loss函数之MarginRankingLoss

作者：weixin_40725706 | 2024-03-29 09:32:19

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marginrankingloss

MarginRankingLoss

排序损失函数

对于包含 $N$ 个样本的batch数据 $D (x 1, x 2, y)$ , $x 1$ , $x 2$ 是给定的待排序的两个输入， $y$ 代表真实的标签，属于 ${1,-1\}$ 。当 $y = 1$ 是， $x 1$ 应该排在 $x 2$ 之前， $y = - 1$ 是， $x 1$ 应该排在 $x 2$ 之后。第 $n$ 个样本对应的 $l o s s$ 计算如下:

$l_{n}=\max (0,-y *(x 1-x 2)+\operatorname{margin})$

若 $x 1$ , $x 2$ 排序正确且 $2)>\operatorname{margin}$ , 则loss为0

class MarginRankingLoss(_Loss):
    __constants__ = ['margin', 'reduction']
    def __init__(self, margin=0., size_average=None, reduce=None, reduction='mean'):
        super(MarginRankingLoss, self).__init__(size_average, reduce, reduction)
        self.margin = margin
    def forward(self, input1, input2, target):
        return F.margin_ranking_loss(input1, input2, target, margin=self.margin, reduction=self.reduction)
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pytorch中通过torch.nn.MarginRankingLoss类实现，也可以直接调用F.margin_ranking_loss 函数，代码中的size_average与reduce已经弃用。reduction有三种取值mean, sum, none，对应不同的返回 $\ell(x, y)$ 。默认为mean，对应于上述 $l o s s$ 的计算

$L=\left\{l_{1}, \ldots, l_{N}\right\}$

$\ell(x, y)=\left\{$

\begin{array}{ll} L, & if reduction ='none' \\ \frac{1}{N} \sum_{i = 1}^{N} l_{i}, & if reduction ='mean' \\ \sum_{i = 1}^{N} l_{i} & if reduction ='sum' \end{array}

$\begin{array}{ll}\operatorname L, & \text { if reduction }=\text { 'none' } \\ \frac1{N}\sum_{i=1}^{N} l_{i}, & \text { if reduction }=\text { 'mean' } \\ \sum_{i=1}^{N} l_{i} & \text { if reduction }=\text { 'sum' }\end{array}$ \right.

ℓ (x, y) = ⎩ ⎨ ⎧ L, \frac{1}{N} \sum_{i = 1}^{N} l_{i}, \sum_{i = 1}^{N} l_{i} if reduction = ’none’ if reduction = ’mean’ if reduction = ’sum’

$m a r g i n$ 默认取值0

例子：

import torch
import torch.nn.functional as F
import torch.nn as nn
import math


def validate_MarginRankingLoss(input1, input2, target, margin):
    val = 0
    for x1, x2, y in zip(input1, input2, target):
        loss_val = max(0, -y * (x1 - x2) + margin)
        val += loss_val
    return val / input1.nelement()


torch.manual_seed(10)
margin = 0
loss = nn.MarginRankingLoss()
input1 = torch.randn([3], requires_grad=True)
input2 = torch.randn([3], requires_grad=True)
target = torch.tensor([1, -1, -1])
print(target)
output = loss(input1, input2, target)
print(output.item())

output = validate_MarginRankingLoss(input1, input2, target, margin)
print(output.item())

loss = nn.MarginRankingLoss(reduction="none")
output = loss(input1, input2, target)
print(output)
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输出：

tensor([ 1, -1, -1])
0.015400052070617676
0.015400052070617676
tensor([0.0000, 0.0000, 0.0462], grad_fn=<ClampMinBackward>)
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