论文的标题:《ArcFace: Additive Angular Margin Loss for Deep Face Recognition》 论文下载链接:https://arxiv.org/pdf/1801.07698v1.pdf
本篇文论提出了一种新的几何可解释性的损失函数:ArcFace。在L2正则化之后的weights和features基础之上,引入了
使得角度空间中类间的决策边界最大化,如下图所示:
上图是ArcFace的几何解释:(a)蓝色和绿色点代表了两个不同类别的向量特征,比如蓝色代表一些猫的图片向量特征,绿色代表一些狗的图片向量特征。ArcFace可以直接进一步增加两种类别间隔。(2)右边更加直观地解释了角度和角度间隔。ArcFace的角度间隔代表了(超)球面上不同种类样本的几何间隔。
(2)网络架构和设置:
(3)损失函数:
该部分我们主要解释下从Softmax到ArcFace演变历程
将
,Softmax公式中分子的部分可以表示为:
将
,那么我们有如下公式:
权重归一化之后,loss也就只跟特征向量和权重之间的角度有关了。在Sphereface论文中表明,权值归一化可以提高一点点效果。
在SphereFace中,角度乘以角度间隔m从而扩大m倍:
其中
由于cosine不是单调的,所以用了一个分段函数
给转成单调的,
其中:
引入
实际上相当于训练的时候加入了softmax帮助收敛,并且权重由动态超参数
控制:
特征和权重正则化消除了径向变化并且让每个特征都分布在超球面上,本文将特征超球面半径设为s=64,也就是将
缩放为s,sphereface的loss变为:
本文把m设为0.35. 与sphereface相比,cosine-face有三个好处:(1)没有超参数简单易实现,(2)清晰且不用softmax监督也能收敛,(3)性能明显提升
服从于:
import torch
import torch.nn.functional as F
from torch import nn, optim
from torch.utils.data import DataLoader
from torchvision import transforms as T, datasets
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import plotly.express as px
from tqdm.notebook import tqdm
from sklearn.metrics import accuracy_score
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
transform = T.Compose([
T.ToTensor(),
T.Normalize((0.5,), (0.5,))
])
trainset = datasets.MNIST('../input/mnist-dataset-pytorch', train = True, transform = transform)
testset = datasets.MNIST('../input/mnist-dataset-pytorch', train = False, transform = transform)
class ArcFace(nn.Module):
def __init__(self,in_features,out_features,margin = 0.7 ,scale = 64):
super().__init__()
self.in_features = in_features
self.out_features = out_features
self.scale = scale
self.margin = margin
self.weights = nn.Parameter(torch.FloatTensor(out_features,in_features))
nn.init.xavier_normal_(self.weights)
def forward(self,features,targets):
cos_theta = F.linear(features,F.normalize(self.weights),bias=None)
cos_theta = cos_theta.clip(-1+1e-7, 1-1e-7)
arc_cos = torch.acos(cos_theta)
M = F.one_hot(targets, num_classes = self.out_features) * self.margin
arc_cos = arc_cos + M
cos_theta_2 = torch.cos(arc_cos)
logits = cos_theta_2 * self.scale
return logits
class MNIST_Model(nn.Module):
def __init__(self):
super(MNIST_Model, self).__init__()
self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
self.conv2_drop = nn.Dropout2d()
self.fc1 = nn.Linear(320, 50)
self.fc2 = nn.Linear(50,3)
self.arc_face = ArcFace(in_features = 3, out_features = 10)
def forward(self,features,targets = None):
x = F.relu(F.max_pool2d(self.conv1(features), 2))
x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
_,c,h,w = x.shape
x = x.view(-1, c*h*w)
x = F.relu(self.fc1(x))
x = F.normalize(self.fc2(x))
if targets is not None:
logits = self.arc_face(x,targets)
return logits
return x
model = MNIST_Model()
model.to(device)
MNIST_Model(
(conv1): Conv2d(1, 10, kernel_size=(5, 5), stride=(1, 1))
(conv2): Conv2d(10, 20, kernel_size=(5, 5), stride=(1, 1))
(conv2_drop): Dropout2d(p=0.5, inplace=False)
(fc1): Linear(in_features=320, out_features=50, bias=True)
(fc2): Linear(in_features=50, out_features=3, bias=True)
(arc_face): ArcFace()
)
class TrainModel():
def __init__(self,criterion = None,optimizer = None,schedular = None,device = None):
self.criterion = criterion
self.optimizer = optimizer
self.schedular = schedular
self.device = device
def accuracy(self,logits,labels):
ps = torch.argmax(logits,dim = 1).detach().cpu().numpy()
acc = accuracy_score(ps,labels.detach().cpu().numpy())
return acc
def get_dataloader(self,trainset,validset):
trainloader = DataLoader(trainset,batch_size = 64, num_workers = 4, pin_memory = True)
validloader = DataLoader(validset,batch_size = 64, num_workers = 4, pin_memory = True)
return trainloader, validloader
def train_batch_loop(self,model,trainloader,i):
epoch_loss = 0.0
epoch_acc = 0.0
pbar_train = tqdm(trainloader, desc = "Epoch" + " [TRAIN] " + str(i+1))
for t,data in enumerate(pbar_train):
images,labels = data
images = images.to(device)
labels = labels.to(device)
logits = model(images,labels)
loss = self.criterion(logits,labels)
self.optimizer.zero_grad()
loss.backward()
self.optimizer.step()
epoch_loss += loss.item()
epoch_acc += self.accuracy(logits,labels)
pbar_train.set_postfix({'loss' : '%.6f' %float(epoch_loss/(t+1)), 'acc' : '%.6f' %float(epoch_acc/(t+1))})
return epoch_loss / len(trainloader), epoch_acc / len(trainloader)
def valid_batch_loop(self,model,validloader,i):
epoch_loss = 0.0
epoch_acc = 0.0
pbar_valid = tqdm(validloader, desc = "Epoch" + " [VALID] " + str(i+1))
for v,data in enumerate(pbar_valid):
images,labels = data
images = images.to(device)
labels = labels.to(device)
logits = model(images,labels)
loss = self.criterion(logits,labels)
epoch_loss += loss.item()
epoch_acc += self.accuracy(logits,labels)
pbar_valid.set_postfix({'loss' : '%.6f' %float(epoch_loss/(v+1)), 'acc' : '%.6f' %float(epoch_acc/(v+1))})
return epoch_loss / len(validloader), epoch_acc / len(validloader)
def run(self,model,trainset,validset,epochs):
trainloader,validloader = self.get_dataloader(trainset,validset)
for i in range(epochs):
model.train()
avg_train_loss, avg_train_acc = self.train_batch_loop(model,trainloader,i)
model.eval()
avg_valid_loss, avg_valid_acc = self.valid_batch_loop(model,validloader,i)
return model
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr = 0.0001)
model = TrainModel(criterion, optimizer, device).run(model, trainset, testset, 20)
emb = []
y = []
testloader = DataLoader(testset,batch_size = 64)
with torch.no_grad():
for images,labels in tqdm(testloader):
images = images.to(device)
embeddings = model(images)
emb += [embeddings.detach().cpu()]
y += [labels]
embs = torch.cat(emb).cpu().numpy()
y = torch.cat(y).cpu().numpy()
tsne_df = pd.DataFrame(
np.column_stack((embs, y)),
columns = ["x","y","z","targets"]
)
fig = px.scatter_3d(tsne_df, x='x', y='y', z='z',
color='targets')
fig.show()
https://www.kaggle.com/parthdhameliya77/simple-arcface-implementation-on-mnist-dataset