CIFAR10数据库
CIFAR10是一套含有60000张大小为32×32彩色RGB图像的10分类图像数据库，其中的50000张图像为训练数据，10000张图像为测试数据，另外验证集的数据从训练集中取出。
隐含层使用的激活函数：ReLU函数
输出层使用的损失函数：Softmax函数
训练集数据特征数量（即维度）：32×32×3，3表示有RGB三个色彩通道。
训练集数据量：1000个
验证集数据量：1000个
由于该案例并不专注于模型的泛化能力，而是专注于如何使用代码实现该网络，所以不需要测试集。
隐含层层数：2层
隐含层神经元数量：从第1层到第2层隐含层 100 100
初始权重矩阵的标准差：0.05
训练迭代次数：100次
每个批次的训练集数量：500个
输出层神经元数量：10，即输出10个类别
学习率：0.001
正则化系数：0.0，无正则化
学习率衰减率：无衰减
优化器：Adam
使用批量归一化
‘i_b_h’： input between hidden 输入层到第一层隐含层
‘h_b_o’：hidden between output 最后一层隐含层到输出层
‘w_h_i_b_h_i+1’：w_ith hidden between i+1th hidden 第i层隐含层到第i+1层隐含层的权重
'b_h_i_b_h_i+1：b_ith hidden between i+1th hidden 第i层隐含层到第i+1层隐含层的偏置
‘w_h_b_o’：w_hidden between output 最后一层隐含层到输出层的权重
‘b_h_b_o’ ：b_hidden between output 最后一层隐含层到输出层的偏置
训练结果
目前存在训练损失与训练准确度共同增大的情况，，，尚不知如何解决
均已对各模块进行测试，无问题
代码
# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
import os
import _pickle as pickle
def rel_error(x, y):
return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))
def eval_numerical_gradient_array(f, x, df, h=1e-5):
"""
Evaluate a numeric gradient for a function that accepts a numpy
array and returns a numpy array.
"""
grad = np.zeros_like(x)
it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
while not it.finished:
ix = it.multi_index
oldval = x[ix]
x[ix] = oldval + h
pos = f(x).copy()
x[ix] = oldval - h
neg = f(x).copy()
x[ix] = oldval
grad[ix] = np.sum((pos - neg) * df) / (2 * h)
it.iternext()
return grad
#获取CIFAR10图像数据集
def get_CIFAR10_data(num_training=1000, num_validation=1000, num_test=0):
cifar10_dir = 'F:/Python programs/Neural Networks/深度学习实战/cifar-10-batches-py'
xs = []
ys = []
for b in range(1,6):
f = os.path.join(cifar10_dir, 'data_batch_%d' % (b, ))
with open(f, 'rb') as f:
datadict = pickle.load(f, encoding = 'latin1')
X = datadict['data']
Y = datadict['labels']
X = X.reshape(10000, 3, 32, 32).transpose(0,2,3,1).astype("float")
Y = np.array(Y)
xs.append(X)
ys.append(Y)
X_train = np.concatenate(xs)
y_train = np.concatenate(ys)
del X, Y
with open(os.path.join(cifar10_dir, 'test_batch'), 'rb') as f:
datadict = pickle.load(f, encoding = 'latin1')
X_test = datadict['data']
y_test = datadict['labels']
X_test = X_test.reshape(10000, 3, 32, 32).transpose(0,2,3,1).astype("float")
y_test = np.array(y_test)
#从原始训练集的50000张图中选出最后1000张图作为验证集
mask = range(num_training, num_training + num_validation)
X_val = X_train[mask]
y_val = y_train[mask]
mask = range(num_training)
X_train = X_train[mask]
y_train = y_train[mask]
#从原始测试集中的10000张图中选出最开始的1000张图作为测试集
mask = range(num_test)
X_test = X_test[mask]
y_test = y_test[mask]
#将训练集数据进行中心化
mean_image = np.mean(X_train, axis=0)
X_train -= mean_image
X_val -= mean_image
X_test -= mean_image
#重构尺寸
X_train = X_train.transpose(0, 3, 1, 2).copy()
X_val = X_val.transpose(0, 3, 1, 2).copy()
X_test = X_test.transpose(0, 3, 1, 2).copy()
return {
'X_train': X_train, 'y_train': y_train,
'X_val': X_val, 'y_val': y_val, \
'X_test': X_test, 'y_test': y_test,
}
#前向传播
def affine_forward(x, w, b):
"""
计算某一层的前向传播。
输入：x，N*D，若为RGB图像，则为N*(长*宽*3)，N为本层的神经元数量，D为特征数量
w，D*M，M为下一层的神经元数量
b，偏置向量，M*1
返回：out，N*M
"""
out = None
#数据量
N = x.shape[0]
#将x整理成二维数组，N行，剩下的组成列
x = np.reshape(x, (N,-1))
#在数据矩阵的最后一列再添加一列1，作为偏置x0，x变成N*(D+1)
x = np.hstack((x, np.ones((N, 1))))
#将偏置向量b添加到权重矩阵w的最后一行，作为偏置x0的权重，w变成(D+1)*M
w = np.vstack((w, np.transpose(b)))
#计算下一层所有神经元对本层所有神经元的激活值，例如本层有2个神经元，下一层有3个，则输出2*3矩阵
out = x.dot(w)
return out
#反向传播
def affine_backward(dout, cache):
"""
计算反向传播
输入：
dout，上层梯度，即残差，N*M
cache， 上层
输出：
dx，输入数据的梯度，N*d1*d2*...*dk
dw，权重矩阵的梯度，D*M
db，偏置项b的梯度，M*1
"""
x, w, b = cache
dx, dw, db = None, None, None
#反向传播
#数据量
N = x.shape[0]
#将x重塑成N*D
x = np.reshape(x, (N, -1))
#计算残差的梯度
dx = dout.dot(np.transpose(w))
#计算权重的梯度
dw = np.transpose(x)
dw = dw.dot(dout)
#计算偏置的梯度
db = np.sum(dout, axis = 0)
#将dx重塑回来
dx = np.reshape(dx, x.shape)
return dx, dw, db
#RelU传播
def relu_forward(x):
"""
计算ReLUs激活函数的前向传播，然后保存结果。
输入：
x - 输入数据
返回：
out - 与输入数据的尺寸相同。
cache - x。
"""
out = None
out = np.max(np.dstack((x,np.zeros(x.shape))),axis = 2)
return out
#ReLUs反向传播
def relu_backward(dout, x):
"""
计算ReLU函数的反向传播。
输入：
dout - 上层误差梯度
x - 输入数据x
返回：
dx - x的梯度
"""
dx = dout
dx[x <= 0] = 0
return dx
#softmax损失函数
def softmax_loss(X, y):
"""
无正则化
输入：
X：神经网络的输出层激活值
y：训练数据的标签，即真实标签
reg：正则化惩罚系数
输出：
loss：损失值
dW：权重W的梯度
"""
#初始化损失值与梯度
loss = 0.0
#计算损失-------------
#训练集数据数量N
num_train = X.shape[0]
#数据类别数量C
num_catogries = X.shape[1]
#归一化概率的分子，N*C
#为了防止指数运算时结果太大导致溢出，这里要将X的每行减去每行的最大值
score_fenzi = X - np.max(X, axis = 1, keepdims = True)
score_fenzi = np.exp(score_fenzi)
#归一化概率的分母，即，将归一化概率的分子按行求和，N*1
score_fenmu = np.sum(score_fenzi, axis = 1, keepdims = True)
#将分母按列复制，
score_fenmu = score_fenmu.dot(np.ones((1, num_catogries)))
#归一化概率，N*C/(N*1)*(1*C)=N*C/N*C
prob = np.log(score_fenzi/score_fenmu + 1)
y_true = np.zeros((num_train, num_catogries))
#把训练数据的标签铺开，例如，x是第3类，则x对应的标签为[0,0,1,0,0,0,0,0,0,0]
y_true[range(num_train), y] = 1.0
#y_true与p对应元素相乘后，只留下了每个数据真实标签对应的分数，例如x属于第3类，则留下第3个归一化概率
#求出每一行归一化概率的和，即把多余的0消除，再计算所有数据归一化概率的和
loss = -np.sum(y_true * prob) / num_train
#计算梯度--------------
dx = (score_fenzi/score_fenmu).copy()
dx[np.arange(num_train), y] -= 1
dx /= num_train
return loss, dx
#dropout前向传播
def dropout_forward(x, param):
"""
执行Dropout前向传播
输入：
x：输入数据
dropout_param：字典类型，dropout参数
p：dropout激活参数，每个神经元激活概率为p
mode：'test'或'train'。train：使用激活概率p与神经元进行与运算
test：去除激活概率p，返回输入值
seed：随机数生成种子
返回：
out：与输入数据形状相同
"""
dropout_p = param['p']
if 'seed' in param:
np.random.seed(param['seed'])
mask = None
out = None
mask = (np.random.rand(*x.shape) < dropout_p) / dropout_p
out = x * mask
out = out.astype(x.dtype, copy = False)
return out, mask
#dropout反向传播
def dropout_backward(dout, mask):
dx = None
dx = dout * mask
return dx
#SGD_Momentum优化器
def SGD_Momentum(w, dw, config = None):
"""
随机批量、动量梯度下降方法。
config：使用格式。
- learning_rate：学习率
- momentum：[0, 1]的动量学习因子，0表示不使用动量，退化为SGD
- velocity：速度，与w和dw形状相同。
"""
if config is None:
config = {}
config.setdefault('learning_rate', 1e-3)
config.setdefault('momentum', 0.9)
config.setdefault('velocity', np.zeros_like(w))
next_w = None
config['velocity'] = config['momentum'] * config['velocity'] - config['learning_rate'] * dw
next_w = w + config['velocity']
return next_w, config
#RMSProp优化器
def RMSProp(w, dw, config = None):
"""
RMSProp更新器
config字典：
learning_rate
decay_rate：历史累积梯度衰减因子，[0,1]
epsilon：用于避免数值溢出
"""
if config is None:
config = {}
config.setdefault('learning_rate', 1e-3)
config.setdefault('decay_rate', 0.99)
config.setdefault('epsilon', 1e-8)
config.setdefault('cache', np.zeros_like(w))
next_w = None
config['cache'] = config['decay_rate'] * config['cache'] + (1 - config['decay_rate']) * dw ** 2
next_w = w - config['learning_rate'] * dw / (np.sqrt(config['cache']) + config['epsilon'])
return next_w, config
#Adam优化器
def Adam(w, dw, config = None):
"""
Adam更新器
config字典：
learning_rate
beta1：动量衰减因子
beta2: 学习率衰减因子
epsilon：避免数值溢出
v：梯度衰减
r：学习率衰减
t：迭代次数
"""
if config is None:
config = {}
config.setdefault('learning_rate', 1e-3)
config.setdefault('beta1', 0.9)
config.setdefault('beta2', 0.999)
config.setdefault('epsilon', 1e-8)
config.setdefault('r', np.zeros_like(w))
config.setdefault('v', np.zeros_like(w))
config.setdefault('t', 0)
config['t'] += 1
next_w = None
config['v'] = config['beta1'] * config['v'] + (1 - config['beta1']) * dw
config['r'] = config['beta2'] * config['r'] + (1 - config['beta2']) * dw ** 2
config['vb'] = config['v'] / (1 - config['beta1'] ** (config['t']))
config['rb'] = config['r'] / (1 - config['beta2'] ** (config['t']))
next_w = w - config['learning_rate'] * config['vb'] / (np.sqrt(config['rb']) + config['epsilon'])
return next_w, config
#前向BN
def BN_forward(x, bn_param):
"""
使用类似动量衰减的运行时平均，计算总体均值与方差
输入：
x：输入数据(N, D)
bn_param：字典，如下
gamma：(D, )
beta：(D, )
eps：防止数据溢出
momentum：平均衰减因子
running_mean：运行时均值(D, )，预测时使用，训练阶段保留就好
running_var：运行时方差(D, )，预测时使用，训练阶段保留就好
输出：
out：输出(N, D)
cache：反向传播的缓存
"""
eps = bn_param.setdefault('eps', 1e-7)
momentum = bn_param.setdefault('momentum', 0.9)
N, D = x.shape
running_mean = bn_param.setdefault('running_mean', np.zeros(D, dtype = x.dtype))
running_var = bn_param.setdefault('running_var', np.zeros(D, dtype = x.dtype))
gamma = bn_param.setdefault('gamma', np.ones((D), dtype = x.dtype))
beta = bn_param.setdefault('beta', np.zeros((D), dtype = x.dtype))
out, cache = None, None #计算均值
mean = np.mean(x, axis = 0, keepdims = True)
#平移为零均值
x_mu = x - mean
#计算方差
var = np.sum(x_mu ** 2, axis = 0, keepdims = True) / N
#得到标准差
x_std = np.sqrt(var + eps)
#数据归一化
x_nor = x_mu / x_std
#数据缩放与平移
out = gamma * x_nor + beta
#更新均值和方差
bn_param['running_mean'] = momentum * running_mean + (1 - momentum) * mean
bn_param['running_var'] = momentum * running_var + (1 - momentum) * var
#保存中间结果，用于反向传播
cache = {'bn_param': bn_param, 'x_nor': x_nor, 'x_std': x_std, 'x_mu': x_mu, 'N': N}
return out, cache
#反向BN
def BN_backward(dout, cache):
"""
BN反向传播
输入：
dout：上层梯度
cache：前向BN的缓存
输出：
dx：数据梯度(N, D)
dgamma：gamma梯度(D, )
dbeta：beta梯度(D, )
"""
dx, dgamma, dbeta = None, None, None
dbeta = np.sum(dout, axis = 0)
dgamma = np.sum(cache['x_nor'] * dout, axis = 0)
N = cache['N']
dx = (1.0 / N) * cache['bn_param']['gamma'] * (cache['x_std'] ** 2 + cache['bn_param']['eps']) ** -0.5 * (N * dout - np.sum(
dout, axis = 0) - cache['x_mu'] / (cache['x_std'] ** 2 + cache['bn_param']['eps']) * np.sum(dout * cache['x_mu'], axis = 0))
return dx, dgamma, dbeta
#前向Dropout测试
x_dropout_test = np.random.randn(500, 500) + 10
out, _ = dropout_forward(x_dropout_test, {'p': 0.5})
print('前向Dropout自检-----------------------')
print('输入数据均值：', x_dropout_test.mean())
print('Dropout操作后的数据均值：', out.mean())
if rel_error(x_dropout_test.mean(), out.mean()) < 1e-3:
print('测试通过^_^\n')
else:
print('测试未通过')
#反向Dropout测试
x_dropout_test = np.random.randn(10, 10) + 10
dout = np.random.randn(*x_dropout_test.shape)
dropout_param = {'p': 0.8, 'seed': 123}
out, mask_test = dropout_forward(x_dropout_test, dropout_param)
dx = dropout_backward(dout, mask_test)
dx_num = eval_numerical_gradient_array(lambda xx: dropout_forward(xx, dropout_param)[0], x_dropout_test, dout)
print('反向Dropout自检-----------------------')
print('相对误差：', rel_error(dx, dx_num))
if rel_error(dx, dx_num) < 1e-10:
print('测试通过^_^\n')
else:
print('测试未通过\n')
#SGD_Momentum函数测试
N, D = 4, 5
w = np.linspace(-0.4, 0.6, num = N * D). reshape(N, D)
dw = np.linspace(-0.6, 0.4, num = N * D). reshape(N, D)
v = np.linspace(0.6, 0.9, num = N * D). reshape(N, D)
config_test = {'learning_rate': 1e-3, 'momentum': 0.9, 'velocity': v}
next_w, config_test = SGD_Momentum(w, dw, config = config_test)
expected_next_w = np.asarray([
[ 0.1406, 0.20738947, 0.27417895, 0.34096842, 0.40775789],
[ 0.47454737, 0.54133684, 0.60812632, 0.67491579, 0.74170526],
[ 0.80849474, 0.87528421, 0.94207368, 1.00886316, 1.07565263],
[ 1.14244211, 1.20923158, 1.27602105, 1.34281053, 1.4096 ]]),
expected_velocity = np.asarray([
[ 0.5406, 0.55475789, 0.56891579, 0.58307368, 0.59723158],
[ 0.61138947, 0.62554737, 0.63970526, 0.65386316, 0.66802105],
[ 0.68217895, 0.69633684, 0.71049474, 0.72465263, 0.73881053],
[ 0.75296842, 0.76712632, 0.78128421, 0.79544211, 0.8096 ]])
print('SGD_Momentum更新器自检---------------------')
print('更新权重误差: ', rel_error(next_w, expected_next_w))
print('速度误差: ', rel_error(expected_velocity, config_test['velocity']))
if rel_error(next_w, expected_next_w) < 1e-8 and rel_error(expected_velocity, config_test['velocity']) < 1e-8:
print('测试通过^_^\n')
else:
print('测试未通过\n')
#RMSProp函数测试
N, D = 4, 5
w = np.linspace(-0.4, 0.6, num = N * D). reshape(N, D)
dw = np.linspace(-0.6, 0.4, num = N * D). reshape(N, D)
cache = np.linspace(0.6, 0.9, num = N * D). reshape(N, D)
config_test = {'learning_rate': 1e-2, 'cache': cache}
next_w, config_test = RMSProp(w, dw, config = config_test)
expected_next_w = np.asarray([
[-0.39223849, -0.34037513, -0.28849239, -0.23659121, -0.18467247],
[-0.132737, -0.08078555, -0.02881884, 0.02316247, 0.07515774],
[ 0.12716641, 0.17918792, 0.23122175, 0.28326742, 0.33532447],
[ 0.38739248, 0.43947102, 0.49155973, 0.54365823, 0.59576619]])
expected_cache = np.asarray([
[ 0.5976, 0.6126277, 0.6277108, 0.64284931, 0.65804321],
[ 0.67329252, 0.68859723, 0.70395734, 0.71937285, 0.73484377],
[ 0.75037008, 0.7659518, 0.78158892, 0.79728144, 0.81302936],
[ 0.82883269, 0.84469141, 0.86060554, 0.87657507, 0.8926 ]])
print('RMSProp更新器自检--------------------------')
print('权重更新误差：', rel_error(expected_next_w, next_w))
print('cache误差：', rel_error(expected_cache, config_test['cache']))
if rel_error(expected_next_w, next_w) < 1e-7 and rel_error(expected_cache, config_test['cache']) < 1e-7:
print('测试通过^_^\n')
else:
print('测试未通过\n')
#Adam函数测试
N, D = 4, 5
w = np.linspace(-0.4, 0.6, num = N * D). reshape(N, D)
dw = np.linspace(-0.6, 0.4, num = N * D). reshape(N, D)
v = np.linspace(0.6, 0.9, num = N * D). reshape(N, D)
r = np.linspace(0.7, 0.5, num = N * D). reshape(N, D)
config_test = {'learning_rate': 1e-2, 'beta1': 0.9, 'beta2': 0.999, 'epsilon': 1e-7, 'r': r, 'v': v, 't': 5}
next_w, config_test = Adam(w, dw, config = config_test)
expected_next_w = np.asarray([
[-0.40094747, -0.34836187, -0.29577703, -0.24319299, -0.19060977],
[-0.1380274, -0.08544591, -0.03286534, 0.01971428, 0.0722929],
[ 0.1248705, 0.17744702, 0.23002243, 0.28259667, 0.33516969],
[ 0.38774145, 0.44031188, 0.49288093, 0.54544852, 0.59801459]])
expected_r = np.asarray([
[ 0.69966, 0.68908382, 0.67851319, 0.66794809, 0.65738853,],
[ 0.64683452, 0.63628604, 0.6257431, 0.61520571, 0.60467385,],
[ 0.59414753, 0.58362676, 0.57311152, 0.56260183, 0.55209767,],
[ 0.54159906, 0.53110598, 0.52061845, 0.51013645, 0.49966, ]])
expected_v = np.asarray([
[ 0.48, 0.49947368, 0.51894737, 0.53842105, 0.55789474],
[ 0.57736842, 0.59684211, 0.61631579, 0.63578947, 0.65526316],
[ 0.67473684, 0.69421053, 0.71368421, 0.73315789, 0.75263158],
[ 0.77210526, 0.79157895, 0.81105263, 0.83052632, 0.85 ]])
print('Adam更新器自检--------------------------')
print('权重更新误差：', rel_error(expected_next_w, next_w))
print('v误差：', rel_error(expected_v, config_test['v']))
print('r误差：', rel_error(expected_r, config_test['r']))
if rel_error(expected_next_w, next_w) < 1e-6 and rel_error(expected_v, config_test['v']) < 1e-7 and rel_error(expected_r, config_test['r']) < 1e-7:
print('测试通过^_^\n')
else:
print('测试未通过\n')
#前向BN测试
N, D1, D2, D3 = 200, 50, 60, 3
X = np.random.randn(N, D1)
W1 = np.random.randn(D1, D2)
W2 = np.random.randn(D2, D3)
a = np.maximum(0, X.dot(W1)).dot(W2)
print('前向BN自检---------------------------------')
print("批量归一化前：")
print('均值：', a.mean(axis = 0))
print('标准差：', a.std(axis = 0))
print('批量归一化后（应该为0均值，1标准差）：')
a_norm, _ = BN_forward(a, {'gamma': np.ones(D3), 'beta': np.zeros(D3)})
print('均值：', a_norm.mean(axis = 0))
print('标准差', a_norm.std(axis = 0))
if (a_norm.mean(axis = 0) - 0.0 < 1e-10).all() and (a_norm.std(axis = 0) - 1.0 < 1e-10).all() == True:
print('测试通过^_^\n')
else:
print('测试未通过\n')
#反向BN测试
N, D = 4, 5
x = 5 * np.random.randn(N, D) + 12
gamma = np.random.randn(D)
beta = np.random.randn(D)
dout = np.random.randn(N, D)
bn_param = {'gamma': gamma, 'beta': beta}
fx = lambda x: BN_forward(x, bn_param)[0]
fg = lambda a: BN_forward(x, bn_param)[0]
fb = lambda b: BN_forward(x, bn_param)[0]
dx_num = eval_numerical_gradient_array(fx, x, dout)
da_num = eval_numerical_gradient_array(fg, gamma, dout)
db_num = eval_numerical_gradient_array(fb, beta, dout)
_, cache = BN_forward(x, bn_param)
dx, dgamma, dbeta = BN_backward(dout, cache)
print('反向BN自检-----------------------------')
print('dx误差：', rel_error(dx_num, dx))
print('dgamma误差：', rel_error(da_num, dgamma))
print('dbeta误差：', rel_error(db_num, dbeta))
if rel_error(dx_num, dx) < 1e-5 and rel_error(da_num, dgamma) < 1e-8 and rel_error(db_num, dbeta) < 1e-8:
print('测试通过^_^\n')
else:
print('测试未通过\n')
#导入CIFAR10数据库
#输入数据
print('输入数据...')
data = get_CIFAR10_data()
X_train = data['X_train']
y_train = data['y_train']
X_val = data['X_val']
y_val = data['y_val']
X_test = data['X_test']
y_test = data['y_test']
for k, v in data.items():
print(f"{k}：", v.shape)
print('完成\n')
#测试含多层隐含层的神经网络-------------------------------------------------
#网络超参数设置
hidden_dim = [100, 100] #从左到右分别表示第一层到最后一层隐含层的神经元数量
hidden_layers_num = len(hidden_dim) #隐含层的层数
weight_scale = 5e-2 #初始权重矩阵中各元素的标准差
input_dim = 32*32*3 #输入数据的特征数量，即维度
num_classes = 10 #输出层神经元数量
params = {} #初始化存储有权重矩阵和偏置矩阵的字典
print("参数初始化...", end = '')
#初始化各权重矩阵与偏置向量
#初始化从输入层到第一层隐含层的权重矩阵与偏置矩阵
params['W_i_b_h'] = np.random.randn(input_dim, hidden_dim[0]) / np.sqrt(input_dim / 2)
params['b_i_b_h'] = np.zeros(hidden_dim[0])
#初始化从第一层到最后一层隐含层之间所有的权重矩阵与偏置矩阵
for i in range(hidden_layers_num - 1):
if hidden_layers_num == 1:
break;
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = np.random.randn(hidden_dim[i], hidden_dim[i + 1]) / np.sqrt(hidden_dim[i] / 2)
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = np.zeros(hidden_dim[i + 1])
#初始化从最后一层隐含层到输出层的权重矩阵与偏置矩阵
params['W_h_b_o'] = np.random.randn(hidden_dim[-1], num_classes) / np.sqrt(hidden_dim[-1] / 2)
params['b_h_b_o'] = np.zeros(num_classes)
#初始化dropout的掩模矩阵字典
dropout_mask = {}
#输入训练超参数
num_iters = 100 #迭代次数
batch_size = 500 #每一次迭代中从训练集中随机选取的数据量，选取出来作为一个批次
dropout_param = {'p': 0.7} #Dropout参数
learning_rate = 1e-3 #学习率
verbose = True #是否在命令行显示训练消息
reg = 0.0 #正则化系数
learning_rate_decay = 1.0 #学习率衰减率
iterations_per_epoch = max(X_train.shape[0] / batch_size, 1) #遍历整个训练集需要多少个批次
#可以选择的更新器：Original, Momentum, RMSProp, Adam
optimizer = 'Adam'
#存储历次迭代的损失值、训练准确率与验证准确率
loss_history = [] #历次损失值
train_history = [] #历次训练准确率
val_history = [] #历次验证准确率
#存储每次迭代生成的权重梯度与偏置梯度的字典
grad = {}
forward_out = {}
#BN传播初始化
bn_param = {}
gamma = {}
beta = {}
#Momentum、RMSProp、Adam更新器参数，BN的gamma和beta初始化
config = {'W_i_b_h': None, 'W_h_b_o': None, 'b_i_b_h': None, 'b_h_b_o': None, 'gamma_i_b_h': None, 'beta_i_b_h': None}
gamma['i_b_h'] = np.ones(hidden_dim[0])
beta['i_b_h'] = np.zeros(hidden_dim[0])
bn_dgamma = {}
bn_dbeta = {}
bn_cache = {}
for i in range(hidden_layers_num - 1):
config['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = None
config['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = None
config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = None
config['beta_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = None
gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = np.ones(hidden_dim[i + 1])
beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = np.zeros(hidden_dim[i + 1])
print('完成\n')
print('开始训练')
#开始训练
for it in range(num_iters):
num_train = X_train.shape[0] #训练集中的总数据量
X_batch = None
y_batch = None
#从训练集中随机取出batch_size个训练数据
#从0到num_train-1中随机取batch_size个数字，作为一个批次的训练数据的索引
i = np.random.choice(range(num_train), batch_size, replace = False)
X_batch = X_train[i,:]
#标签y和训练数据X必须对应，例如取出了第3个数据，则必须取出第3个标签
y_batch = y_train[i]
#前向传播------------------------
#从输入层传到第一层隐含层
#前向仿射变换
forward_out_i2h = affine_forward(X_batch, params['W_i_b_h'], params['b_i_b_h'])
#前向批量归一化
forward_out_i2h, bn_cache['i_b_h'] = BN_forward(forward_out_i2h, {'gamma': gamma['i_b_h'], 'beta': beta['i_b_h']})
#前向ReLU激活
forward_out['i2h'] = relu_forward(forward_out_i2h)
#前向Dropout
forward_out['i2h'], dropout_mask['i2h'] = dropout_forward(forward_out['i2h'], dropout_param)
#从第二层隐含层到最后一层隐含层
if hidden_layers_num > 1:
for i in range(hidden_layers_num - 1):
if i == 0:
forward_out['h' + str(i) + '_2_' + 'h' + str(i + 1)] = forward_out['i2h']
#前向仿射变换
forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)] = affine_forward(forward_out['h' + str(i) + '_2_' + 'h' + str(i + 1)],
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
#前向批量归一化
forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)], bn_cache['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = BN_forward(forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)],
{'gamma': gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], 'beta': beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]})
#前向ReLU激活
forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)] = relu_forward(forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)])
#前向Dropout
forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)], dropout_mask['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)] = dropout_forward(forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)], dropout_param)
forward_out_hidden = forward_out['h' + str(hidden_layers_num - 1) + '_2_' + 'h' + str(hidden_layers_num)]
else:
forward_out_hidden = forward_out['i2h']
#从最后一层隐含层到输出层
scores = affine_forward(forward_out_hidden, params['W_h_b_o'], params['b_h_b_o'])
#在输出层使用softmax损失函数，计算网络的总损失与梯度
loss, grad_out = softmax_loss(scores, y_batch)
#对总损失加入正则项
loss += 0.5 * reg * np.sum(params['W_i_b_h'] ** 2) + np.sum(params['W_h_b_o'] ** 2)
for i in range(hidden_layers_num - 1):
loss += 0.5 * reg * (np.sum(params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] ** 2))
#存储损失值
loss_history.append(loss)
#反向传播-------------------------------------------------------------------
#计算输出层到最后一层隐含层的残差、权重梯度与偏置梯度
dx, grad['W_o_b_h'], grad['b_o_b_h'] = affine_backward(grad_out, (forward_out_hidden, params['W_h_b_o'], params['b_h_b_o']))
#对输出层到隐含层的权重梯度加入正则项
grad['W_o_b_h'] += reg * params['W_h_b_o']
#从最后一层隐含层到第一层隐含层的所有残差、权重梯度与偏置梯度
if hidden_layers_num > 1:
for i in range(hidden_layers_num - 1, 0, -1):
if i == hidden_layers_num - 1:
forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)] = forward_out_hidden
#计算第i+1层到第i层隐含层的残差、权重梯度与偏置梯度
#反向Dropout
dx = dropout_backward(dx, dropout_mask['h' + str(i) + '_2_' + 'h' + str(i + 1)])
#反向ReLU
dx = relu_backward(dx, forward_out['h' + str(i + 1) + '_2_' + 'h' + str(i + 2)])
#反向批量归一化
dx, bn_dgamma['h' + str(i) + '_b_' + 'h' + str(i + 1)], bn_dbeta['h' + str(i) + '_b_' + 'h' + str(i + 1)] = BN_backward(dx, bn_cache['h' + str(i) + '_b_' + 'h' + str(i + 1)])
#反向传播
dx, grad['W_h' + str(i + 1) + '_b_' + 'h' + str(i)], grad['b_h' + str(i + 1) + '_b_' + 'h' + str(i)] = affine_backward(dx,
(forward_out['h' + str(i - 1) + '_2_' + 'h' + str(i)],
params['W_h' + str(i) + '_b_' + 'h' + str(i + 1)],
params['b_h' + str(i) + '_b_' + 'h' + str(i + 1)]))
#对第i+1层到第i层隐含层的权重梯度加入正则项
grad['W_h' + str(i + 1) + '_b_' + 'h' + str(i)] += reg * params['W_h' + str(i) + '_b_' + 'h' + str(i + 1)]
forward_relu_out = forward_out['h' + str(0) + '_2_' + 'h' + str(1)]
else:
forward_relu_out = forward_out_hidden
#计算第一层隐含层到输入层的残差、权重梯度与偏置梯度
#反向Dropout
dx = dropout_backward(dx, dropout_mask['i2h'])
#反向ReLU
dx = relu_backward(dx, forward_relu_out)
#反向批量归一化
dx, bn_dgamma['i_b_h'], bn_dbeta['i_b_h'] = BN_backward(dx, bn_cache['i_b_h'])
dx, grad['W_h_b_i'], grad['b_h_b_i'] = affine_backward(dx, (X_batch, params['W_i_b_h'], params['b_i_b_h']))
#对第第一层隐含层到输入层的权重梯度加入正则项
grad['W_h_b_i'] += reg * params['W_i_b_h']
#反向传播完成，此时回到了输入层
#通过梯度和学习率更新权重与偏置
#先更新输入层与第一层隐含层之间的权重和偏置，与，最后一层隐含层与输出层之间的权重和偏置
if optimizer is 'Original':
params['W_i_b_h'] -= learning_rate * grad['W_h_b_i']
params['W_h_b_o'] -= learning_rate * grad['W_o_b_h']
params['b_i_b_h'] -= learning_rate * grad['b_h_b_i']
params['b_h_b_o'] -= learning_rate * grad['b_o_b_h']
gamma['i_b_h'] -= learning_rate * bn_dgamma['i_b_h']
beta['i_b_h'] -= learning_rate * bn_dbeta['i_b_h']
learning_rate *= learning_rate_decay
elif optimizer is 'Momentum':
params['W_i_b_h'], config['W_i_b_h'] = SGD_Momentum(params['W_i_b_h'], grad['W_h_b_i'], config['W_i_b_h'])
params['W_h_b_o'], config['W_h_b_o'] = SGD_Momentum(params['W_h_b_o'], grad['W_o_b_h'], config['W_h_b_o'])
params['b_i_b_h'], config['b_i_b_h'] = SGD_Momentum(params['b_i_b_h'], grad['b_h_b_i'], config['b_i_b_h'])
params['b_h_b_o'], config['b_h_b_o'] = SGD_Momentum(params['b_h_b_o'], grad['b_o_b_h'], config['b_h_b_o'])
gamma['i_b_h'], config['gamma_i_b_h'] = SGD_Momentum(gamma['i_b_h'], bn_dgamma['i_b_h'], config['gamma_i_b_h'])
beta['i_b_h'], config['beta_i_b_h'] = SGD_Momentum(beta['i_b_h'], bn_dbeta['i_b_h'], config['beta_i_b_h'])
elif optimizer is 'RMSProp':
params['W_i_b_h'], config['W_i_b_h'] = RMSProp(params['W_i_b_h'], grad['W_h_b_i'], config['W_i_b_h'])
params['W_h_b_o'], config['W_h_b_o'] = RMSProp(params['W_h_b_o'], grad['W_o_b_h'], config['W_h_b_o'])
params['b_i_b_h'], config['b_i_b_h'] = RMSProp(params['b_i_b_h'], grad['b_h_b_i'], config['b_i_b_h'])
params['b_h_b_o'], config['b_h_b_o'] = RMSProp(params['b_h_b_o'], grad['b_o_b_h'], config['b_h_b_o'])
gamma['i_b_h'], config['gamma_i_b_h'] = RMSProp(gamma['i_b_h'], bn_dgamma['i_b_h'], config['gamma_i_b_h'])
beta['i_b_h'], config['beta_i_b_h'] = RMSProp(beta['i_b_h'], bn_dbeta['i_b_h'], config['beta_i_b_h'])
elif optimizer is 'Adam':
params['W_i_b_h'], config['W_i_b_h'] = Adam(params['W_i_b_h'], grad['W_h_b_i'], config['W_i_b_h'])
params['W_h_b_o'], config['W_h_b_o'] = Adam(params['W_h_b_o'], grad['W_o_b_h'], config['W_h_b_o'])
params['b_i_b_h'], config['b_i_b_h'] = Adam(params['b_i_b_h'], grad['b_h_b_i'], config['b_i_b_h'])
params['b_h_b_o'], config['b_h_b_o'] = Adam(params['b_h_b_o'], grad['b_o_b_h'], config['b_h_b_o'])
gamma['i_b_h'], config['gamma_i_b_h'] = Adam(gamma['i_b_h'], bn_dgamma['i_b_h'], config['gamma_i_b_h'])
beta['i_b_h'], config['beta_i_b_h'] = Adam(beta['i_b_h'], bn_dbeta['i_b_h'], config['beta_i_b_h'])
#如果隐含层数量大于1层，则再更新从第一层隐含层到最后一层隐含层之间的权重和偏置
if hidden_layers_num > 1:
if optimizer is 'Original':
for i in range(hidden_layers_num - 1):
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] -= learning_rate * grad['W_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)]
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] -= learning_rate * grad['b_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)]
gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] -= learning_rate * bn_dgamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]
beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] -= learning_rate * bn_dbeta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]
learning_rate *= learning_rate_decay
elif optimizer is 'Momentum':
for i in range(hidden_layers_num - 1):
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = SGD_Momentum(params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
grad['W_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)],
config['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = SGD_Momentum(params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
grad['b_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)],
config['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = SGD_Momentum(beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
bn_dgamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = SGD_Momentum(gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
bn_dbeta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
config['beta_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
elif optimizer is 'RMSProp':
for i in range(hidden_layers_num - 1):
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = RMSProp(params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
grad['W_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)],
config['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = RMSProp(params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
grad['b_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)],
config['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = RMSProp(gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
bn_dgamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['beta_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = RMSProp(beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
bn_dbeta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
config['beta_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
elif optimizer is 'Adam':
for i in range(hidden_layers_num - 1):
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = Adam(params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
grad['W_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)],
config['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = Adam(params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
grad['b_h' + str(i + 2) + '_b_' + 'h' + str(i + 1)],
config['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = Adam(gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
bn_dgamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
config['gamma_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], config['beta_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] = Adam(beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
bn_dbeta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
config['beta_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)])
if verbose == True:
print(f"第{it}/{num_iters}次迭代，损失为{loss}，", end = '\n')
if it % iterations_per_epoch == 0:
#做一个预测，计算此次迭代的训练准确率、验证准确率
#计算训练准确率
pred_out = affine_forward(X_batch, params['W_i_b_h'], params['b_i_b_h'])
pred_out = (pred_out - bn_cache['i_b_h']['bn_param']['running_mean']) / np.sqrt(bn_cache['i_b_h']['bn_param']['running_var'])
pred_out = gamma['i_b_h'] * pred_out + beta['i_b_h']
pred_out = relu_forward(pred_out)
if hidden_layers_num > 1:
for i in range(hidden_layers_num - 1):
pred_out = affine_forward(pred_out,
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], )
pred_out = (pred_out - bn_cache['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]['bn_param']['running_mean']) / \
np.sqrt(bn_cache['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]['bn_param']['running_var'])
pred_out = gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] * pred_out + beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]
pred_out = relu_forward(pred_out)
pred_out = affine_forward(pred_out, params['W_h_b_o'], params['b_h_b_o'])
pred_out = np.argmax(pred_out, axis = 1)
train_acc = np.mean(pred_out == y_batch)
train_history.append(train_acc)
#计算验证准确率
valpred_out = affine_forward(X_val, params['W_i_b_h'], params['b_i_b_h'])
valpred_out = (valpred_out - bn_cache['i_b_h']['bn_param']['running_mean']) / np.sqrt(bn_cache['i_b_h']['bn_param']['running_var'])
valpred_out = gamma['i_b_h'] * valpred_out + beta['i_b_h']
valpred_out = relu_forward(valpred_out)
if hidden_layers_num > 1:
for i in range(hidden_layers_num - 1):
valpred_out = affine_forward(valpred_out,
params['W_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)],
params['b_h' + str(i + 1) + '_b_' + 'h' + str(i + 2)], )
valpred_out = (valpred_out - bn_cache['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]['bn_param']['running_mean']) / \
np.sqrt(bn_cache['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]['bn_param']['running_var'])
valpred_out = gamma['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)] * valpred_out + beta['h' + str(i + 1) + '_b_' + 'h' + str(i + 2)]
valpred_out = relu_forward(valpred_out)
valpred_out = affine_forward(valpred_out, params['W_h_b_o'], params['b_h_b_o'])
valpred_out = np.argmax(valpred_out, axis = 1)
val_acc = np.mean(valpred_out == y_val)
val_history.append(val_acc)
print(f'训练准确度为{train_acc}, 验证准确度为{val_acc}')
#结果显示
plt.figure(1)
plt.plot(loss_history)
plt.title('Training Loss')
plt.figure(2)
plt.plot(train_history, label = 'Training Accuracy')
plt.legend()
plt.title('Accuracy')
plt.plot(val_history, label = 'Validation Accuracy')
plt.legend()