2020年2月13日在IEEE官网公布。

在调参记录14里，只有2个残差模块，结果遭遇欠拟合了。这次增加一个残差模块试试。

自适应参数化ReLU激活函数的基本原理如下：

Keras程序如下：

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Apr 14 04:17:45 2020
Implemented using TensorFlow 1.0.1 and Keras 2.2.1

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,
Date of Publication: 13 February 2020

@author: Minghang Zhao
"""

from __future__ import print_function
import keras
import numpy as np
from keras.datasets import cifar10
from keras.layers import Dense, Conv2D, BatchNormalization, Activation, Minimum
from keras.layers import AveragePooling2D, Input, GlobalAveragePooling2D, Concatenate, Reshape
from keras.regularizers import l2
from keras import backend as K
from keras.models import Model
from keras import optimizers
from keras.preprocessing.image import ImageDataGenerator
from keras.callbacks import LearningRateScheduler
K.set_learning_phase(1)

# The data, split between train and test sets
(x_train, y_train), (x_test, y_test) = cifar10.load_data()
x_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 matrices
y_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 epoches
def 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//8, 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 Block
def 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 model
inputs = 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, 1, 16, downsample=False)
net = residual_block(net, 1, 32, downsample=True)
# net = residual_block(net, 2, 32, downsample=False)
net = residual_block(net, 1, 64, downsample=True)
# net = residual_block(net, 2, 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 augmentation
datagen = 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=1000),
                    validation_data=(x_test, y_test), epochs=5000, 
                    verbose=1, callbacks=[reduce_lr], workers=4)

# get results
K.set_learning_phase(0)
DRSN_train_score = model.evaluate(x_train, y_train, batch_size=1000, 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=1000, verbose=0)
print('Test loss:', DRSN_test_score[0])
print('Test accuracy:', DRSN_test_score[1])

实验结果如下：

Epoch 2575/5000
10s 197ms/step - loss: 0.3505 - acc: 0.9039 - val_loss: 0.4548 - val_acc: 0.8745
Epoch 2576/5000
10s 198ms/step - loss: 0.3571 - acc: 0.9003 - val_loss: 0.4483 - val_acc: 0.8732
Epoch 2577/5000
10s 194ms/step - loss: 0.3536 - acc: 0.9033 - val_loss: 0.4547 - val_acc: 0.8725
Epoch 2578/5000
10s 196ms/step - loss: 0.3514 - acc: 0.9033 - val_loss: 0.4429 - val_acc: 0.8766

程序还没跑完，似乎也没必要跑完了。

训练集上还没拟合得很好，测试集准确率已经低于训练集准确率大约2.5%了。这是同时存在欠拟合和过拟合呀！

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, Date of Publication: 13 February 2020

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