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来自于：Knowledge Distillation Tutorial
将大模型蒸馏为小模型，可以节省计算资源，加快推理过程，更高效的运行。

使用CIFAR-10数据集

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision.transforms as transforms
import torchvision.datasets as datasetsdevice = "cuda" #CPU也可
transforms_cifar = transforms.Compose([transforms.ToTensor(),transforms.Normalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225]),
])# Loading the CIFAR-10 dataset:
train_dataset = datasets.CIFAR10(root='./data', train=True, download=True, transform=transforms_cifar)
test_dataset = datasets.CIFAR10(root='./data', train=False, download=True, transform=transforms_cifar)
#Dataloaders
train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=128, shuffle=True, num_workers=2)
test_loader = torch.utils.data.DataLoader(test_dataset, batch_size=128, shuffle=False, num_workers=2)

定义模型

定义两个结构相似，只是在宽度和深度不同的模型。
教师模型DeepNN

# Deeper neural network class to be used as teacher:
class DeepNN(nn.Module):def __init__(self, num_classes=10):super(DeepNN, self).__init__()self.features = nn.Sequential(nn.Conv2d(3, 128, kernel_size=3, padding=1),nn.ReLU(),nn.Conv2d(128, 64, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),nn.Conv2d(64, 64, kernel_size=3, padding=1),nn.ReLU(),nn.Conv2d(64, 32, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),)self.classifier = nn.Sequential(nn.Linear(2048, 512),nn.ReLU(),nn.Dropout(0.1),nn.Linear(512, num_classes))def forward(self, x):x = self.features(x)x = torch.flatten(x, 1)x = self.classifier(x)return x

学生模型LightNN

# Lightweight neural network class to be used as student:
class LightNN(nn.Module):def __init__(self, num_classes=10):super(LightNN, self).__init__()self.features = nn.Sequential(nn.Conv2d(3, 16, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),nn.Conv2d(16, 16, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),)self.classifier = nn.Sequential(nn.Linear(1024, 256),nn.ReLU(),nn.Dropout(0.1),nn.Linear(256, num_classes))def forward(self, x):x = self.features(x)x = torch.flatten(x, 1)x = self.classifier(x)return x

训练并测试模型

def train(model, train_loader, epochs, learning_rate, device):criterion = nn.CrossEntropyLoss()optimizer = optim.Adam(model.parameters(), lr=learning_rate)model.train()for epoch in range(epochs):running_loss = 0.0for inputs, labels in train_loader:# inputs: A collection of batch_size images# labels: A vector of dimensionality batch_size with integers denoting class of each imageinputs, labels = inputs.to(device), labels.to(device)optimizer.zero_grad()outputs = model(inputs)# outputs: Output of the network for the collection of images. A tensor of dimensionality batch_size x num_classes# labels: The actual labels of the images. Vector of dimensionality batch_sizeloss = criterion(outputs, labels)loss.backward()optimizer.step()running_loss += loss.item()print(f"Epoch {epoch+1}/{epochs}, Loss: {running_loss / len(train_loader)}")def test(model, test_loader, device):model.to(device)model.eval()correct = 0total = 0with torch.no_grad():for inputs, labels in test_loader:inputs, labels = inputs.to(device), labels.to(device)outputs = model(inputs)_, predicted = torch.max(outputs.data, 1)total += labels.size(0)correct += (predicted == labels).sum().item()accuracy = 100 * correct / totalprint(f"Test Accuracy: {accuracy:.2f}%")return accuracy

torch.manual_seed(42)
nn_deep = DeepNN(num_classes=10).to(device)
train(nn_deep, train_loader, epochs=10, learning_rate=0.001, device=device)
test_accuracy_deep = test(nn_deep, test_loader, device)# Instantiate the lightweight network:
torch.manual_seed(42)
nn_light = LightNN(num_classes=10).to(device)
train(nn_light, train_loader, epochs=10, learning_rate=0.001, device=device)
test_accuracy_light_ce = test(nn_light, test_loader, device)

DeepNN的参数量为1,186,986，准确率为75.98%。
LightNN的参数量为267,738，准确率为70.65%。

total_params_deep = "{:,}".format(sum(p.numel() for p in nn_deep.parameters()))
print(f"DeepNN parameters: {total_params_deep}")
total_params_light = "{:,}".format(sum(p.numel() for p in nn_light.parameters()))
print(f"LightNN parameters: {total_params_light}")
print(f"Teacher accuracy: {test_accuracy_deep:.2f}%")
print(f"Student accuracy: {test_accuracy_light_ce:.2f}%")

知识蒸馏

教师模型和学生模型都输出了关于类别的概率分布，假设认为，经过训练的教师模型输出的softmax结果携带了更多的信息，有助于提高学生模型的准确率。例如，在默认情况下，汽车、火车、摩托车的对应的label为 [1,0,0]，经过训练的教师模型输出结果可能是 [0.6,0.2,0.2]，而对于汽车、狗、猫，教师模型输出的结果可能是[0.8,0.1,0.1]，汽车和火车、摩托车要比狗、猫更相似。让学生模型学习到教师模型的这部分知识，就称为知识蒸馏。

学生模型与真实值的损失使用交叉熵损失。
学生模型与教师模型的损失使用KL散度损失。

在蒸馏过程中，冻结教师模型，只训练学生模型。

增加参数：

• T：温度，温度控制着输出分布的平滑度。较大的 T 会导致更平滑的分布，因此较小的概率会得到更大的提升。
• soft_target_loss_weight：学生模型与教师模型的损失的权重。
• ce_loss_weight：学生模型与真实值的损失的权重。

def train_knowledge_distillation(teacher, student, train_loader, epochs, learning_rate, T, soft_target_loss_weight, ce_loss_weight, device):ce_loss = nn.CrossEntropyLoss()optimizer = optim.Adam(student.parameters(), lr=learning_rate)teacher.eval()  # Teacher set to evaluation modestudent.train() # Student to train modefor epoch in range(epochs):running_loss = 0.0for inputs, labels in train_loader:inputs, labels = inputs.to(device), labels.to(device)optimizer.zero_grad()# Forward pass with the teacher model - do not save gradients here as we do not change the teacher's weightswith torch.no_grad():teacher_logits = teacher(inputs)# Forward pass with the student modelstudent_logits = student(inputs)#Soften the student logits by applying softmax first and log() secondsoft_targets = nn.functional.softmax(teacher_logits / T, dim=-1)soft_prob = nn.functional.log_softmax(student_logits / T, dim=-1)# Calculate the soft targets loss. Scaled by T**2 as suggested by the authors of the paper "Distilling the knowledge in a neural network"soft_targets_loss = torch.sum(soft_targets * (soft_targets.log() - soft_prob)) / soft_prob.size()[0] * (T**2)# Calculate the true label losslabel_loss = ce_loss(student_logits, labels)# Weighted sum of the two lossesloss = soft_target_loss_weight * soft_targets_loss + ce_loss_weight * label_lossloss.backward()optimizer.step()running_loss += loss.item()print(f"Epoch {epoch+1}/{epochs}, Loss: {running_loss / len(train_loader)}")# Apply ``train_knowledge_distillation`` with a temperature of 2. Arbitrarily set the weights to 0.75 for CE and 0.25 for distillation loss.
train_knowledge_distillation(teacher=nn_deep, student=new_nn_light, train_loader=train_loader, epochs=10, learning_rate=0.001, T=2, soft_target_loss_weight=0.25, ce_loss_weight=0.75, device=device)
test_accuracy_light_ce_and_kd = test(new_nn_light, test_loader, device)# Compare the student test accuracy with and without the teacher, after distillation
print(f"Teacher accuracy: {test_accuracy_deep:.2f}%")
print(f"Student accuracy without teacher: {test_accuracy_light_ce:.2f}%")
print(f"Student accuracy with CE + KD: {test_accuracy_light_ce_and_kd:.2f}%")#Test Accuracy: 70.49%
#Teacher accuracy: 75.98%
#Student accuracy without teacher: 70.65%
#Student accuracy with CE + KD: 70.49%

CosineEmbeddingLoss

蒸馏的目标是让学生模型学习教师模型的知识，那么不只是学习最终的输出分布，也可以学习教师模型的内部表示hidden states。
可以比较两个模型的中间输出向量，使用CosineEmbeddingLoss。
在前面的模型中，教师模型flatten输出维度为2048，而学生模型为1024，因此在教师模型中加入额外池化层，让两个模型在同一个维度。

class ModifiedDeepNNCosine(nn.Module):def __init__(self, num_classes=10):super(ModifiedDeepNNCosine, self).__init__()self.features = nn.Sequential(nn.Conv2d(3, 128, kernel_size=3, padding=1),nn.ReLU(),nn.Conv2d(128, 64, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),nn.Conv2d(64, 64, kernel_size=3, padding=1),nn.ReLU(),nn.Conv2d(64, 32, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),)self.classifier = nn.Sequential(nn.Linear(2048, 512),nn.ReLU(),nn.Dropout(0.1),nn.Linear(512, num_classes))def forward(self, x):x = self.features(x)flattened_conv_output = torch.flatten(x, 1)x = self.classifier(flattened_conv_output)flattened_conv_output_after_pooling = torch.nn.functional.avg_pool1d(flattened_conv_output, 2)return x, flattened_conv_output_after_pooling# Create a similar student class where we return a tuple. We do not apply pooling after flattening.
class ModifiedLightNNCosine(nn.Module):def __init__(self, num_classes=10):super(ModifiedLightNNCosine, self).__init__()self.features = nn.Sequential(nn.Conv2d(3, 16, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),nn.Conv2d(16, 16, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),)self.classifier = nn.Sequential(nn.Linear(1024, 256),nn.ReLU(),nn.Dropout(0.1),nn.Linear(256, num_classes))def forward(self, x):x = self.features(x)flattened_conv_output = torch.flatten(x, 1)x = self.classifier(flattened_conv_output)return x, flattened_conv_output# We do not have to train the modified deep network from scratch of course, we just load its weights from the trained instance
modified_nn_deep = ModifiedDeepNNCosine(num_classes=10).to(device)
modified_nn_deep.load_state_dict(nn_deep.state_dict())# Once again ensure the norm of the first layer is the same for both networks
print("Norm of 1st layer for deep_nn:", torch.norm(nn_deep.features[0].weight).item())
print("Norm of 1st layer for modified_deep_nn:", torch.norm(modified_nn_deep.features[0].weight).item())# Initialize a modified lightweight network with the same seed as our other lightweight instances. This will be trained from scratch to examine the effectiveness of cosine loss minimization.
torch.manual_seed(42)
modified_nn_light = ModifiedLightNNCosine(num_classes=10).to(device)
print("Norm of 1st layer:", torch.norm(modified_nn_light.features[0].weight).item())

训练函数和测试函数也随之发生变化。

def train_cosine_loss(teacher, student, train_loader, epochs, learning_rate, hidden_rep_loss_weight, ce_loss_weight, device):ce_loss = nn.CrossEntropyLoss()cosine_loss = nn.CosineEmbeddingLoss()optimizer = optim.Adam(student.parameters(), lr=learning_rate)teacher.to(device)student.to(device)teacher.eval()  # Teacher set to evaluation modestudent.train() # Student to train modefor epoch in range(epochs):running_loss = 0.0for inputs, labels in train_loader:inputs, labels = inputs.to(device), labels.to(device)optimizer.zero_grad()# Forward pass with the teacher model and keep only the hidden representationwith torch.no_grad():_, teacher_hidden_representation = teacher(inputs)# Forward pass with the student modelstudent_logits, student_hidden_representation = student(inputs)# Calculate the cosine loss. Target is a vector of ones. From the loss formula above we can see that is the case where loss minimization leads to cosine similarity increase.hidden_rep_loss = cosine_loss(student_hidden_representation, teacher_hidden_representation, target=torch.ones(inputs.size(0)).to(device))# Calculate the true label losslabel_loss = ce_loss(student_logits, labels)# Weighted sum of the two lossesloss = hidden_rep_loss_weight * hidden_rep_loss + ce_loss_weight * label_lossloss.backward()optimizer.step()running_loss += loss.item()print(f"Epoch {epoch+1}/{epochs}, Loss: {running_loss / len(train_loader)}")
def test_multiple_outputs(model, test_loader, device):model.to(device)model.eval()correct = 0total = 0with torch.no_grad():for inputs, labels in test_loader:inputs, labels = inputs.to(device), labels.to(device)outputs, _ = model(inputs) # Disregard the second tensor of the tuple_, predicted = torch.max(outputs.data, 1)total += labels.size(0)correct += (predicted == labels).sum().item()accuracy = 100 * correct / totalprint(f"Test Accuracy: {accuracy:.2f}%")return accuracy# Train and test the lightweight network with cross entropy loss
train_cosine_loss(teacher=modified_nn_deep, student=modified_nn_light, train_loader=train_loader, epochs=10, learning_rate=0.001, hidden_rep_loss_weight=0.25, ce_loss_weight=0.75, device=device)
test_accuracy_light_ce_and_cosine_loss = test_multiple_outputs(modified_nn_light, test_loader, device)
#Test Accuracy: 70.12%

Intermediate regressor run

对于高维度向量，余弦相似度通常比欧几里得距离效果更好，但我们处理的是每个具有 1024 个分量的向量，因此更难提取有意义的相似性。此外，正如我们所提到的，从理论上讲，推动教师和学生的隐藏表示相匹配是不被支持的。我们没有充分的理由应该追求这些向量的 1:1 匹配。
作者认为前面的蒸馏，学生模型和教师模型学习的是向量，即学习的是torch.flatten(x, 1)，是一个向量，表达能力有限。因此选取 flatten 的前一层，学习卷积层的输出特征图。
教师模型的特征图shape为[128, 32, 8, 8]，学生模型的特征图为[128, 16, 8, 8]，需要添加一个卷积层，对齐维度。

在学生模型中加入了regressor层。

class ModifiedDeepNNRegressor(nn.Module):def __init__(self, num_classes=10):super(ModifiedDeepNNRegressor, self).__init__()self.features = nn.Sequential(nn.Conv2d(3, 128, kernel_size=3, padding=1),nn.ReLU(),nn.Conv2d(128, 64, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),nn.Conv2d(64, 64, kernel_size=3, padding=1),nn.ReLU(),nn.Conv2d(64, 32, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),)self.classifier = nn.Sequential(nn.Linear(2048, 512),nn.ReLU(),nn.Dropout(0.1),nn.Linear(512, num_classes))def forward(self, x):x = self.features(x)conv_feature_map = xx = torch.flatten(x, 1)x = self.classifier(x)return x, conv_feature_mapclass ModifiedLightNNRegressor(nn.Module):def __init__(self, num_classes=10):super(ModifiedLightNNRegressor, self).__init__()self.features = nn.Sequential(nn.Conv2d(3, 16, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),nn.Conv2d(16, 16, kernel_size=3, padding=1),nn.ReLU(),nn.MaxPool2d(kernel_size=2, stride=2),)# Include an extra regressor (in our case linear)self.regressor = nn.Sequential(nn.Conv2d(16, 32, kernel_size=3, padding=1))self.classifier = nn.Sequential(nn.Linear(1024, 256),nn.ReLU(),nn.Dropout(0.1),nn.Linear(256, num_classes))def forward(self, x):x = self.features(x)regressor_output = self.regressor(x)x = torch.flatten(x, 1)x = self.classifier(x)return x, regressor_output

def train_mse_loss(teacher, student, train_loader, epochs, learning_rate, feature_map_weight, ce_loss_weight, device):ce_loss = nn.CrossEntropyLoss()mse_loss = nn.MSELoss()optimizer = optim.Adam(student.parameters(), lr=learning_rate)teacher.to(device)student.to(device)teacher.eval()  # Teacher set to evaluation modestudent.train() # Student to train modefor epoch in range(epochs):running_loss = 0.0for inputs, labels in train_loader:inputs, labels = inputs.to(device), labels.to(device)optimizer.zero_grad()# Again ignore teacher logitswith torch.no_grad():_, teacher_feature_map = teacher(inputs)# Forward pass with the student modelstudent_logits, regressor_feature_map = student(inputs)# Calculate the losshidden_rep_loss = mse_loss(regressor_feature_map, teacher_feature_map)# Calculate the true label losslabel_loss = ce_loss(student_logits, labels)# Weighted sum of the two lossesloss = feature_map_weight * hidden_rep_loss + ce_loss_weight * label_lossloss.backward()optimizer.step()running_loss += loss.item()print(f"Epoch {epoch+1}/{epochs}, Loss: {running_loss / len(train_loader)}")# Notice how our test function remains the same here with the one we used in our previous case. We only care about the actual outputs because we measure accuracy.# Initialize a ModifiedLightNNRegressor
torch.manual_seed(42)
modified_nn_light_reg = ModifiedLightNNRegressor(num_classes=10).to(device)# We do not have to train the modified deep network from scratch of course, we just load its weights from the trained instance
modified_nn_deep_reg = ModifiedDeepNNRegressor(num_classes=10).to(device)
modified_nn_deep_reg.load_state_dict(nn_deep.state_dict())# Train and test once again
train_mse_loss(teacher=modified_nn_deep_reg, student=modified_nn_light_reg, train_loader=train_loader, epochs=10, learning_rate=0.001, feature_map_weight=0.25, ce_loss_weight=0.75, device=device)
test_accuracy_light_ce_and_mse_loss = test_multiple_outputs(modified_nn_light_reg, test_loader, device)

print(f"Teacher accuracy: {test_accuracy_deep:.2f}%")
print(f"Student accuracy without teacher: {test_accuracy_light_ce:.2f}%")
print(f"Student accuracy with CE + KD: {test_accuracy_light_ce_and_kd:.2f}%")
print(f"Student accuracy with CE + CosineLoss: {test_accuracy_light_ce_and_cosine_loss:.2f}%")
print(f"Student accuracy with CE + RegressorMSE: {test_accuracy_light_ce_and_mse_loss:.2f}%")#Teacher accuracy: 75.98%
#Student accuracy without teacher: 70.65%
#Student accuracy with CE + KD: 70.49%
#Student accuracy with CE + CosineLoss: 70.12%
#Student accuracy with CE + RegressorMSE: 70.61%

RegressorMSE的方法会比 CosineLoss 效果更好，因为在教师和学生之间允许了一个可训练的层，这在学习方面给了学生模型一些回旋的余地，而不是迫使学生模型复制教师模型的表示。包括额外网络是基于提示蒸馏背后的理念。（Including the extra network is the idea behind hint-based distillation.）