基本信息
实验名称：网络优化实验姓名：学号：日期：2022/11/14
文章目录
基本信息一、在多分类任务中分别手动实现和用torch.nn实现dropout1.1 任务内容1.2 任务思路及代码1.2.0数据集定义1.2.1 手动实现-设置dropout = 01.2.2 手动实现-设置dropout = 0.31.2.3 手动实现-设置dropout = 0.61.2.4 手动实现-设置dropout = 0.91.2.5 torch.nn实现-设置dropout = 01.2.6 torch.nn实现-设置dropout = 0.31.2.7 torch.nn实现-设置dropout = 0.61.2.8 torch.nn实现-设置dropout = 0.9
1.3 实验结果分析
二、在多分类任务中分别手动实现和用torch.nn实现
L
2
L_2
L2 正则化2.1 任务内容2.2 任务思路及代码2.2.1 手动实现-设置惩罚权重lambd= 0(即无惩罚权重)2.2.2 手动实现-设置惩罚权重lambd= 22.2.3 利用torch.nn实现-设置惩罚权重weight_decay=0.0(即无惩罚权重)2.2.4 利用torch.nn实现-设置惩罚权重weight_decay = 1e-2
2.3 实验结果分析
三、）在多分类任务实验中实现momentum、rmsprop、adam优化器3.1 任务内容3.2 任务思路及代码3.2.1 手动实现RMSprop算法3.2.2 手动实现Momentum算法3.2.3 手动实现Adam算法3.2.4 torch.nn实现RMSprop算法3.2.5 torch.nn实现Momentum算法3.2.6torch.nn 实现Adam算法
四、在多分类任务实验上实现早停机制4.1 任务内容4.2 任务思路及代码4.3 结果分析
A1 实验心得A2 参考文献
一、在多分类任务中分别手动实现和用torch.nn实现dropout
1.1 任务内容
任务具体要求 在多分类任务实验中分别手动和利用torch.nn实现dropout 探究不同丢弃率对实验结果的影响（可用loss曲线进行展示）任务目的 探究不同丢弃率对实验结果的影响任务算法或原理介绍 Dropout 原理 任务所用数据集 Fashion-MNIST数据集:
该数据集包含60,000个用于训练的图像样本和10,000个用于测试的图像样本。图像是固定大小(28x28像素)，其值为0到1。为每个图像都被平展并转换为784
1.2 任务思路及代码
构建数据集构建前馈神经网络，损失函数，优化函数手动实现dropout进行反向传播，和梯度更新使用网络预测结果，得到损失值对loss、acc等指标进行分析，探究不同丢弃率对实验结果的影响
1.2.0数据集定义
import time
import matplotlib.pyplot as plt
import numpy as np
import torch
import torch.nn as nn
import torchvision
from torch.nn.functional import cross_entropy, binary_cross_entropy
from torch.nn import CrossEntropyLoss
from torchvision import transforms
from sklearn import metrics
device = torch.device("cuda" if torch.cuda.is_available() else "cpu") # 如果有gpu则在gpu上计算 加快计算速度
print(f'当前使用的device为{device}')
# 数据集定义
# 定义多分类数据集 - train_dataloader - test_dataloader
batch_size = 128
# Build the training and testing dataset
traindataset = torchvision.datasets.FashionMNIST(root='E:\\DataSet\\FashionMNIST\\Train',
train=True,
download=True,
transform=transforms.ToTensor())
testdataset = torchvision.datasets.FashionMNIST(root='E:\\DataSet\\FashionMNIST\\Test',
train=False,
download=True,
transform=transforms.ToTensor())
traindataloader = torch.utils.data.DataLoader(traindataset, batch_size=batch_size, shuffle=True)
testdataloader = torch.utils.data.DataLoader(testdataset, batch_size=batch_size, shuffle=False)
# 绘制图像的代码
def picture(name, trainl, testl,xlabel='Epoch',ylabel='Loss'):
plt.rcParams["font.sans-serif"]=["SimHei"] #设置字体
plt.rcParams["axes.unicode_minus"]=False #该语句解决图像中的“-”负号的乱码问题
plt.figure(figsize=(8, 3))
plt.title(name[-1]) # 命名
color = ['g','r','b','c']
if trainl is not None:
plt.subplot(121)
for i in range(len(name)-1):
plt.plot(trainl[i], c=color[i],label=name[i])
plt.xlabel(xlabel)
plt.ylabel(ylabel)
plt.legend()
if testl is not None:
plt.subplot(122)
for i in range(len(name)-1):
plt.plot(testl[i], c=color[i], label=name[i])
plt.xlabel(xlabel)
plt.ylabel(ylabel)
plt.legend()
print(f'多分类数据集 样本总数量{len(traindataset) + len(testdataset)},训练样本数量{len(traindataset)},测试样本数量{len(testdataset)}')
当前使用的device为cuda
多分类数据集 样本总数量70000,训练样本数量60000,测试样本数量10000
1.手动实现前馈神经网络代码
代码中MyNet为手动实现的前馈神经网络模型，包含一个参数 dropout 表示丢失率用作实验一中设置不同的丢失率代码设置函数train_and_test可供之后需要手动实现多分类的实验调用，默认的损失函数为 CrossEntropyLoss(),优化函数为自己定义的随机梯度下降函数mySGD(),其余参数设置如下：
epochs=30 表示需要训练的总epoch数 默认为 30lr=0.01 表示设置的学习率, 默认值为 0.01L2=False 表示是否需要加入L2惩罚范数，默认值为Falselambd=0 如果需要加入L2惩罚范数，则lambd有用，该值为惩罚权重，默认值为0
# 定义自己的前馈神经网络
from torch.nn import CrossEntropyLoss
from torch.optim import SGD
# dropout = 0.2
class MyNet():
def __init__(self,dropout=0.0):
# 设置隐藏层和输出层的节点数
# global dropout
self.dropout = dropout
print('dropout: ',self.dropout)
self.is_train = None
num_inputs, num_hiddens, num_outputs = 28 * 28, 256, 10 # 十分类问题
w_1 = torch.tensor(np.random.normal(0, 0.01, (num_hiddens, num_inputs)), dtype=torch.float32,
requires_grad=True)
b_1 = torch.zeros(num_hiddens, dtype=torch.float32, requires_grad=True)
w_2 = torch.tensor(np.random.normal(0, 0.01, (num_outputs, num_hiddens)), dtype=torch.float32,
requires_grad=True)
b_2 = torch.zeros(num_outputs, dtype=torch.float32, requires_grad=True)
self.params = [w_1, b_1, w_2, b_2]
self.w = [w_1,w_2]
# 定义模型结构
self.input_layer = lambda x: x.view(x.shape[0], -1)
self.hidden_layer = lambda x: self.my_relu(torch.matmul(x, w_1.t()) + b_1)
self.output_layer = lambda x: torch.matmul(x, w_2.t()) + b_2
def my_relu(self, x):
return torch.max(input=x, other=torch.tensor(0.0))
# 以下两个函数分别在训练和测试前调用，选择是否需要dropout
def train(self):
self.is_train = True
def test(self):
self.is_train = False
"""
定义dropout层
x: 输入数据
dropout: 随机丢弃的概率
"""
def dropout_layer(self, x):
dropout =self.dropout
assert 0 <= dropout <= 1 #dropout值必须在0-1之间
# dropout==1，所有元素都被丢弃。
if dropout == 1:
return torch.zeros_like(x)
# 在本情况中，所有元素都被保留。
if dropout == 0:
return x
mask = (torch.rand(x.shape) < 1.0 - dropout).float() #rand()返回一个张量，包含了从区间[0, 1)的均匀分布中抽取的一组随机数
return mask * x / (1.0 - dropout)
# 定义前向传播
def forward(self, x):
x = self.input_layer(x)
if self.is_train: # 如果是训练过程，则需要开启dropout 否则 需要关闭 dropout
x = dropout_layer(x,dropout=self.dropout)
x = self.my_relu(self.hidden_layer(x))
if self.is_train:
x = dropout_layer(x,dropout=self.dropout)
x = self.output_layer(x)
return x
# 默认的优化函数为手写的mySGD
def mySGD(params, lr, batchsize):
for param in params:
param.data -= lr * param.grad
# 定义L2范数惩罚项 参数 w 为模型的 w 在本次实验中为[w_1, w_2] batch_size=128
def l2_penalty(w):
cost = 0
for i in range(len(w)):
cost += (w[i]**2).sum()
return cost / batch_size / 2
"""
定义训练函数
model:定义的模型 默认为MyNet(0) 即无dropout的初始网络
epochs:训练总轮数 默认为30
criterion:定义的损失函数，默认为cross_entropy
lr :学习率 默认为0.1
optimizer:定义的优化函数，默认为自己定义的mySGD函数
"""
def train_and_test(model=MyNet(),init_states=None,optimizer=mySGD,epochs=20,lr=0.01,L2=False,lambd=0):
train_all_loss = [] # 记录训练集上得loss变化
test_all_loss = [] # 记录测试集上的loss变化
train_ACC, test_ACC = [], [] # 记录正确的个数
begintime = time.time()
# 激活函数为自己定义的mySGD函数
# criterion = cross_entropy # 损失函数为交叉熵函数
criterion = CrossEntropyLoss() # 损失函数
model.train() #表明当前处于训练状态，允许使用dropout
for epoch in range(epochs):
train_l,train_acc_num = 0, 0
for data, labels in traindataloader:
pred = model.forward(data)
train_each_loss = criterion(pred, labels) # 计算每次的损失值
# 若L2为True则表示需要添加L2范数惩罚项
if L2 == True:
train_each_loss += lambd * l2_penalty(model.w)
train_l += train_each_loss.item()
train_each_loss.backward() # 反向传播
# 若当前states为 None表示 使用的是 默认的优化函数mySGD
if init_states == None:
optimizer(model.params, lr, 128) # 使用小批量随机梯度下降迭代模型参数
# 否则的话使用的是自己定义的优化器，通过传入的参数，来实现优化效果
else:
states = init_states(model.params)
optimizer(model.params,states,lr=lr)
# 梯度清零
train_acc_num += (pred.argmax(dim=1)==labels).sum().item()
for param in model.params:
param.grad.data.zero_()
# print(train_each_loss)
train_all_loss.append(train_l) # 添加损失值到列表中
train_ACC.append(train_acc_num / len(traindataset)) # 添加准确率到列表中
model.test() # 表明当前处于测试状态，无需使用dropout
with torch.no_grad():
is_train = False # 表明当前为测试阶段，不需要dropout参与
test_l, test_acc_num = 0, 0
for data, labels in testdataloader:
pred = model.forward(data)
test_each_loss = criterion(pred, labels)
test_l += test_each_loss.item()
test_acc_num += (pred.argmax(dim=1)==labels).sum().item()
test_all_loss.append(test_l)
test_ACC.append(test_acc_num / len(testdataset)) # # 添加准确率到列表中
if epoch == 0 or (epoch + 1) % 2 == 0:
print('epoch: %d | train loss:%.5f | test loss:%.5f | train acc: %.2f | test acc: %.2f'
% (epoch + 1, train_l, test_l, train_ACC[-1],test_ACC[-1]))
endtime = time.time()
print("手动实现dropout = %d, %d轮 总用时: %.3f" % (model.dropout, epochs, endtime - begintime))
return train_all_loss,test_all_loss,train_ACC,test_ACC
dropout: 0.0
1.2.1 手动实现-设置dropout = 0
# 设置dropout = 0 dropout = 0 epoch = 30 lr = 0.01 optimizer = mySGD
model_11 = MyNet(dropout = 0.0)
train_all_loss11,test_all_loss11,\
train_ACC11,test_ACC11 \
= train_and_test(model=model_11,epochs=20,lr=0.01)
dropout: 0.0
epoch: 1 | train loss:872.64942 | test loss:101.62506 | train acc: 0.49 | test acc: 0.62
epoch: 2 | train loss:484.90760 | test loss:70.47120 | train acc: 0.65 | test acc: 0.66
epoch: 4 | train loss:337.69529 | test loss:55.50412 | train acc: 0.74 | test acc: 0.75
epoch: 6 | train loss:288.98904 | test loss:48.69153 | train acc: 0.79 | test acc: 0.78
epoch: 8 | train loss:261.24783 | test loss:44.77175 | train acc: 0.81 | test acc: 0.80
epoch: 10 | train loss:244.54166 | test loss:42.56631 | train acc: 0.82 | test acc: 0.81
epoch: 12 | train loss:233.17713 | test loss:40.83642 | train acc: 0.83 | test acc: 0.82
epoch: 14 | train loss:225.23643 | test loss:39.74532 | train acc: 0.83 | test acc: 0.82
epoch: 16 | train loss:219.29802 | test loss:38.82166 | train acc: 0.84 | test acc: 0.83
epoch: 18 | train loss:214.22844 | test loss:38.12609 | train acc: 0.84 | test acc: 0.83
epoch: 20 | train loss:210.15229 | test loss:37.73654 | train acc: 0.84 | test acc: 0.83
手动实现dropout = 0, 20轮 总用时: 203.126
1.2.2 手动实现-设置dropout = 0.3
# 设置dropout = 0.3 epoch = 30 lr = 0.01 optimizer = mySGD
dropout=0.3
model_12 = MyNet()
train_all_loss12,test_all_loss12,\
train_ACC12,test_ACC12 \
= train_and_test(model=model_12,epochs=20,lr=0.01)
dropout: 0.3
epoch: 1 | train loss:879.17995 | test loss:102.15184 | train acc: 0.41 | test acc: 0.62
epoch: 2 | train loss:487.08636 | test loss:70.85480 | train acc: 0.65 | test acc: 0.67
epoch: 4 | train loss:339.05907 | test loss:55.81440 | train acc: 0.74 | test acc: 0.75
epoch: 6 | train loss:290.52114 | test loss:48.84491 | train acc: 0.79 | test acc: 0.78
epoch: 8 | train loss:262.59252 | test loss:45.04938 | train acc: 0.81 | test acc: 0.80
epoch: 10 | train loss:245.22824 | test loss:42.48761 | train acc: 0.82 | test acc: 0.81
epoch: 12 | train loss:233.72414 | test loss:40.87166 | train acc: 0.83 | test acc: 0.82
epoch: 14 | train loss:225.33460 | test loss:39.64226 | train acc: 0.84 | test acc: 0.82
epoch: 16 | train loss:218.90282 | test loss:38.89728 | train acc: 0.84 | test acc: 0.83
epoch: 18 | train loss:213.85560 | test loss:38.04384 | train acc: 0.84 | test acc: 0.83
epoch: 20 | train loss:209.63276 | test loss:37.77163 | train acc: 0.85 | test acc: 0.83
手动实现dropout = 0, 20轮 总用时: 200.632
1.2.3 手动实现-设置dropout = 0.6
# 设置dropout = 0.6 dropout = 0.6 epoch = 30 lr = 0.01 optimizer = mySGD
model_13 = MyNet(dropout=0.6)
train_all_loss13,test_all_loss13,\
train_ACC13,test_ACC13 \
= train_and_test(model=model_13,epochs=20,lr=0.01)
dropout: 0.6
epoch: 1 | train loss:909.44703 | test loss:107.27103 | train acc: 0.35 | test acc: 0.59
epoch: 2 | train loss:504.39541 | test loss:72.46001 | train acc: 0.64 | test acc: 0.66
epoch: 4 | train loss:341.84676 | test loss:56.07868 | train acc: 0.74 | test acc: 0.74
epoch: 6 | train loss:291.11752 | test loss:48.94307 | train acc: 0.79 | test acc: 0.78
epoch: 8 | train loss:262.59137 | test loss:45.16227 | train acc: 0.81 | test acc: 0.80
epoch: 10 | train loss:245.31536 | test loss:42.67761 | train acc: 0.82 | test acc: 0.81
epoch: 12 | train loss:233.70658 | test loss:40.84980 | train acc: 0.83 | test acc: 0.82
epoch: 14 | train loss:225.42686 | test loss:39.89094 | train acc: 0.84 | test acc: 0.82
epoch: 16 | train loss:219.13081 | test loss:39.07038 | train acc: 0.84 | test acc: 0.83
epoch: 18 | train loss:214.17095 | test loss:38.72034 | train acc: 0.84 | test acc: 0.82
epoch: 20 | train loss:209.99137 | test loss:37.43517 | train acc: 0.85 | test acc: 0.83
手动实现dropout = 0, 20轮 总用时: 234.203
1.2.4 手动实现-设置dropout = 0.9
# 设置dropout = 0.9 dropout = 0.9 epoch = 20 lr = 0.01 optimizer = mySGD
model_14 = MyNet(dropout=0.9)
train_all_loss14,test_all_loss14,\
train_ACC14,test_ACC14 \
= train_and_test(model=model_14,epochs=20,lr=0.01)
dropout: 0.9
epoch: 1 | train loss:998.39192 | test loss:131.15014 | train acc: 0.20 | test acc: 0.53
epoch: 2 | train loss:569.14506 | test loss:76.94013 | train acc: 0.61 | test acc: 0.65
epoch: 4 | train loss:351.53705 | test loss:57.61345 | train acc: 0.73 | test acc: 0.74
epoch: 6 | train loss:297.49190 | test loss:49.77498 | train acc: 0.78 | test acc: 0.78
epoch: 8 | train loss:266.77583 | test loss:45.55881 | train acc: 0.81 | test acc: 0.80
epoch: 10 | train loss:248.14114 | test loss:43.03852 | train acc: 0.82 | test acc: 0.81
epoch: 12 | train loss:235.84031 | test loss:41.16744 | train acc: 0.83 | test acc: 0.82
epoch: 14 | train loss:227.23696 | test loss:40.22656 | train acc: 0.83 | test acc: 0.82
epoch: 16 | train loss:220.65873 | test loss:39.36629 | train acc: 0.84 | test acc: 0.82
epoch: 18 | train loss:215.42647 | test loss:38.41269 | train acc: 0.84 | test acc: 0.83
epoch: 20 | train loss:211.04093 | test loss:37.67217 | train acc: 0.84 | test acc: 0.83
手动实现dropout = 0, 20轮 总用时: 188.600
2.利用torch.nn实现前馈神经网络代码
# 利用torch.nn实现前馈神经网络-多分类任务
from collections import OrderedDict
from torch.nn import CrossEntropyLoss
from torch.optim import SGD
# 定义自己的前馈神经网络
class MyNet_NN(nn.Module):
def __init__(self,dropout=0.0):
super(MyNet_NN, self).__init__()
# 设置隐藏层和输出层的节点数
self.num_inputs, self.num_hiddens, self.num_outputs = 28 * 28, 256, 10 # 十分类问题
# 定义模型结构
self.input_layer = nn.Flatten()
self.hidden_layer = nn.Linear(28*28,256)
# 根据设置的dropout设置丢失率
self.drop = nn.Dropout(dropout)
self.output_layer = nn.Linear(256,10)
# 使用relu激活函数
self.relu = nn.ReLU()
# 定义前向传播
def forward(self, x):
x = self.drop(self.input_layer(x))
x = self.drop(self.hidden_layer(x))
x = self.relu(x)
x = self.output_layer(x)
return x
# 训练
# 使用默认的参数即： num_inputs=28*28,num_hiddens=256,num_outs=10,act='relu'
model = MyNet_NN()
model = model.to(device)
# 将训练过程定义为一个函数，方便调用
def train_and_test_NN(model=model,epochs=30,lr=0.01,weight_decay=0.0,optimizer=None):
MyModel = model
print(MyModel)
# 优化函数, 默认情况下weight_decay为0 通过更改weight_decay的值可以实现L2正则化。
# 默认的优化函数为SGD 可以根据参数来修改优化函数
if optimizer == None:
optimizer = SGD(MyModel.parameters(), lr=lr,weight_decay=weight_decay)
criterion = CrossEntropyLoss() # 损失函数
criterion = criterion.to(device)
train_all_loss = [] # 记录训练集上得loss变化
test_all_loss = [] # 记录测试集上的loss变化
train_ACC, test_ACC = [], []
begintime = time.time()
for epoch in range(epochs):
train_l, train_epoch_count, test_epoch_count = 0, 0, 0
for data, labels in traindataloader:
data, labels = data.to(device), labels.to(device)
pred = MyModel(data)
train_each_loss = criterion(pred, labels.view(-1)) # 计算每次的损失值
optimizer.zero_grad() # 梯度清零
train_each_loss.backward() # 反向传播
optimizer.step() # 梯度更新
train_l += train_each_loss.item()
train_epoch_count += (pred.argmax(dim=1)==labels).sum()
train_ACC.append(train_epoch_count/len(traindataset))
train_all_loss.append(train_l) # 添加损失值到列表中
with torch.no_grad():
test_loss, test_epoch_count= 0, 0
for data, labels in testdataloader:
data, labels = data.to(device), labels.to(device)
pred = MyModel(data)
test_each_loss = criterion(pred,labels)
test_loss += test_each_loss.item()
test_epoch_count += (pred.argmax(dim=1)==labels).sum()
test_all_loss.append(test_loss)
test_ACC.append(test_epoch_count.cpu()/len(testdataset))
if epoch == 0 or (epoch + 1) % 2 == 0:
print('epoch: %d | train loss:%.5f | test loss:%.5f | train acc:%5f test acc:%.5f:' % (epoch + 1, train_all_loss[-1], test_all_loss[-1],
train_ACC[-1],test_ACC[-1]))
endtime = time.time()
print("torch.nn实现前馈网络-多分类任务 %d轮 总用时: %.3fs" % (epochs, endtime - begintime))
# 返回训练集和测试集上的 损失值 与 准确率
return train_all_loss,test_all_loss,train_ACC,test_ACC
1.2.5 torch.nn实现-设置dropout = 0
# 设置dropout = 0 dropout = 0 epoch = 20 lr = 0.01 optimizer = SGD
model_15 = MyNet_NN(dropout=0)
model_15 = model_15.to(device)
train_all_loss15,test_all_loss15,\
train_ACC15,test_ACC15 \
= train_and_test_NN(model=model_15,epochs=20,lr=0.01)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:655.58136 | test loss:74.47299 | train acc:0.622167 test acc:0.67990:
epoch: 2 | train loss:383.53553 | test loss:59.61930 | train acc:0.721167 test acc:0.73540:
epoch: 4 | train loss:293.89208 | test loss:48.96072 | train acc:0.790733 test acc:0.78950:
epoch: 6 | train loss:259.49087 | test loss:44.43671 | train acc:0.815433 test acc:0.80620:
epoch: 8 | train loss:240.91520 | test loss:41.87740 | train acc:0.826550 test acc:0.81700:
epoch: 10 | train loss:229.37972 | test loss:40.24408 | train acc:0.833583 test acc:0.82250:
epoch: 12 | train loss:221.02299 | test loss:39.09193 | train acc:0.838850 test acc:0.82610:
epoch: 14 | train loss:214.61364 | test loss:38.23125 | train acc:0.843517 test acc:0.83120:
epoch: 16 | train loss:209.39514 | test loss:37.83912 | train acc:0.846883 test acc:0.82850:
epoch: 18 | train loss:204.97675 | test loss:36.86500 | train acc:0.849483 test acc:0.83560:
epoch: 20 | train loss:201.09988 | test loss:36.50862 | train acc:0.852667 test acc:0.83650:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 169.970s
1.2.6 torch.nn实现-设置dropout = 0.3
# 设置dropout = 0 dropout = 0 epoch = 20 lr = 0.01 optimizer = SGD
model_16 = MyNet_NN(dropout=0.3)
model_16 = model_16.to(device)
train_all_loss16,test_all_loss16,\
train_ACC16,test_ACC16 \
= train_and_test_NN(model=model_16,epochs=20,lr=0.01)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0.3, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:702.54659 | test loss:80.90724 | train acc:0.542983 test acc:0.64540:
epoch: 2 | train loss:421.96581 | test loss:65.55994 | train acc:0.686283 test acc:0.69950:
epoch: 4 | train loss:332.59721 | test loss:55.84150 | train acc:0.753833 test acc:0.74820:
epoch: 6 | train loss:299.84487 | test loss:51.16118 | train acc:0.778217 test acc:0.77110:
epoch: 8 | train loss:282.70475 | test loss:48.75440 | train acc:0.791150 test acc:0.78030:
epoch: 10 | train loss:271.02193 | test loss:46.89236 | train acc:0.797250 test acc:0.78890:
epoch: 12 | train loss:262.19408 | test loss:45.14446 | train acc:0.806817 test acc:0.79860:
epoch: 14 | train loss:255.17918 | test loss:43.83435 | train acc:0.809567 test acc:0.80310:
epoch: 16 | train loss:248.88366 | test loss:43.53325 | train acc:0.814300 test acc:0.80210:
epoch: 18 | train loss:242.04225 | test loss:42.59759 | train acc:0.817517 test acc:0.80700:
epoch: 20 | train loss:238.39859 | test loss:41.80848 | train acc:0.821833 test acc:0.81500:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 166.926s
1.2.7 torch.nn实现-设置dropout = 0.6
# 设置dropout = 0 dropout = 0 epoch = 20 lr = 0.01 optimizer = SGD
model_17 = MyNet_NN(dropout=0.6)
model_17 = model_17.to(device)
train_all_loss17,test_all_loss17,\
train_ACC17,test_ACC17 \
= train_and_test_NN(model=model_17,epochs=20,lr=0.01)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0.6, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:773.29946 | test loss:94.92489 | train acc:0.444217 test acc:0.58040:
epoch: 2 | train loss:494.37014 | test loss:76.87856 | train acc:0.622967 test acc:0.65040:
epoch: 4 | train loss:400.60366 | test loss:66.31284 | train acc:0.694850 test acc:0.69800:
epoch: 6 | train loss:365.91697 | test loss:62.46187 | train acc:0.723167 test acc:0.71640:
epoch: 8 | train loss:343.86994 | test loss:58.71530 | train acc:0.737933 test acc:0.73280:
epoch: 10 | train loss:330.31647 | test loss:56.35195 | train acc:0.748017 test acc:0.73650:
epoch: 12 | train loss:321.14122 | test loss:54.33575 | train acc:0.754500 test acc:0.75220:
epoch: 14 | train loss:312.09657 | test loss:53.44632 | train acc:0.760450 test acc:0.75670:
epoch: 16 | train loss:306.95581 | test loss:52.45056 | train acc:0.765567 test acc:0.75630:
epoch: 18 | train loss:300.05030 | test loss:51.08243 | train acc:0.768783 test acc:0.77060:
epoch: 20 | train loss:295.16722 | test loss:51.24780 | train acc:0.773500 test acc:0.76530:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 160.365s
1.2.8 torch.nn实现-设置dropout = 0.9
# 设置dropout = 0 dropout = 0 epoch = 20 lr = 0.01 optimizer = SGD
model_18 = MyNet_NN(dropout=0.9)
model_18 = model_18.to(device)
train_all_loss18,test_all_loss18,\
train_ACC18,test_ACC18 \
= train_and_test_NN(model=model_18,epochs=20,lr=0.01)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0.9, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:1031.86029 | test loss:152.73935 | train acc:0.192783 test acc:0.26440:
epoch: 2 | train loss:832.82668 | test loss:132.52133 | train acc:0.317433 test acc:0.34840:
epoch: 4 | train loss:701.72601 | test loss:115.61146 | train acc:0.413683 test acc:0.42660:
epoch: 6 | train loss:652.82964 | test loss:109.09122 | train acc:0.453233 test acc:0.46170:
epoch: 8 | train loss:618.55567 | test loss:104.19970 | train acc:0.485717 test acc:0.48220:
epoch: 10 | train loss:596.50939 | test loss:100.95779 | train acc:0.505933 test acc:0.50250:
epoch: 12 | train loss:580.25755 | test loss:98.08979 | train acc:0.518717 test acc:0.51810:
epoch: 14 | train loss:562.10516 | test loss:96.48224 | train acc:0.530767 test acc:0.52650:
epoch: 16 | train loss:550.00569 | test loss:91.92824 | train acc:0.544350 test acc:0.54050:
epoch: 18 | train loss:545.92920 | test loss:92.90535 | train acc:0.545083 test acc:0.54730:
epoch: 20 | train loss:536.47559 | test loss:89.90178 | train acc:0.554950 test acc:0.55680:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 155.538s
1.3 实验结果分析
手动实现的dropout-Loss打印
#完成loss的显示
drop_name_1 = ['dropout=0','dropout=0.3','dropout=0.6','dropout=0.9','手动实现不同的dropout-Loss变化']
drop_train_1 = [train_all_loss11,train_all_loss12,train_all_loss13,train_all_loss14]
drop_test_1 = [test_all_loss11,test_all_loss12,test_all_loss13,test_all_loss14]
picture(drop_name_2, drop_train_2,drop_test_2)
torch.nn实现的dropout-Loss打印
#完成loss的显示
drop_name_2 = ['dropout=0','dropout=0.3','dropout=0.6','dropout=0.9','手动实现不同的dropout-Loss变化']
drop_train_2 = [train_all_loss15,train_all_loss16,train_all_loss17,train_all_loss18]
drop_test_2 = [test_all_loss15,test_all_loss16,test_all_loss16,test_all_loss18]
picture(drop_name_2, drop_train_2, drop_test_2)
上图为手动实现和torch.nn实现的dropout实验的损失值的变化，左边的为训练集上得，右边的为测试集合上的。 由上两图dropout的设置值越大，初始的损失值越大，随后随着训练次数的增加，损失值不断降低。dropout的值越大，模型过拟合的概率越小。
dropout的作用： Dropout使得在每个训练批次中，通过忽略一半数量的特征检测器（让一半的隐层节点值为0），可以明显地减少过拟合现象。这种方式可以减少特征检测器（隐层节点）间的相互作用。
二、在多分类任务中分别手动实现和用torch.nn实现
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L2 正则化
2.1 任务内容
任务具体要求 在多分类任务中分别手动实现和用torch.nn实现
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L2正则化任务目的 探究惩罚项的权重对实验结果的影响（可用loss曲线进行展示）任务算法或原理介绍
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L2 原理 任务所用数据集 Fashion-MNIST数据集:
该数据集包含60,000个用于训练的图像样本和10,000个用于测试的图像样本。图像是固定大小(28x28像素)，其值为0到1。为每个图像都被平展并转换为784
2.2 任务思路及代码
构建数据集构建前馈神经网络，损失函数，优化函数构建L2范数惩罚项进行反向传播，和梯度更新使用网络预测结果，得到损失值探究惩罚项的权重对实验结果的影响
2.2.1 手动实现-设置惩罚权重lambd= 0(即无惩罚权重)
# 设置dropout = 0 dropout = 0 epoch = 20 lr = 0.01 optimizer = SGD L2=True lambd=0
model_21 = MyNet(dropout=0)
train_all_loss21,test_all_loss21,\
train_ACC21,test_ACC21\
= train_and_test(model=model_21,epochs=20,lr=0.01,L2=True,lambd=0)
dropout: 0
epoch: 1 | train loss:866.45301 | test loss:101.49811 | train acc: 0.45 | test acc: 0.60
epoch: 2 | train loss:486.26606 | test loss:70.56476 | train acc: 0.65 | test acc: 0.67
epoch: 4 | train loss:336.08916 | test loss:55.07089 | train acc: 0.75 | test acc: 0.75
epoch: 6 | train loss:286.81197 | test loss:48.24101 | train acc: 0.79 | test acc: 0.78
epoch: 8 | train loss:259.50061 | test loss:44.47255 | train acc: 0.81 | test acc: 0.80
epoch: 10 | train loss:243.31417 | test loss:42.31028 | train acc: 0.82 | test acc: 0.81
epoch: 12 | train loss:232.23276 | test loss:41.08155 | train acc: 0.83 | test acc: 0.82
epoch: 14 | train loss:224.23518 | test loss:39.63520 | train acc: 0.84 | test acc: 0.82
epoch: 16 | train loss:218.08964 | test loss:38.81029 | train acc: 0.84 | test acc: 0.83
epoch: 18 | train loss:213.08018 | test loss:38.25762 | train acc: 0.84 | test acc: 0.83
epoch: 20 | train loss:208.77749 | test loss:37.60064 | train acc: 0.85 | test acc: 0.83
手动实现dropout = 0, 20轮 总用时: 206.190
2.2.2 手动实现-设置惩罚权重lambd= 2
# 设置dropout = 0 dropout = 0 epoch = 20 lr = 0.01 optimizer = SGD L2=True lambd=1
model_22 = MyNet(dropout=0)
train_all_loss22,test_all_loss22,\
train_ACC22,test_ACC22\
= train_and_test(model=model_22,epochs=20,lr=0.01,L2=True,lambd=1)
dropout: 0
epoch: 1 | train loss:905.61759 | test loss:102.07449 | train acc: 0.46 | test acc: 0.60
epoch: 2 | train loss:539.61660 | test loss:71.66011 | train acc: 0.65 | test acc: 0.67
epoch: 4 | train loss:407.31129 | test loss:57.25353 | train acc: 0.74 | test acc: 0.74
epoch: 6 | train loss:365.83306 | test loss:51.18184 | train acc: 0.78 | test acc: 0.78
epoch: 8 | train loss:342.00613 | test loss:47.03204 | train acc: 0.80 | test acc: 0.80
epoch: 10 | train loss:327.25394 | test loss:44.71919 | train acc: 0.82 | test acc: 0.81
epoch: 12 | train loss:317.70518 | test loss:43.34584 | train acc: 0.82 | test acc: 0.81
epoch: 14 | train loss:310.83809 | test loss:42.27092 | train acc: 0.83 | test acc: 0.82
epoch: 16 | train loss:305.72729 | test loss:41.80292 | train acc: 0.83 | test acc: 0.81
epoch: 18 | train loss:301.85856 | test loss:40.95933 | train acc: 0.83 | test acc: 0.82
epoch: 20 | train loss:298.56079 | test loss:40.83248 | train acc: 0.84 | test acc: 0.82
手动实现dropout = 0, 20轮 总用时: 204.461
2.2.3 利用torch.nn实现-设置惩罚权重weight_decay=0.0(即无惩罚权重)
# 设置dropout = 0 dropout = 0 epoch = 30 lr = 0.01 optimizer = SGD weight_decay=0.0
model_24 = MyNet_NN(dropout=0)
model_24 = model_24.to(device)
train_all_loss24,test_all_loss24,\
train_ACC24,test_ACC24 \
= train_and_test_NN(model=model_24,epochs=20,lr=0.01,weight_decay=0.0)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:659.27534 | test loss:74.52569 | train acc:0.616133 test acc:0.67780:
epoch: 2 | train loss:382.77867 | test loss:59.38335 | train acc:0.722317 test acc:0.74080:
epoch: 4 | train loss:292.84218 | test loss:48.83517 | train acc:0.791800 test acc:0.78720:
epoch: 6 | train loss:258.79662 | test loss:44.28819 | train acc:0.815900 test acc:0.80610:
epoch: 8 | train loss:240.63736 | test loss:41.84953 | train acc:0.827000 test acc:0.81660:
epoch: 10 | train loss:229.37524 | test loss:40.13170 | train acc:0.833183 test acc:0.82340:
epoch: 12 | train loss:221.23428 | test loss:39.13591 | train acc:0.838783 test acc:0.82780:
epoch: 14 | train loss:215.19242 | test loss:38.60563 | train acc:0.842200 test acc:0.83020:
epoch: 16 | train loss:210.06449 | test loss:37.52553 | train acc:0.846350 test acc:0.83320:
epoch: 18 | train loss:206.02604 | test loss:36.85281 | train acc:0.849067 test acc:0.83510:
epoch: 20 | train loss:202.39181 | test loss:36.56123 | train acc:0.852200 test acc:0.83890:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 136.719s
2.2.4 利用torch.nn实现-设置惩罚权重weight_decay = 1e-2
# 设置dropout = 0 dropout = 0 epoch = 20 lr = 0.01 optimizer = SGD weight_decay=1e-3
model_26 = MyNet_NN(dropout=0)
model_26 = model_26.to(device)
train_all_loss26,test_all_loss26,\
train_ACC26,test_ACC26 \
= train_and_test_NN(model=model_26,epochs=20,lr=0.01,weight_decay=1e-3)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:680.87843 | test loss:76.15495 | train acc:0.605317 test acc:0.67710:
epoch: 2 | train loss:389.25886 | test loss:60.02418 | train acc:0.719550 test acc:0.73310:
epoch: 4 | train loss:296.29670 | test loss:49.37372 | train acc:0.788817 test acc:0.78670:
epoch: 6 | train loss:261.61639 | test loss:44.95376 | train acc:0.813367 test acc:0.80070:
epoch: 8 | train loss:243.03708 | test loss:42.29602 | train acc:0.825467 test acc:0.81430:
epoch: 10 | train loss:231.52064 | test loss:40.79951 | train acc:0.833133 test acc:0.81730:
epoch: 12 | train loss:223.04548 | test loss:39.49103 | train acc:0.837983 test acc:0.82460:
epoch: 14 | train loss:216.66145 | test loss:38.59491 | train acc:0.841867 test acc:0.82670:
epoch: 16 | train loss:211.67088 | test loss:37.71256 | train acc:0.845367 test acc:0.83050:
epoch: 18 | train loss:207.27632 | test loss:37.09026 | train acc:0.848200 test acc:0.83260:
epoch: 20 | train loss:203.70357 | test loss:36.68534 | train acc:0.851017 test acc:0.83330:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 153.349s
2.3 实验结果分析
手动实现的惩罚权重lambd得Loss的打印
#完成loss的显示
drop_name_3 = ['lambd= 0','lambd=2','手动实现不同的惩罚权重lambd-Loss变化']
drop_train_3 = [train_all_loss21,train_all_loss22]
drop_test_3= [test_all_loss21,test_all_loss22]
picture(drop_name_3, drop_train_3,drop_test_3)
torch.nn实现-设置惩罚权重weight_decayLoss的打印
#完成loss的显示
drop_name_4= ['weight_decay=0.0','weight_decay = 1e-2','torch.nn实现不同的惩罚权重lambd-Loss变化']
drop_train_4 = [train_all_loss24,train_all_loss26]
drop_test_4= [test_all_loss24,test_all_loss26]
picture(drop_name_4, drop_train_4,drop_test_4)
上图为手动实现和torch.nn实现的不同惩罚权重的实验的 损失值的变化，左边的为训练集上得，右边的为测试集合上的。 对比上图我们可以看出，惩罚权重越大，模型的也会随之损失值越大 当未使用权重衰减(lambd=0)时，训练集上的误差远小于测试集，使用权重衰减(lambd=3 or 6)时，训练误差虽然提高，但是测试集上的误差下降，过拟合得到一定程度上缓解 权重衰退通过L2正则项使得模型参数不会过大，也不会过小，从而控制模型的复杂度不会太复杂。
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L2 正则化的好处： 1）学习理论的角度： 从学习理论的角度来说，L2范数可以防止过拟合，提升模型的泛化能力。越小的参数说明模型越简单，越简单的模型则越不容易产生过拟合现象。 2）优化计算的角度： 从优化或者数值计算的角度来说，L2范数有助于处理 condition number不好的情况下矩阵求逆很困难的问题。
三、）在多分类任务实验中实现momentum、rmsprop、adam优化器
3.1 任务内容
任务具体要求
在手动实现多分类的任务中手动实现三种优化算法，并补全Adam中计算部分的内容在torch.nn实现多分类的任务中使用torch.nn实现各种优化器，并对比其效果
任务目的 对比不同优化器的效果任务算法或原理介绍
任务所用数据集 Fashion-MNIST数据集:
该数据集包含60,000个用于训练的图像样本和10,000个用于测试的图像样本。图像是固定大小(28x28像素)，其值为0到1。为每个图像都被平展并转换为784
3.2 任务思路及代码
构建数据集构建前馈神经网络，损失函数，优化函数手动和torch.nn构建不同的优化器进行反向传播，和梯度更新使用网络预测结果，得到损失值对比不同优化器的效果
3.2.1 手动实现RMSprop算法
# 初始化
def init_rmsprop(params):
s_w1, s_b1, s_w2, s_b2 = torch.zeros(params[0].shape), torch.zeros(params[1].shape),\
torch.zeros(params[2].shape), torch.zeros(params[3].shape)
return (s_w1, s_b1, s_w2, s_b2)
# 对每一个参数进行RMSprop法
def rmsprop(params,states,lr=0.01,gamma=0.9):
gamma, eps = gamma, 1e-6
for p, s in zip(params,states):
with torch.no_grad():
s[:] = gamma * s + (1 - gamma) * torch.square(p.grad)
p[:] -= lr * p.grad / torch.sqrt(s + eps)
p.grad.data.zero_()
model_31 = MyNet(dropout=0)
train_all_loss31,test_all_loss31,\
train_ACC31,test_ACC31 \
= train_and_test(model=model_31,epochs=20,init_states=init_rmsprop,optimizer=rmsprop)
dropout: 0
epoch: 1 | train loss:496.50297 | test loss:85.90571 | train acc: 0.70 | test acc: 0.75
epoch: 2 | train loss:397.04907 | test loss:71.54532 | train acc: 0.77 | test acc: 0.80
epoch: 4 | train loss:352.24937 | test loss:62.14564 | train acc: 0.79 | test acc: 0.79
epoch: 6 | train loss:327.49242 | test loss:59.53483 | train acc: 0.80 | test acc: 0.76
epoch: 8 | train loss:326.74552 | test loss:66.19045 | train acc: 0.80 | test acc: 0.81
epoch: 10 | train loss:317.08560 | test loss:55.85927 | train acc: 0.81 | test acc: 0.80
epoch: 12 | train loss:314.16541 | test loss:70.23939 | train acc: 0.81 | test acc: 0.78
epoch: 14 | train loss:312.43203 | test loss:57.75320 | train acc: 0.81 | test acc: 0.80
epoch: 16 | train loss:304.61697 | test loss:62.12512 | train acc: 0.81 | test acc: 0.80
epoch: 18 | train loss:300.99380 | test loss:65.22936 | train acc: 0.81 | test acc: 0.81
epoch: 20 | train loss:294.28814 | test loss:63.74287 | train acc: 0.81 | test acc: 0.80
手动实现dropout = 0, 20轮 总用时: 187.376
3.2.2 手动实现Momentum算法
# 初始化
def init_momentum(params):
v_w1, v_b1, v_w2, v_b2 = torch.zeros(params[0].shape), torch.zeros(params[1].shape),\
torch.zeros(params[2].shape), torch.zeros(params[3].shape)
return (v_w1, v_b1, v_w2, v_b2)
# 对每一个参数进行momentum法
def sgd_momentum(params,states,lr=0.01,momentum=0.5):
for p, v in zip(params,states):
with torch.no_grad():
v[:] = momentum * v - p.grad
p[:] += lr * v
p.grad.data.zero_()
model_32 = MyNet(dropout=0)
train_all_loss32,test_all_loss32,\
train_ACC32,test_ACC32 \
= train_and_test(model=model_32,epochs=20,init_states=init_momentum, optimizer=sgd_momentum)
dropout: 0
epoch: 1 | train loss:865.42947 | test loss:100.80932 | train acc: 0.46 | test acc: 0.63
epoch: 2 | train loss:482.56232 | test loss:70.22495 | train acc: 0.65 | test acc: 0.67
epoch: 4 | train loss:336.58501 | test loss:55.26826 | train acc: 0.74 | test acc: 0.75
epoch: 6 | train loss:287.67661 | test loss:48.56195 | train acc: 0.79 | test acc: 0.78
epoch: 8 | train loss:260.36843 | test loss:44.56490 | train acc: 0.81 | test acc: 0.80
epoch: 10 | train loss:243.72953 | test loss:42.35971 | train acc: 0.82 | test acc: 0.81
epoch: 12 | train loss:232.50333 | test loss:40.94901 | train acc: 0.83 | test acc: 0.82
epoch: 14 | train loss:224.56540 | test loss:39.67798 | train acc: 0.84 | test acc: 0.82
epoch: 16 | train loss:218.58376 | test loss:38.94638 | train acc: 0.84 | test acc: 0.83
epoch: 18 | train loss:213.26769 | test loss:38.23061 | train acc: 0.84 | test acc: 0.83
epoch: 20 | train loss:209.36230 | test loss:37.92049 | train acc: 0.85 | test acc: 0.83
手动实现dropout = 0, 20轮 总用时: 180.386
3.2.3 手动实现Adam算法
def init_adam_states(params):
v_w1, v_b1, v_w2, v_b2 = torch.zeros(params[0].shape), torch.zeros(params[1].shape),\
torch.zeros(params[2].shape), torch.zeros(params[3].shape)
s_w1, s_b1, s_w2, s_b2 = torch.zeros(params[0].shape), torch.zeros(params[1].shape),\
torch.zeros(params[2].shape), torch.zeros(params[3].shape)
return ((v_w1, s_w1), (v_b1, s_b1),(v_w2, s_w2), (v_b2, s_b2))
# 根据Adam算法思想手动实现Adam
Adam_t = 0.01
def Adam(params, states, lr=0.01, t=Adam_t):
global Adam_t
beta1, beta2, eps = 0.9, 0.999, 1e-6
for p, (v, s) in zip(params, states):
with torch.no_grad():
v[:] = beta1 * v + (1 - beta1) * p.grad
s[:] = beta2 * s + (1 - beta2) * (p.grad**2)
v_bias_corr = v / (1 - beta1 ** Adam_t)
s_bias_corr = s / (1 - beta2 ** Adam_t)
p.data -= lr * v_bias_corr / (torch.sqrt(s_bias_corr + eps))
p.grad.data.zero_()
Adam_t += 1
model_33 = MyNet(dropout=0)
train_all_loss33,test_all_loss33,\
train_ACC33,test_ACC33 \
= train_and_test(model=model_33,epochs=20,init_states=init_adam_states, optimizer=Adam)
dropout: 0
epoch: 1 | train loss:977.12287 | test loss:39.80734 | train acc: 0.69 | test acc: 0.81
epoch: 2 | train loss:218.54420 | test loss:36.52055 | train acc: 0.83 | test acc: 0.83
epoch: 4 | train loss:178.49854 | test loss:32.04532 | train acc: 0.86 | test acc: 0.86
epoch: 6 | train loss:158.68488 | test loss:32.94441 | train acc: 0.88 | test acc: 0.86
epoch: 8 | train loss:146.79713 | test loss:33.73590 | train acc: 0.89 | test acc: 0.86
epoch: 10 | train loss:137.06564 | test loss:32.62384 | train acc: 0.89 | test acc: 0.85
epoch: 12 | train loss:130.34835 | test loss:33.36391 | train acc: 0.90 | test acc: 0.86
epoch: 14 | train loss:122.98791 | test loss:30.13885 | train acc: 0.90 | test acc: 0.87
epoch: 16 | train loss:118.01618 | test loss:34.34515 | train acc: 0.91 | test acc: 0.85
epoch: 18 | train loss:111.67874 | test loss:33.48384 | train acc: 0.91 | test acc: 0.87
epoch: 20 | train loss:108.85642 | test loss:28.81685 | train acc: 0.91 | test acc: 0.88
手动实现dropout = 0, 20轮 总用时: 195.174
3.2.4 torch.nn实现RMSprop算法
# 使用torch 提供的 RMSprop
model_34 = MyNet_NN(dropout=0)
model_34 = model_34.to(device)
opti_RMSprop = torch.optim.RMSprop(model_34.parameters(), lr=0.01, alpha=0.9, eps=1e-6)
train_all_loss34,test_all_loss34,\
train_ACC34,test_ACC34 \
= train_and_test_NN(model=model_34,epochs=20,optimizer=opti_RMSprop)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:327.75258 | test loss:36.48523 | train acc:0.771633 test acc:0.82990:
epoch: 2 | train loss:207.45770 | test loss:38.46234 | train acc:0.839867 test acc:0.83590:
epoch: 4 | train loss:185.50436 | test loss:34.74823 | train acc:0.863683 test acc:0.85480:
epoch: 6 | train loss:175.43034 | test loss:39.56436 | train acc:0.872400 test acc:0.84330:
epoch: 8 | train loss:166.55864 | test loss:42.55430 | train acc:0.878000 test acc:0.84070:
epoch: 10 | train loss:162.49881 | test loss:40.32271 | train acc:0.883033 test acc:0.86420:
epoch: 12 | train loss:157.36479 | test loss:39.31301 | train acc:0.884267 test acc:0.86580:
epoch: 14 | train loss:155.47657 | test loss:49.91537 | train acc:0.888567 test acc:0.85810:
epoch: 16 | train loss:155.83041 | test loss:44.48253 | train acc:0.889767 test acc:0.86320:
epoch: 18 | train loss:150.08707 | test loss:42.73475 | train acc:0.892683 test acc:0.86040:
epoch: 20 | train loss:150.37581 | test loss:45.74147 | train acc:0.893817 test acc:0.86320:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 160.811s
3.2.5 torch.nn实现Momentum算法
# 使用torch 提供的 Momentum
model_35 = MyNet_NN(dropout=0)
model_35 = model_35.to(device)
opt_Momentum = torch.optim.SGD(model_35.parameters(),lr=0.01, momentum=0.5)
train_all_loss35,test_all_loss35,\
train_ACC35,test_ACC35 \
= train_and_test_NN(model=model_35,epochs=20,optimizer=opt_Momentum)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:527.70305 | test loss:59.81030 | train acc:0.660100 test acc:0.73150:
epoch: 2 | train loss:311.16962 | test loss:49.36548 | train acc:0.776650 test acc:0.78220:
epoch: 4 | train loss:246.42763 | test loss:42.30816 | train acc:0.822983 test acc:0.81500:
epoch: 6 | train loss:224.65415 | test loss:39.68113 | train acc:0.835917 test acc:0.82290:
epoch: 8 | train loss:213.19915 | test loss:37.97090 | train acc:0.844800 test acc:0.82850:
epoch: 10 | train loss:205.16319 | test loss:36.42515 | train acc:0.849933 test acc:0.83740:
epoch: 12 | train loss:198.74544 | test loss:35.57186 | train acc:0.854350 test acc:0.84030:
epoch: 14 | train loss:193.31012 | test loss:34.89748 | train acc:0.857350 test acc:0.84250:
epoch: 16 | train loss:188.62091 | test loss:34.22897 | train acc:0.861083 test acc:0.84590:
epoch: 18 | train loss:184.45801 | test loss:34.43188 | train acc:0.864250 test acc:0.84520:
epoch: 20 | train loss:180.47259 | test loss:33.40635 | train acc:0.866550 test acc:0.85010:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 158.962s
3.2.6torch.nn 实现Adam算法
# 使用torch 提供的 Adam
model_36 = MyNet_NN(dropout=0)
model_36 = model_36.to(device)
opt_Adam = torch.optim.Adam(model_36.parameters(), lr=0.01, betas=(0.9,0.999),eps=1e-6)
train_all_loss36,test_all_loss36,\
train_ACC36,test_ACC36 \
= train_and_test_NN(model=model_36,epochs=20,optimizer=opt_Adam)
MyNet_NN(
(input_layer): Flatten(start_dim=1, end_dim=-1)
(hidden_layer): Linear(in_features=784, out_features=256, bias=True)
(drop): Dropout(p=0, inplace=False)
(output_layer): Linear(in_features=256, out_features=10, bias=True)
(relu): ReLU()
)
epoch: 1 | train loss:239.72011 | test loss:40.29385 | train acc:0.817000 test acc:0.82140:
epoch: 2 | train loss:177.92484 | test loss:33.07817 | train acc:0.861700 test acc:0.85240:
epoch: 4 | train loss:160.04629 | test loss:32.41718 | train acc:0.875867 test acc:0.85010:
epoch: 6 | train loss:149.91095 | test loss:31.50968 | train acc:0.882550 test acc:0.85340:
epoch: 8 | train loss:142.18498 | test loss:29.33314 | train acc:0.887667 test acc:0.87310:
epoch: 10 | train loss:135.84223 | test loss:30.49203 | train acc:0.892883 test acc:0.86750:
epoch: 12 | train loss:134.24267 | test loss:30.44989 | train acc:0.894433 test acc:0.86640:
epoch: 14 | train loss:130.88283 | test loss:33.12540 | train acc:0.894767 test acc:0.86780:
epoch: 16 | train loss:128.21076 | test loss:33.35650 | train acc:0.897533 test acc:0.86220:
epoch: 18 | train loss:125.64576 | test loss:31.23838 | train acc:0.900550 test acc:0.87000:
epoch: 20 | train loss:123.62410 | test loss:31.14968 | train acc:0.902250 test acc:0.87080:
torch.nn实现前馈网络-多分类任务 20轮 总用时: 145.588s
手动实现的各种优化器的效果-以Loss值的变化显示
#完成loss的显示
drop_name_5= ['RMSprop','Momentum','Adam','手动实现不同的优化器-Loss变化']
drop_train_5 = [train_all_loss31,train_all_loss32,train_all_loss33]
drop_test_5= [test_all_loss31,test_all_loss32,test_all_loss33]
picture(drop_name_5, drop_train_5,drop_test_5)
torch.nn实现的各种优化器的效果-以Loss值的变化显示
#完成loss的显示
drop_name_6= ['RMSprop','Momentum','Adam','torch.nn实现不同的优化器-Loss变化']
drop_train_6 = [train_all_loss34,train_all_loss35,train_all_loss36]
drop_test_6= [test_all_loss34,test_all_loss35,test_all_loss36]
picture(drop_name_6, drop_train_6,drop_test_6)
上图为手动实现和torch.nn实现的不同的实验的损失值的变化，左边的为训练集上的结果，右边的为测试集合上的结果。 从图中可以看出，不同的优化器有着不同的特点，故损失函数的下降有所不同。
SGD： 它的思想是，将样本数据挨个送入网络，每次使用一个样本就更新一次参数，这样可以极快地收敛到最优值，但会产生较大的波动。还有一种是小批量梯度下降法，它的思想是，将数据拆分成一小批一小批的，分批送入神经网络，每送一批就更新一次网络参数。Momentum： 在更新网络参数时，如果前几次都是朝着一个方向更新，那么下一次就有很大的可能也是朝着那个方向更新，那么我们可以利用上一次的方向作为我这次更新的依据. 这种方法还可以从一定程度上避免网络陷入到局部极小值。RMSprop: 为了进一步优化损失函数在更新中存在摆动幅度过大的问题，并且进一步加快函数的收敛速度，RMSProp算法对权重W和偏置b的梯度使用了微分平方加权平均数。Adam: Adam算法可以看做是RMSProp算法与动量法的结合
四、在多分类任务实验上实现早停机制
4.1 任务内容
任务具体要求 选择上述实验中效果最好的组合，手动将训练数据划分为训练集和验证集，实现早停机制，并在测试集上进行测试。训练集：验证集=8：2，早停轮数为5.任务目的 学习早停机制任务算法或原理介绍
L
2
L_2
L2 原理 即当模型在训练集上的误差降低的时候，其在验证集上的误差表现不会变差。反之，当模型在训练集上表现很好，在验证集上表现很差的时候，我们认为模型出现了过拟合。当模型在验证集上的表现开始下降的时候，停止训练，这样就能避免继续训练导致过拟合的问题。 任务所用数据集 Fashion-MNIST数据集:
该数据集包含60,000个用于训练的图像样本和10,000个用于测试的图像样本。图像是固定大小(28x28像素)，其值为0到1。为每个图像都被平展并转换为784
4.2 任务思路及代码
构建数据集构建前馈神经网络，损失函数，优化函数进行反向传播，和梯度更新使用网络预测结果，得到损失值构建早停机制
按照要求构建数据集
import random
# 得到0-60000的下标
index = list(range(len(traindataset)))
# 利用shuffle随机打乱下标
random.shuffle(index)
# 按照 训练集和验证集 8：2 的比例分配各自下标
train_index, val_index = index[ : 48000], index[48000 : ]
# 由分配的下标得到对应的训练和验证及的数据以及他们对应的标签
train_dataset, train_labels = traindataset.data[train_index], traindataset.targets[train_index]
val_dataset, val_labels = traindataset.data[val_index], traindataset.targets[val_index]
print('训练集:', train_dataset.shape, train_labels.shape)
print('验证集:', val_dataset.shape,val_labels.shape)
# 构建相应的dataset以及dataloader
T_dataset = torch.utils.data.TensorDataset(train_dataset,train_labels)
V_dataset = torch.utils.data.TensorDataset(val_dataset,val_labels)
T_dataloader = torch.utils.data.DataLoader(dataset=T_dataset,batch_size=128,shuffle=True)
V_dataloader = torch.utils.data.DataLoader(dataset=V_dataset,batch_size=128,shuffle=True)
print('T_dataset',len(T_dataset),'T_dataloader batch_size: 128')
print('V_dataset',len(V_dataset),'V_dataloader batch_size: 128')
训练集: torch.Size([48000, 28, 28]) torch.Size([48000])
验证集: torch.Size([12000, 28, 28]) torch.Size([12000])
T_dataset 48000 T_dataloader batch_size: 128
V_dataset 12000 V_dataloader batch_size: 128
def train_and_test_4(model=model,epochs=30,lr=0.01,weight_decay=0.0):
print(model)
# 优化函数, 默认情况下weight_decay为0 通过更改weight_decay的值可以实现L2正则化。
optimizer = torch.optim.Adam(model.parameters(), lr=0.01, betas=(0.9,0.999),eps=1e-6)
criterion = CrossEntropyLoss() # 损失函数
train_all_loss = [] # 记录训练集上得loss变化
val_all_loss = [] # 记录测试集上的loss变化
train_ACC, val_ACC = [], []
begintime = time.time()
flag_stop = 0
for epoch in range(1000):
train_l, train_epoch_count, val_epoch_count = 0, 0, 0
for data, labels in traindataloader:
data, labels = data.to(torch.float32).to(device), labels.to(device)
pred = model(data)
train_each_loss = criterion(pred, labels.view(-1)) # 计算每次的损失值
optimizer.zero_grad() # 梯度清零
train_each_loss.backward() # 反向传播
optimizer.step() # 梯度更新
train_l += train_each_loss.item()
train_epoch_count += (pred.argmax(dim=1)==labels).sum()
train_ACC.append(train_epoch_count/len(traindataset))
train_all_loss.append(train_l) # 添加损失值到列表中
with torch.no_grad():
val_loss, val_epoch_count= 0, 0
for data, labels in testdataloader:
data, labels = data.to(torch.float32).to(device), labels.to(device)
pred = model(data)
val_each_loss = criterion(pred,labels)
val_loss += val_each_loss.item()
val_epoch_count += (pred.argmax(dim=1)==labels).sum()
val_all_loss.append(val_loss)
val_ACC.append(val_epoch_count / len(testdataset))
# 实现早停机制
# 若连续五次验证集的损失值连续增大，则停止运行，否则继续运行，
if epoch > 5 and val_all_loss[-1] > val_all_loss[-2]:
flag_stop += 1
if flag_stop == 5 or epoch > 35:
print('停止运行，防止过拟合')
break
else:
flag_stop = 0
if epoch == 0 or (epoch + 1) % 4 == 0:
print('epoch: %d | train loss:%.5f | val loss:%.5f | train acc:%5f val acc:%.5f:' % (epoch + 1, train_all_loss[-1], val_all_loss[-1],
train_ACC[-1],val_ACC[-1]))
endtime = time.time()
print("torch.nn实现前馈网络-多分类任务 %d轮 总用时: %.3fs" % (epochs, endtime - begintime))
# 返回训练集和测试集上的 损失值 与 准确率
return train_all_loss,val_all_loss,train_ACC,val_ACC
model_41 = MyNet_NN(dropout=0.5)
model_41 = model_41.to(device)
train_all_loss41,test_all_loss41,\
train_ACC41,test_ACC41 \
= train_and_test_4(model=model_41,epochs = 10000,lr=0.1)
4.3 结果分析
得到的loss曲线如下
#完成loss的显示
drop_name_6= ['','早停机制']
drop_train_6 = [train_all_loss41]
drop_test_6= [test_all_loss41]
picture(drop_name_6, drop_train_6,drop_test_6)
随着epoch的增加，如果在验证集上发现测试误差上升超过五轮，则停止训练
A1 实验心得
学会手动构建前馈神经网络和利用torch.nn构建前馈神经网络，并且在此之上实现dropout 添加惩罚权重，运用不同的优化函数，以及实现早停机制
实验中发现dropout的设置会有效防止模型的过拟合现象惩罚权重在一定程度上增大模型输出的loss，有防止过拟合的作用。不同的优化器有着不同的效果,在进行训练的时候可以选择不同的优化器作比较早停机制，随着epoch的增加，如果在验证集上发现测试误差上升，则停止训练；起着防止网络过拟合的作用
A2 参考文献
参考课程PPT
参考链接
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