用于约束图像生成，作为loss。

可梯度优化

• pytorch structural similarity (SSIM) loss https://github.com/Po-Hsun-Su/pytorch-ssim
• https://github.com/harveyslash/Facial-Similarity-with-Siamese-Networks-in-Pytorch/blob/master/Siamese-networks-medium.ipynb

class ContrastiveLoss(torch.nn.Module):"""Contrastive loss function.Based on: http://yann.lecun.com/exdb/publis/pdf/hadsell-chopra-lecun-06.pdf"""def __init__(self, margin=2.0):super(ContrastiveLoss, self).__init__()self.margin = margindef forward(self, output1, output2, label):euclidean_distance = F.pairwise_distance(output1, output2, keepdim = True)loss_contrastive = torch.mean((1-label) * torch.pow(euclidean_distance, 2) +(label) * torch.pow(torch.clamp(self.margin - euclidean_distance, min=0.0), 2))return loss_contrastive

• 多个集合，参看写法 Multi-Similarity Loss for Deep Metric Learning (MS-Loss)
• 参考 https://blog.csdn.net/m0_46204224/article/details/117997854

@LOSS.register('ms_loss')
class MultiSimilarityLoss(nn.Module):def __init__(self, cfg):super(MultiSimilarityLoss, self).__init__()self.thresh = 0.5self.margin = 0.1self.scale_pos = cfg.LOSSES.MULTI_SIMILARITY_LOSS.SCALE_POSself.scale_neg = cfg.LOSSES.MULTI_SIMILARITY_LOSS.SCALE_NEGdef forward(self, feats, labels):assert feats.size(0) == labels.size(0), \f"feats.size(0): {feats.size(0)} is not equal to labels.size(0): {labels.size(0)}"batch_size = feats.size(0)sim_mat = torch.matmul(feats, torch.t(feats))epsilon = 1e-5loss = list()for i in range(batch_size):pos_pair_ = sim_mat[i][labels == labels[i]]pos_pair_ = pos_pair_[pos_pair_ < 1 - epsilon]neg_pair_ = sim_mat[i][labels != labels[i]]neg_pair = neg_pair_[neg_pair_ + self.margin > min(pos_pair_)]pos_pair = pos_pair_[pos_pair_ - self.margin < max(neg_pair_)]if len(neg_pair) < 1 or len(pos_pair) < 1:continue# weighting steppos_loss = 1.0 / self.scale_pos * torch.log(1 + torch.sum(torch.exp(-self.scale_pos * (pos_pair - self.thresh))))neg_loss = 1.0 / self.scale_neg * torch.log(1 + torch.sum(torch.exp(self.scale_neg * (neg_pair - self.thresh))))loss.append(pos_loss + neg_loss)if len(loss) == 0:return torch.zeros([], requires_grad=True)loss = sum(loss) / batch_sizereturn loss

• Recall@k Surrogate Loss with Large Batches and Similarity Mixup https://github.com/yash0307/RecallatK_surrogate

class RecallatK(torch.nn.Module):def __init__(self, anneal, batch_size, num_id, feat_dims, k_vals, k_temperatures, mixup):super(RecallatK, self).__init__()assert(batch_size%num_id==0)self.anneal = annealself.batch_size = batch_sizeself.num_id = num_idself.feat_dims = feat_dimsself.k_vals = [min(batch_size, k) for k in k_vals]self.k_temperatures = k_temperaturesself.mixup = mixupself.samples_per_class = int(batch_size/num_id)def forward(self, preds, q_id):batch_size = preds.shape[0]num_id = self.num_idanneal = self.annealfeat_dims = self.feat_dimsk_vals = self.k_valsk_temperatures = self.k_temperaturessamples_per_class = int(batch_size/num_id)norm_vals = torch.Tensor([min(k, (samples_per_class-1)) for k in k_vals]).cuda()group_num = int(q_id/samples_per_class)q_id_ = group_num*samples_per_classsim_all = (preds[q_id]*preds).sum(1)sim_all_g = sim_all.view(num_id, int(batch_size/num_id))sim_diff_all = sim_all.unsqueeze(-1) - sim_all_g[group_num, :].unsqueeze(0).repeat(batch_size,1)sim_sg = sigmoid(sim_diff_all, temp=anneal)for i in range(samples_per_class): sim_sg[group_num*samples_per_class+i,i] = 0.sim_all_rk = (1.0 + torch.sum(sim_sg, dim=0)).unsqueeze(dim=0)sim_all_rk[:, q_id%samples_per_class] = 0.sim_all_rk = sim_all_rk.unsqueeze(dim=-1).repeat(1,1,len(k_vals))k_vals = torch.Tensor(k_vals).cuda()k_vals = k_vals.unsqueeze(dim=0).unsqueeze(dim=0).repeat(1, samples_per_class, 1)sim_all_rk = k_vals - sim_all_rkfor given_k in range(0, len(self.k_vals)):sim_all_rk[:,:,given_k] = sigmoid(sim_all_rk[:,:,given_k], temp=float(k_temperatures[given_k]))sim_all_rk[:,q_id%samples_per_class,:] = 0.k_vals_loss = torch.Tensor(self.k_vals).cuda()k_vals_loss = k_vals_loss.unsqueeze(dim=0)recall = torch.sum(sim_all_rk, dim=1)recall = torch.minimum(recall, k_vals_loss)recall = torch.sum(recall, dim=0)recall = torch.div(recall, norm_vals)recall = torch.sum(recall)/len(self.k_vals)return (1.-recall)/batch_size

• Circle Loss https://github.com/TinyZeaMays/CircleLoss/blob/master/circle_loss.py

• Torch的官方 https://pytorch.org/docs/1.12/nn.functional.html#loss-functions

• KL散度

• Hard Triplet loss

from __future__ import absolute_import
import sysimport torch
from torch import nn
DEVICE = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")class TripletLoss(nn.Module):"""Triplet loss with hard positive/negative mining.Reference:Hermans et al. In Defense of the Triplet Loss for Person Re-Identification. arXiv:1703.07737.Code imported from https://github.com/Cysu/open-reid/blob/master/reid/loss/triplet.py.Args:margin (float): margin for triplet."""def __init__(self, margin=0.3):#三元组的阈值marginsuper(TripletLoss, self).__init__()self.margin = marginself.ranking_loss = nn.MarginRankingLoss(margin=margin)#三元组损失函数#ap an margin y:倍率   Relu(ap - anxy + margin)这个relu就起到和0比较的作用def forward(self, inputs, targets):"""Args:inputs: visualization_feature_map matrix with shape (batch_size, feat_dim)#32x2048targets: ground truth labels with shape (num_classes)#tensor([32])[1,1,1,1,2,3,2,,,,2]32个数，一个数代表ID的真实标签"""n = inputs.size(0)#取出输入的batch# Compute pairwise distance, replace by the official when merged#计算距离矩阵，其实就是计算两个2048维之间的距离平方(a-b)**2=a^2+b^2-2ab#[1,2,3]*[1,2,3]=[1,4,9].sum()=14  点乘dist = torch.pow(inputs, 2).sum(dim=1, keepdim=True).expand(n, n)dist = dist + dist.t()dist.addmm_(1, -2, inputs, inputs.t())#生成距离矩阵32x32，.t()表示转置dist = dist.clamp(min=1e-12).sqrt()  # for numerical stability#clamp(min=1e-12)加这个防止矩阵中有0，对梯度下降不好# For each anchor, find the hardest positive and negativemask = targets.expand(n, n).eq(targets.expand(n, n).t())#利用target标签的expand，并eq，获得mask的范围，由0，1组成，，红色1表示是同一个人，绿色0表示不是同一个人dist_ap, dist_an = [], []#用来存放ap，anfor i in range(n):#i表示行# dist[i][mask[i]],,i=0时，取mask的第一行，取距离矩阵的第一行，然后得到tensor([1.0000e-06, 1.0000e-06, 1.0000e-06, 1.0000e-06])dist_ap.append(dist[i][mask[i]].max().unsqueeze(0))#取某一行中，红色区域的最大值，mask前4个是1，与dist相乘dist_an.append(dist[i][mask[i] == 0].min().unsqueeze(0))#取某一行，绿色区域的最小值,加一个.unsqueeze(0)将其变成带有维度的tensordist_ap = torch.cat(dist_ap)dist_an = torch.cat(dist_an)# Compute ranking hinge lossy = torch.ones_like(dist_an)#y是个权重，长度像dist-anloss = self.ranking_loss(dist_an, dist_ap, y) #ID损失：交叉商输入的是32xf f.shape=分类数,然后loss用于计算损失#度量三元组：输入的是dist_an（从距离矩阵中，挑出一行（即一个ID）的最大距离），dist_ap#ranking_loss输入 an ap margin y:倍率  loss： Relu(ap - anxy + margin)这个relu就起到和0比较的作用# from IPython import embed# embed()return lossclass MultiSimilarityLoss(nn.Module):def __init__(self, margin=0.7):super(MultiSimilarityLoss, self).__init__()self.thresh = 0.5self.margin = marginself.scale_pos = 2.0self.scale_neg = 40.0def forward(self, feats, labels):assert feats.size(0) == labels.size(0), \f"feats.size(0): {feats.size(0)} is not equal to labels.size(0): {labels.size(0)}"batch_size = feats.size(0)feats = nn.functional.normalize(feats, p=2, dim=1)# Shape: batchsize * batch sizesim_mat = torch.matmul(feats, torch.t(feats))epsilon = 1e-5loss = list()mask = labels.expand(batch_size, batch_size).eq(labels.expand(batch_size, batch_size).t())for i in range(batch_size):pos_pair_ = sim_mat[i][mask[i]]pos_pair_ = pos_pair_[pos_pair_ < 1 - epsilon]neg_pair_ = sim_mat[i][mask[i] == 0]neg_pair = neg_pair_[neg_pair_ + self.margin > min(pos_pair_)]pos_pair = pos_pair_[pos_pair_ - self.margin < max(neg_pair_)]if len(neg_pair) < 1 or len(pos_pair) < 1:continue# weighting steppos_loss = 1.0 / self.scale_pos * torch.log(1 + torch.sum(torch.exp(-self.scale_pos * (pos_pair - self.thresh))))neg_loss = 1.0 / self.scale_neg * torch.log(1 + torch.sum(torch.exp(self.scale_neg * (neg_pair - self.thresh))))loss.append(pos_loss + neg_loss)# pos_loss =if len(loss) == 0:return torch.zeros([], requires_grad=True, device=feats.device)loss = sum(loss) / batch_sizereturn lossif __name__ == '__main__':#测试TripletLoss(nn.Module)use_gpu = Falsemodel = TripletLoss()features = torch.rand(32, 2048)label= torch.Tensor([1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5, 5, 5,  5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8,8]).long()loss = model(features, label)print(loss)

不可梯度优化