学习笔记|Pytorch使用教程15(损失函数(二))

学习笔记|Pytorch使用教程15

本学习笔记主要摘自“深度之眼”，做一个总结，方便查阅。
使用Pytorch版本为1.2

• 其他的损失函数

一.其他的损失函数

1.nn.L1Loss
功能:计算inputs与target之差的绝对值
2.nn.MSELoss
功能:计 算inputs与target之差的平方

主要参数:

• reduction :计算模式，可为none/sum/mean
  none-逐个元素计算
  sum-所有元素求和，返回标量
  mean-加权平均，返回标量

测试L1Loss和MSELoss代码：

import torch
import torch.nn as nn
import torch.nn.functional as F
import matplotlib.pyplot as plt
import numpy as np
from tools.common_tools import set_seed

set_seed(1)  # 设置随机种子

# ------------------------------------------------- 5 L1 loss ----------------------------------------------
# flag = 0
flag = 1
if flag:

    inputs = torch.ones((2, 2))
    target = torch.ones((2, 2)) * 3

    loss_f = nn.L1Loss(reduction='none')
    loss = loss_f(inputs, target)

    print("input:{}\ntarget:{}\nL1 loss:{}".format(inputs, target, loss))

输出：

input:tensor([[1., 1.],
        [1., 1.]])
target:tensor([[3., 3.],
        [3., 3.]])
L1 loss:tensor([[2., 2.],
        [2., 2.]])
MSE loss:tensor([[4., 4.],
        [4., 4.]])

3.SmoothL1Loss
功能:平滑的L1Loss

主要参数:

• reduction :计算模式，可为none/sum/mean
  none-逐个元素计算
  sum-所有元素求和，返回标量
  mean-加权平均，返回标量

测试代码：

# ------------------------------------------------- 7 Smooth L1 loss ----------------------------------------------
# flag = 0
flag = 1
if flag:
    inputs = torch.linspace(-3, 3, steps=500)
    target = torch.zeros_like(inputs)

    loss_f = nn.SmoothL1Loss(reduction='none')

    loss_smooth = loss_f(inputs, target)

    loss_l1 = np.abs(inputs.numpy())

    plt.plot(inputs.numpy(), loss_smooth.numpy(), label='Smooth L1 Loss')
    plt.plot(inputs.numpy(), loss_l1, label='L1 loss')
    plt.xlabel('x_i - y_i')
    plt.ylabel('loss value')
    plt.legend()
    plt.grid()
    plt.show()

输出：

4.PoissonNLLLoss
功能:泊松分布的负对数似然损失函数

主要参数:

• log_input:输入是否为对数形式，决定计算公式
• full :计算所有loss,默认为False
• eps: 修正项，避免log (input) 为nan

测试代码：

# ------------------------------------------------- 8 Poisson NLL Loss ----------------------------------------------
# flag = 0
flag = 1
if flag:

    inputs = torch.randn((2, 2))
    target = torch.randn((2, 2))

    loss_f = nn.PoissonNLLLoss(log_input=True, full=False, reduction='none')
    loss = loss_f(inputs, target)
    print("input:{}\ntarget:{}\nPoisson NLL loss:{}".format(inputs, target, loss))

输出：

input:tensor([[0.6614, 0.2669],
        [0.0617, 0.6213]])
target:tensor([[-0.4519, -0.1661],
        [-1.5228,  0.3817]])
Poisson NLL loss:tensor([[2.2363, 1.3503],
        [1.1575, 1.6242]])

手动计算验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:

    idx = 0

    loss_1 = torch.exp(inputs[idx, idx]) - target[idx, idx]*inputs[idx, idx]

    print("第一个元素loss:", loss_1)

输出：第一个元素loss: tensor(2.2363)

5.nn.KLDivLoss
功能:计算KLD (divergence), KL散度，相对熵

注意事项:需提前将输入计算log-probabilities,如通过nn.logsoftmax()
主要参数:

• reduction : none/sum/mean/batchmean
  none-逐个元素计算
  sum-所有元素求和，返回标量
  mean-加权平均，返回标量
• batchmean: batchsize维度求平均值

测试代码：

# ------------------------------------------------- 9 KL Divergence Loss ----------------------------------------------
# flag = 0
flag = 1
if flag:

    inputs = torch.tensor([[0.5, 0.3, 0.2], [0.2, 0.3, 0.5]])
    inputs_log = torch.log(inputs)
    target = torch.tensor([[0.9, 0.05, 0.05], [0.1, 0.7, 0.2]], dtype=torch.float)

    loss_f_none = nn.KLDivLoss(reduction='none')
    loss_f_mean = nn.KLDivLoss(reduction='mean')
    loss_f_bs_mean = nn.KLDivLoss(reduction='batchmean')

    loss_none = loss_f_none(inputs, target)
    loss_mean = loss_f_mean(inputs, target)
    loss_bs_mean = loss_f_bs_mean(inputs, target)

    print("loss_none:\n{}\nloss_mean:\n{}\nloss_bs_mean:\n{}".format(loss_none, loss_mean, loss_bs_mean))

输出：

loss_none:
tensor([[-0.5448, -0.1648, -0.1598],
        [-0.2503, -0.4597, -0.4219]])
loss_mean:
-0.3335360288619995
loss_bs_mean:
-1.0006080865859985

mean是所有值之和除以个数(6)。
bs_mean是所有值之和除以批(2)。
手动验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:

    idx = 0

    loss_1 = target[idx, idx] * (torch.log(target[idx, idx]) - inputs[idx, idx])

    print("第一个元素loss:", loss_1)

输出：第一个元素loss: tensor(-0.5448)

6.nn. MarginRankingLoss
功能:计算两个向量之间的相似度，用于排序任务

• y= 1时，希望x1比x2大，当x1>x2时， 不产生loss
• y = -1时，希望x2比x1大，当x2>x1时，不产生loss

特别说明:该方法计算两组数据之间的差异，返回一个个n*n的loss矩阵
主要参数:

• margin :边界值，x1与x2之间的差异值
• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 10 Margin Ranking Loss --------------------------------------------
# flag = 0
flag = 1
if flag:

    x1 = torch.tensor([[1], [2], [3]], dtype=torch.float)
    x2 = torch.tensor([[2], [2], [2]], dtype=torch.float)

    target = torch.tensor([1, 1, -1], dtype=torch.float)

    loss_f_none = nn.MarginRankingLoss(margin=0, reduction='none')

    loss = loss_f_none(x1, x2, target)

    print(loss)

输出：

tensor([[1., 1., 0.],
        [0., 0., 0.],
        [0., 0., 1.]])

7.nn.MultiLabelMarginLoss
功能:多标签边界损失函数

举例:四分类任务，样本x属于0类和3类。
标签: [0, 3, -1,-1]， 不是[1, 0,0, 1]
主要参数:

• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 11 Multi Label Margin Loss -----------------------------------------
# flag = 0
flag = 1
if flag:

    x = torch.tensor([[0.1, 0.2, 0.4, 0.8]])
    y = torch.tensor([[0, 3, -1, -1]], dtype=torch.long)

    loss_f = nn.MultiLabelMarginLoss(reduction='none')

    loss = loss_f(x, y)

    print(loss)

输出：

tensor([0.8500])

手动验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:

    x = x[0]
    item_1 = (1-(x[0] - x[1])) + (1 - (x[0] - x[2]))    # [0]
    item_2 = (1-(x[3] - x[1])) + (1 - (x[3] - x[2]))    # [3]

    loss_h = (item_1 + item_2) / x.shape[0]

    print(loss_h)

输出：tensor(0.8500)

8.nn.SoftMarginLoss
功能:计算二分类的logistic损失

主要参数:

• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 12 SoftMargin Loss -----------------------------------------
# flag = 0
flag = 1
if flag:

    inputs = torch.tensor([[0.3, 0.7], [0.5, 0.5]])
    target = torch.tensor([[-1, 1], [1, -1]], dtype=torch.float)

    loss_f = nn.SoftMarginLoss(reduction='none')

    loss = loss_f(inputs, target)

    print("SoftMargin: ", loss)

输出：

SoftMargin:  tensor([[0.8544, 0.4032],
        [0.4741, 0.9741]])

手动计算验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:

    idx = 0

    inputs_i = inputs[idx, idx]
    target_i = target[idx, idx]

    loss_h = np.log(1 + np.exp(-target_i * inputs_i))

    print(loss_h)

输出：tensor(0.8544)

9.nn.MultiLabelSoftMarginLoss
功能: SoftMarginLoss多标签版本


主要参数:

• weight:各类别的loss设置权值
• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 13 MultiLabel SoftMargin Loss -----------------------------------------
# flag = 0
flag = 1
if flag:

    inputs = torch.tensor([[0.3, 0.7, 0.8]])
    target = torch.tensor([[0, 1, 1]], dtype=torch.float)

    loss_f = nn.MultiLabelSoftMarginLoss(reduction='none')

    loss = loss_f(inputs, target)

    print("MultiLabel SoftMargin: ", loss)

输出：MultiLabel SoftMargin: tensor([0.5429])
手动验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:

    i_0 = torch.log(torch.exp(-inputs[0, 0]) / (1 + torch.exp(-inputs[0, 0])))

    i_1 = torch.log(1 / (1 + torch.exp(-inputs[0, 1])))
    i_2 = torch.log(1 / (1 + torch.exp(-inputs[0, 2])))

    loss_h = (i_0 + i_1 + i_2) / -3

    print(loss_h)

输出：tensor(0.5429)

10.nn. MultiMarginLoss
功能:计算多分类的折页损失


主要参数:

• p:可选1或2
• weight:各类别的loss设置权值
• margin :边界值
• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 14 Multi Margin Loss -----------------------------------------
# flag = 0
flag = 1
if flag:

    x = torch.tensor([[0.1, 0.2, 0.7], [0.2, 0.5, 0.3]])
    y = torch.tensor([1, 2], dtype=torch.long)

    loss_f = nn.MultiMarginLoss(reduction='none')

    loss = loss_f(x, y)

    print("Multi Margin Loss: ", loss)

输出：Multi Margin Loss: tensor([0.8000, 0.7000])

手动验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:

    x = x[0]
    margin = 1

    i_0 = margin - (x[1] - x[0])
    # i_1 = margin - (x[1] - x[1])
    i_2 = margin - (x[1] - x[2])

    loss_h = (i_0 + i_2) / x.shape[0]

    print(loss_h)

输出：tensor(0.8000)

11.nn.TripletMarginLoss
功能:计算三元组损失，人脸验证中常用


主要参数:

• p:范数的阶，默认为2
• margin :边界值
• reduction :计算模式，可为none/sum/mean

测试代码:

# ---------------------------------------------- 15 Triplet Margin Loss -----------------------------------------
# flag = 0
flag = 1
if flag:

    anchor = torch.tensor([[1.]])
    pos = torch.tensor([[2.]])
    neg = torch.tensor([[0.5]])

    loss_f = nn.TripletMarginLoss(margin=1.0, p=1)

    loss = loss_f(anchor, pos, neg)

    print("Triplet Margin Loss", loss)

输出：Triplet Margin Loss tensor(1.5000)
手动验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:

    margin = 1
    a, p, n = anchor[0], pos[0], neg[0]

    d_ap = torch.abs(a-p)
    d_an = torch.abs(a-n)

    loss = d_ap - d_an + margin

    print(loss)

输出：tensor([1.5000])

12.nn.HingeEmbeddingLoss
功能:计算两个输入的相似性，常用于非线性embedding和半监督学习。

特别注意:输入x应为两个输入之差的绝对值
主要参数:

• margin :边界值
• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 16 Hinge Embedding Loss -----------------------------------------
# flag = 0
flag = 1
if flag:

    inputs = torch.tensor([[1., 0.8, 0.5]])
    target = torch.tensor([[1, 1, -1]])

    loss_f = nn.HingeEmbeddingLoss(margin=1, reduction='none')

    loss = loss_f(inputs, target)

    print("Hinge Embedding Loss", loss)

输出：Hinge Embedding Loss tensor([[1.0000, 0.8000, 0.5000]])
手动验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:
    margin = 1.
    loss = max(0, margin - inputs.numpy()[0, 2])

    print(loss)

输出：0.5

13.nn.CosineEmbeddingLoss
功能:采用余弦相似度计算两个输入的相似性

主要参数:

• margin:可取值[-1, 1]，推荐为[0, 0.5]
• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 17 Cosine Embedding Loss -----------------------------------------
# flag = 0
flag = 1
if flag:

    x1 = torch.tensor([[0.3, 0.5, 0.7], [0.3, 0.5, 0.7]])
    x2 = torch.tensor([[0.1, 0.3, 0.5], [0.1, 0.3, 0.5]])

    target = torch.tensor([[1, -1]], dtype=torch.float)

    loss_f = nn.CosineEmbeddingLoss(margin=0., reduction='none')

    loss = loss_f(x1, x2, target)

    print("Cosine Embedding Loss", loss)

输出：Cosine Embedding Loss tensor([[0.0167, 0.9833]])
手动验证：

# --------------------------------- compute by hand
# flag = 0
flag = 1
if flag:
    margin = 0.

    def cosine(a, b):
        numerator = torch.dot(a, b)
        denominator = torch.norm(a, 2) * torch.norm(b, 2)
        return float(numerator/denominator)

    l_1 = 1 - (cosine(x1[0], x2[0]))

    l_2 = max(0, cosine(x1[0], x2[0]))

    print(l_1, l_2)

输出：0.016662120819091797 0.9833378791809082
14.nn.CTCLoss
功能:计算CTC损失， 解决时序类数据的分类

主要参数:

• blank : blank label
• zero infinity :无穷大的值或梯度置0
• reduction :计算模式，可为none/sum/mean

测试代码：

# ---------------------------------------------- 18 CTC Loss -----------------------------------------
# flag = 0
flag = 1
if flag:
    T = 50      # Input sequence length
    C = 20      # Number of classes (including blank)
    N = 16      # Batch size
    S = 30      # Target sequence length of longest target in batch
    S_min = 10  # Minimum target length, for demonstration purposes

    # Initialize random batch of input vectors, for *size = (T,N,C)
    inputs = torch.randn(T, N, C).log_softmax(2).detach().requires_grad_()

    # Initialize random batch of targets (0 = blank, 1:C = classes)
    target = torch.randint(low=1, high=C, size=(N, S), dtype=torch.long)

    input_lengths = torch.full(size=(N,), fill_value=T, dtype=torch.long)
    target_lengths = torch.randint(low=S_min, high=S, size=(N,), dtype=torch.long)

    ctc_loss = nn.CTCLoss()
    loss = ctc_loss(inputs, target, input_lengths, target_lengths)

    print("CTC loss: ", loss)

输出：CTC loss: tensor(7.5385, grad_fn=<MeanBackward0>)