1. nn.CrossEntropyLoss()
计算公式如下：
L o s s ( x , c l a s s ) = − l n ( e x c l a s s ∑ i e x i ) = − x c l a s s + l n ( ∑ i e x i ) Loss(x, class) = -ln(\frac{e^{xclass}}{\sum_{i}e^{xi}}) = -xclass + ln(\sum_{i}e^{xi}) Loss(x,class)=−ln(∑iexiexclass)=−xclass+ln(i∑exi)
代码实现如下：
python
import torch
import torch.nn as nn
import math
import numpy as np
def cross_entorpy(logits, labels):
loss = 0
batch = len(labels)
for b_idx in range(batch):
hou = 0
for j in logits[b_idx]: # 计算累加部分
hou += np.exp(j)
loss += -logits[b_idx][labels[b_idx]] + np.log(hou) # -logits[b_idx][labels[b_idx]]表示计算-x[class]
return np.around(loss / batch, 4) # 保留四位小数
if __name__ == "__main__":
entroy = nn.CrossEntropyLoss()
logits = torch.Tensor([[0.1234, 0.5555,0.3211], [0.1234, 0.5555,0.3211], [0.1234, 0.5555,0.3211]])
labels = torch.tensor([0, 1, 2])
loss1 = entroy(logits, labels) # 调用pytorch接口
print("loss1: ", loss1) # tensor(1.1142)
logits = np.array(logits)
labels = np.array(labels)
loss2 = cross_entorpy(logits, labels) # 调用自定义函数
print("loss2: ", loss2) # 1.1142
print("All Done!")2. nn.BCELoss()
计算公式如下：
L o s s ( x , y ) = − 1 n ∑ i n ( y i ∗ l n ( x i ) + ( 1 − y i ) ∗ l n ( 1 − x i ) ) Loss(x, y) = -\frac{1}{n}\sum_{i}^{n}(y_{i}*ln(x_{i}) + (1-y_{i})*ln(1 - x_{i})) Loss(x,y)=−n1i∑n(yi∗ln(xi)+(1−yi)∗ln(1−xi))
代码实现如下：
python
import torch
import torch.nn as nn
import math
import numpy as np
def BCE_loss(logits, labels):
func = nn.Sigmoid()
logits = func(logits)
batch = logits.shape[0]
Num_class = logits.shape[1]
total_loss = 0
for b_idx in range(batch):
single_sample_loss = 0
for j in range(Num_class):
single_sample_loss += labels[b_idx][j].item() * math.log(logits[b_idx][j].item()) + (1 - labels[b_idx][j].item()) * math.log(1 - logits[b_idx][j].item())
total_loss += single_sample_loss / Num_class
loss = -1 * (total_loss / batch)
return np.around(loss, 4)
if __name__ == "__main__":
BCEloss = nn.BCELoss()
func = nn.Sigmoid()
logits = torch.Tensor([[1.1234, 1.5555, 1.3211], [1.1234, 1.5555, 1.3211], [1.1234, 1.5555, 1.3211]])
labels = torch.Tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) # 转换成one-hot的形式
loss1 = BCEloss(func(logits), labels) # 调用nn.BCELoss()时，logits的数值必须在区间(0, 1)之间
print("loss1: ", loss1) # tensor(1.1254)
loss2 = BCE_loss(logits, labels)
print("loss2: ", loss2) # 1.1254
print("All Done!")3. nn.BCEWithLogitsLoss()
计算公式如下：
L o s s ( x , y ) = − 1 n ∑ i n ( y i ∗ l n ( x i ) + ( 1 − y i ) ∗ l n ( 1 − x i ) ) Loss(x, y) = -\frac{1}{n}\sum_{i}^{n}(y_{i}*ln(x_{i}) + (1-y_{i})*ln(1 - x_{i})) Loss(x,y)=−n1i∑n(yi∗ln(xi)+(1−yi)∗ln(1−xi))
nn.BCEWithLogitsLoss() 和 nn.BCELoss()的区别在于nn.BCEWithLogitsLoss()自带Sigmoid()函数来处理输入。
代码实现如下：
python
import torch
import torch.nn as nn
import math
import numpy as np
def BCE_loss(logits, labels):
func = nn.Sigmoid()
logits = func(logits)
batch = logits.shape[0]
Num_class = logits.shape[1]
total_loss = 0
for b_idx in range(batch):
single_sample_loss = 0
for j in range(Num_class):
single_sample_loss += labels[b_idx][j].item() * math.log(logits[b_idx][j].item()) + (1 - labels[b_idx][j].item()) * math.log(1 - logits[b_idx][j].item())
total_loss += single_sample_loss / Num_class
loss = -1 * (total_loss / batch)
return np.around(loss, 4)
if __name__ == "__main__":
BCEWithLogitsLoss = nn.BCEWithLogitsLoss() # 自带Sigmoid()函数
logits = torch.Tensor([[1.1234, 1.5555, 1.3211], [1.1234, 1.5555, 1.3211], [1.1234, 1.5555, 1.3211]])
labels = torch.Tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) # 转换成one-hot的形式
loss1 = BCEWithLogitsLoss(logits, labels) # 调用nn.BCELoss()时，logits的数值必须在区间(0, 1)之间
print("loss1: ", loss1) # tensor(1.1254)
loss2 = BCE_loss(logits, labels)
print("loss2: ", loss2) # 1.1254
print("All Done!")