Torch and Numpy
变量 (Variable)
激励函数
关系拟合(回归)
区分类型 (分类)
快速搭建法
批训练
加速神经网络训练
Optimizer优化器
卷积神经网络 CNN
卷积神经网络(RNN、LSTM)
RNN 循环神经网络 (分类)
RNN 循环神经网络 (回归)
自编码 (Autoencoder)
DQN 强化学习
生成对抗网络 (GAN)
为什么 Torch 是动态的
GPU 加速运算
过拟合 (Overfitting)
批标准化 (Batch Normalization)
伪数据
为了对比各种优化器的效果, 我们需要有一些数据, 今天我们还是自己编一些伪数据, 这批数据是这样的:
import torch
import torch.utils.data as Data
import torch.nn.functional as F
import matplotlib.pyplot as plt
torch.manual_seed(1) # reproducible
LR = 0.01
BATCH_SIZE = 32
EPOCH = 12
# fake dataset
x = torch.unsqueeze(torch.linspace(-1, 1, 1000), dim=1)
y = x.pow(2) + 0.1*torch.normal(torch.zeros(*x.size()))
# plot dataset
plt.scatter(x.numpy(), y.numpy())
plt.show()
# 使用上节内容提到的 data loader
torch_dataset = Data.TensorDataset(x, y)
loader = Data.DataLoader(dataset=torch_dataset, batch_size=BATCH_SIZE, shuffle=True, num_workers=2,)
每个优化器优化一个神经网络
为了对比每一种优化器, 我们给他们各自创建一个神经网络, 但这个神经网络都来自同一个 Net
形式.
# 默认的 network 形式
class Net(torch.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hidden = torch.nn.Linear(1, 20) # hidden layer
self.predict = torch.nn.Linear(20, 1) # output layer
def forward(self, x):
x = F.relu(self.hidden(x)) # activation function for hidden layer
x = self.predict(x) # linear output
return x
# 为每个优化器创建一个 net
net_SGD = Net()
net_Momentum = Net()
net_RMSprop = Net()
net_Adam = Net()
nets = [net_SGD, net_Momentum, net_RMSprop, net_Adam]
优化器 Optimizer
接下来在创建不同的优化器, 用来训练不同的网络. 并创建一个 loss_func
用来计算误差. 我们用几种常见的优化器, SGD
, Momentum
, RMSprop
, Adam
.
# different optimizers
opt_SGD = torch.optim.SGD(net_SGD.parameters(), lr=LR)
opt_Momentum = torch.optim.SGD(net_Momentum.parameters(), lr=LR, momentum=0.8)
opt_RMSprop = torch.optim.RMSprop(net_RMSprop.parameters(), lr=LR, alpha=0.9)
opt_Adam = torch.optim.Adam(net_Adam.parameters(), lr=LR, betas=(0.9, 0.99))
optimizers = [opt_SGD, opt_Momentum, opt_RMSprop, opt_Adam]
loss_func = torch.nn.MSELoss()
losses_his = [[], [], [], []] # 记录 training 时不同神经网络的 loss
训练/出图
接下来训练和 loss 画图.
for epoch in range(EPOCH):
print('Epoch: ', epoch)
for step, (b_x, b_y) in enumerate(loader):
# 对每个优化器, 优化属于他的神经网络
for net, opt, l_his in zip(nets, optimizers, losses_his):
output = net(b_x) # get output for every net
loss = loss_func(output, b_y) # compute loss for every net
opt.zero_grad() # clear gradients for next train
loss.backward() # backpropagation, compute gradients
opt.step() # apply gradients
l_his.append(loss.data.numpy()) # loss recoder
SGD
是最普通的优化器, 也可以说没有加速效果, 而 Momentum
是 SGD
的改良版, 它加入了动量原则. 后面的 RMSprop
又是 Momentum
的升级版. 而 Adam
又是 RMSprop
的升级版. 不过从这个结果中我们看到, Adam
的效果似乎比 RMSprop
要差一点. 所以说并不是越先进的优化器, 结果越佳. 我们在自己的试验中可以尝试不同的优化器, 找到那个最适合你数据/网络的优化器.
import torch
import torch.utils.data as Data
import torch.nn.functional as F
import matplotlib.pyplot as plt
# torch.manual_seed(1) # reproducible
LR = 0.01
BATCH_SIZE = 32
EPOCH = 12
# fake dataset
x = torch.unsqueeze(torch.linspace(-1, 1, 1000), dim=1)
y = x.pow(2) + 0.1*torch.normal(torch.zeros(*x.size()))
# plot dataset
plt.scatter(x.numpy(), y.numpy())
plt.show()
# put dateset into torch dataset
torch_dataset = Data.TensorDataset(x, y)
loader = Data.DataLoader(dataset=torch_dataset, batch_size=BATCH_SIZE, shuffle=True, num_workers=2,)
# default network
class Net(torch.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hidden = torch.nn.Linear(1, 20) # hidden layer
self.predict = torch.nn.Linear(20, 1) # output layer
def forward(self, x):
x = F.relu(self.hidden(x)) # activation function for hidden layer
x = self.predict(x) # linear output
return x
if __name__ == '__main__':
# different nets
net_SGD = Net()
net_Momentum = Net()
net_RMSprop = Net()
net_Adam = Net()
nets = [net_SGD, net_Momentum, net_RMSprop, net_Adam]
# different optimizers
opt_SGD = torch.optim.SGD(net_SGD.parameters(), lr=LR)
opt_Momentum = torch.optim.SGD(net_Momentum.parameters(), lr=LR, momentum=0.8)
opt_RMSprop = torch.optim.RMSprop(net_RMSprop.parameters(), lr=LR, alpha=0.9)
opt_Adam = torch.optim.Adam(net_Adam.parameters(), lr=LR, betas=(0.9, 0.99))
optimizers = [opt_SGD, opt_Momentum, opt_RMSprop, opt_Adam]
loss_func = torch.nn.MSELoss()
losses_his = [[], [], [], []] # record loss
# training
for epoch in range(EPOCH):
print('Epoch: ', epoch)
for step, (b_x, b_y) in enumerate(loader): # for each training step
for net, opt, l_his in zip(nets, optimizers, losses_his):
output = net(b_x) # get output for every net
loss = loss_func(output, b_y) # compute loss for every net
opt.zero_grad() # clear gradients for next train
loss.backward() # backpropagation, compute gradients
opt.step() # apply gradients
l_his.append(loss.data.numpy()) # loss recoder
labels = ['SGD', 'Momentum', 'RMSprop', 'Adam']
for i, l_his in enumerate(losses_his):
plt.plot(l_his, label=labels[i]) #len(l_his)=32*12=384
plt.legend(loc='best')
plt.xlabel('Steps')
plt.ylabel('Loss')
plt.ylim((0, 0.2))
plt.show()