激活函数
1. sigmoid函数

缺陷:
- 梯度消失
- 偏执现象:输出均大于0,使得输出均值不是0
tanh函数

relu函数
优势:
- 计算简单
- 单边的输出特性和生物学意义上的神经元阈值机制相似
- 当x>0时,梯度不变,解决了sigmoid以及tanh常见的梯度消失问题
- 一般用于多层感知机以及卷积神经网络,在循环神经网络中并不常见
损失函数
回归问题
1.MSE 均方误差

2. RMSE 均方根误差

3. MAE 平均绝对误差

分类问题
- 交叉熵:表示不同分布之间的差异


线性层完成MNIST
import torch
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optim
# prepare dataset
'''
tranforms:变换数据形态
'''
batch_size = 64
transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,))]) # 归一化,均值和方差
train_dataset = datasets.MNIST(root='./data/mnist/', train=True, download=False, transform=transform)
train_loader = DataLoader(train_dataset, shuffle=True, batch_size=batch_size)
test_dataset = datasets.MNIST(root='./data/mnist/', train=False, download=False, transform=transform)
test_loader = DataLoader(test_dataset, shuffle=False, batch_size=batch_size)
# design model using class
class Net(torch.nn.Module):
def __init__(self):
super().__init__()
self.l1 = torch.nn.Linear(784, 512)
self.l2 = torch.nn.Linear(512, 256)
self.l3 = torch.nn.Linear(256, 128)
self.l4 = torch.nn.Linear(128, 64)
self.l5 = torch.nn.Linear(64, 10)
def forward(self, x):
x = x.view(-1, 784) # -1其实就是自动获取mini_batch
x = F.relu(self.l1(x))
x = F.relu(self.l2(x))
x = F.relu(self.l3(x))
x = F.relu(self.l4(x))
return self.l5(x) # 最后一层不做激活,不进行非线性变换
model = Net()
# construct loss and optimizer
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)
# training cycle forward, backward, update
def train(epoch):
running_loss = 0.0
for batch_idx, data in enumerate(train_loader):
# 获得一个批次的数据和标签
inputs, target = data
# 获得模型预测结果(64, 10)
outputs = model(inputs)
# 交叉熵代价函数outputs(64,10),target(64)
optimizer.zero_grad()
loss = criterion(outputs, target)
loss.backward()
optimizer.step()
running_loss += loss.item()
if batch_idx % 300 == 299:
print('[%d, %5d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
running_loss = 0.0
def test():
correct = 0
total = 0
with torch.no_grad():
for data in test_loader:
images, labels = data
outputs = model(images)
_, predicted = torch.max(outputs.data, dim=1) # dim = 1 列是第0个维度,行是第1个维度
total += labels.size(0)
correct += (predicted == labels).sum().item() # 张量之间的比较运算
print('accuracy on test set: %d %% ' % (100 * correct / total))
if __name__ == '__main__':
for epoch in range(10):
train(epoch)
test()
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