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beginner/knowledge_distillation_tutorial

在 Google Colab 中运行

注意

转到页面底部下载完整示例代码。

知识蒸馏教程#

创建日期：2023年8月22日 | 最后更新：2025年1月24日 | 最后验证：2024年11月5日

作者: Alexandros Chariton

知识蒸馏是一种能够在不损失有效性的前提下，将知识从大型、计算昂贵的模型迁移到小型模型的技术。这使得模型能够在性能较弱的硬件上部署，从而实现更快、更高效的推理。

在本教程中，我们将进行一系列实验，旨在通过使用功能更强大的网络作为“教师”，来提高轻量级神经网络的准确性。轻量级网络的计算成本和速度将不受影响，我们的干预仅集中在其权重上，而不影响其前向传播。这项技术的应用场景包括无人机或手机等设备。在本教程中，我们不使用任何外部包，因为我们所需的一切在 torch 和 torchvision 中均已提供。

在本教程中，你将学习

如何修改模型类以提取隐藏层表征，并将其用于后续计算
如何在 PyTorch 中修改常规训练循环，以在交叉熵等分类损失之外加入额外的损失函数
如何利用更复杂的模型作为教师来提升轻量级模型的性能

先决条件#

1 个 GPU，4GB 显存
PyTorch v2.0 或更高版本
CIFAR-10 数据集（由脚本下载并保存到名为 /data 的目录中）

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision.transforms as transforms
import torchvision.datasets as datasets

# Check if the current `accelerator <https://pytorch.ac.cn/docs/stable/torch.html#accelerators>`__
# is available, and if not, use the CPU
device = torch.accelerator.current_accelerator().type if torch.accelerator.is_available() else "cpu"
print(f"Using {device} device")

Using cuda device

加载 CIFAR-10#

CIFAR-10 是一个包含十个类别的流行图像数据集。我们的目标是为每张输入图像预测以下类别之一。

../_static/img/cifar10.png — CIFAR-10 图像示例#

输入图像为 RGB 格式，因此具有 3 个通道，尺寸为 32x32 像素。基本上，每张图像由 3 x 32 x 32 = 3072 个 0 到 255 之间的数字描述。神经网络中的常见做法是对输入进行归一化，这样做的原因有很多，包括避免常用激活函数的饱和以及增加数值稳定性。我们的归一化过程包括沿每个通道减去均值并除以标准差。张量“mean=[0.485, 0.456, 0.406]”和“std=[0.229, 0.224, 0.225]”是预先计算好的，它们代表了 CIFAR-10 训练集预定义子集中每个通道的均值和标准差。请注意，我们对测试集也使用了这些值，而不是重新计算均值和标准差。这是因为网络是在通过减去和除以上述数值所产生的特征上进行训练的，我们需要保持一致性。此外，在现实生活中，由于我们的假设，在测试阶段无法获取该数据，因此我们无法计算测试集的均值和标准差。

最后，我们通常将该留出集称为验证集，并在优化模型在验证集上的性能后，使用一个单独的集合（称为测试集）。这样做是为了避免基于单一指标的贪婪和有偏见的优化来选择模型。

# Below we are preprocessing data for CIFAR-10. We use an arbitrary batch size of 128.
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)

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注意

本节仅适用于对快速结果感兴趣的 CPU 用户。仅在进行小规模实验时使用此选项。请记住，使用任何 GPU，代码运行速度应该都相当快。仅保留训练/测试数据集中的前 num_images_to_keep 张图像

#from torch.utils.data import Subset
#num_images_to_keep = 2000
#train_dataset = Subset(train_dataset, range(min(num_images_to_keep, 50_000)))
#test_dataset = Subset(test_dataset, range(min(num_images_to_keep, 10_000)))

#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)

定义模型类和工具函数#

接下来，我们需要定义模型类。这里需要设置几个用户定义的参数。我们使用两种不同的架构，并在实验中保持卷积核数量固定，以确保公平比较。两种架构都是卷积神经网络 (CNN)，但具有不同数量的卷积层作为特征提取器，随后是一个 10 分类的分类器。学生的卷积核和神经元数量较少。

# 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

# 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

我们采用 2 个函数来帮助我们在原始分类任务上生成并评估结果。一个函数名为 train，它接受以下参数

model: 通过此函数进行训练（更新权重）的模型实例。
train_loader: 我们在上面定义了 train_loader，其作用是将数据馈送到模型中。
epochs: 我们在数据集上循环的次数。
learning_rate: 学习率决定了我们向收敛迈进的步长。步长过大或过小都可能产生不利影响。
device: 决定在何种设备上运行工作负载。可以是 CPU 或 GPU，具体取决于可用性。

我们的测试函数类似，但它将使用 test_loader 来加载测试集中的图像。

../_static/img/knowledge_distillation/ce_only.png — 使用交叉熵训练两个网络。学生网络将作为基准：#

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 = 0.0
        for 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 image
            inputs, 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_size
            loss = 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 = 0
    total = 0

    with 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 / total
    print(f"Test Accuracy: {accuracy:.2f}%")
    return accuracy

交叉熵运行#

为了可重复性，我们需要设置 torch 手动种子。我们使用不同的方法训练网络，因此为了公平比较，让网络使用相同的权重进行初始化是有意义的。首先使用交叉熵训练教师网络

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)

Epoch 1/10, Loss: 1.3310377070361086
Epoch 2/10, Loss: 0.8632269683091537
Epoch 3/10, Loss: 0.6758259801608523
Epoch 4/10, Loss: 0.5363973272426049
Epoch 5/10, Loss: 0.4174100675851183
Epoch 6/10, Loss: 0.3153729905633975
Epoch 7/10, Loss: 0.23504667761533157
Epoch 8/10, Loss: 0.17814523168384572
Epoch 9/10, Loss: 0.14531727511521494
Epoch 10/10, Loss: 0.11876600291437048
Test Accuracy: 74.93%

我们实例化另一个轻量级网络模型来比较它们的性能。反向传播对权重初始化非常敏感，因此我们需要确保这两个网络具有完全相同的初始化。

torch.manual_seed(42)
new_nn_light = LightNN(num_classes=10).to(device)

为了确保我们创建了第一个网络的副本，我们检查其第一层的范数。如果匹配，那么我们可以安全地得出结论，这两个网络确实是相同的。

# Print the norm of the first layer of the initial lightweight model
print("Norm of 1st layer of nn_light:", torch.norm(nn_light.features[0].weight).item())
# Print the norm of the first layer of the new lightweight model
print("Norm of 1st layer of new_nn_light:", torch.norm(new_nn_light.features[0].weight).item())

Norm of 1st layer of nn_light: 2.327361822128296
Norm of 1st layer of new_nn_light: 2.327361822128296

打印每个模型中参数的总数

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}")

DeepNN parameters: 1,186,986
LightNN parameters: 267,738

使用交叉熵损失训练并测试轻量级网络

train(nn_light, train_loader, epochs=10, learning_rate=0.001, device=device)
test_accuracy_light_ce = test(nn_light, test_loader, device)

Epoch 1/10, Loss: 1.4677157115448467
Epoch 2/10, Loss: 1.1535490597300517
Epoch 3/10, Loss: 1.0227490462305602
Epoch 4/10, Loss: 0.9213633671441042
Epoch 5/10, Loss: 0.8465468417043271
Epoch 6/10, Loss: 0.7804479326128655
Epoch 7/10, Loss: 0.7138122039682725
Epoch 8/10, Loss: 0.6579287147430508
Epoch 9/10, Loss: 0.6035494638983246
Epoch 10/10, Loss: 0.5544769009360877
Test Accuracy: 70.48%

正如我们所见，根据测试准确率，我们现在可以将用作教师的更深层网络与作为学生的轻量级网络进行比较。到目前为止，学生网络尚未与教师网络进行任何交互，因此该性能是由学生网络独立实现的。目前的指标可以通过以下行查看

print(f"Teacher accuracy: {test_accuracy_deep:.2f}%")
print(f"Student accuracy: {test_accuracy_light_ce:.2f}%")

Teacher accuracy: 74.93%
Student accuracy: 70.48%

知识蒸馏运行#

现在，让我们尝试通过引入教师网络来提高学生网络的测试准确率。知识蒸馏是实现这一目标的一种直接技术，其基础是两个网络都输出关于类别的概率分布。因此，两个网络共享相同数量的输出神经元。该方法的工作原理是在传统的交叉熵损失中加入额外的损失，该损失基于教师网络的 softmax 输出。其假设是，训练良好的教师网络的输出激活携带了额外信息，学生网络可以在训练期间利用这些信息。原始论文建议，利用软目标中较小概率的比率有助于实现深度神经网络的潜在目标，即在数据上创建一种相似性结构，使相似的对象在映射中靠得更近。例如，在 CIFAR-10 中，如果卡车有轮子，它可能会被误认为是汽车或飞机，但不太可能被误认为是狗。因此，假设有价值的信息不仅存在于训练良好的模型的最高预测中，而且存在于整个输出分布中，这是有道理的。然而，仅靠交叉熵不足以充分利用这些信息，因为非预测类别的激活往往非常小，导致反向传播的梯度无法显著改变权重来构建这种理想的向量空间。

在我们继续定义引入师生动态的第一个辅助函数时，我们需要包含一些额外的参数

T: 温度（Temperature）控制输出分布的平滑度。较大的 T 会导致更平滑的分布，从而使较小的概率获得更大的提升。
soft_target_loss_weight: 分配给我们即将加入的额外目标的权重。
ce_loss_weight: 分配给交叉熵的权重。调整这些权重会促使网络优化其中某一个目标。

../_static/img/knowledge_distillation/distillation_output_loss.png — 蒸馏损失是从网络的 logits 计算得出的。它仅将梯度返回给学生：#

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 mode
    student.train() # Student to train mode

    for epoch in range(epochs):
        running_loss = 0.0
        for 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 weights
            with torch.no_grad():
                teacher_logits = teacher(inputs)

            # Forward pass with the student model
            student_logits = student(inputs)

            #Soften the student logits by applying softmax first and log() second
            soft_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 loss
            label_loss = ce_loss(student_logits, labels)

            # Weighted sum of the two losses
            loss = soft_target_loss_weight * soft_targets_loss + ce_loss_weight * label_loss

            loss.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}%")

Epoch 1/10, Loss: 2.4043647569158804
Epoch 2/10, Loss: 1.8842278694557717
Epoch 3/10, Loss: 1.6626370721460912
Epoch 4/10, Loss: 1.5040314664011416
Epoch 5/10, Loss: 1.3779708583031773
Epoch 6/10, Loss: 1.2635214232727694
Epoch 7/10, Loss: 1.1710618411183662
Epoch 8/10, Loss: 1.0871370439334294
Epoch 9/10, Loss: 1.0129010977647495
Epoch 10/10, Loss: 0.9450075749850944
Test Accuracy: 70.56%
Teacher accuracy: 74.93%
Student accuracy without teacher: 70.48%
Student accuracy with CE + KD: 70.56%

余弦损失最小化运行#

请随意尝试控制 softmax 函数平滑度的温度参数以及损失系数。在神经网络中，很容易在主要目标中加入额外的损失函数以实现更好的泛化等目标。让我们尝试为学生加入一个目标，但这次我们关注它们的隐藏状态而不是输出层。我们的目标是通过包含一个朴素的损失函数，将信息从教师的表征传递给学生。最小化该函数意味着，随着损失的减小，随后传递给分类器的展平向量变得更加相似。当然，教师不会更新其权重，因此最小化仅取决于学生的权重。该方法背后的基本原理是，我们假设教师模型具有更好的内部表征，学生在没有外部干预的情况下很难实现这一目标，因此我们人为地推动学生模仿教师的内部表征。但这是否最终能帮助到学生并不简单，因为推动轻量级网络达到这一点可能是一件好事（假设我们找到了能带来更好测试准确率的内部表征），但也可能是有害的，因为网络具有不同的架构，且学生没有与教师相同的学习能力。换句话说，这两个向量（学生和教师的）没有理由按分量匹配。学生可以达到一种与教师的表征仅仅是置换后的内部表征，而其效率是相同的。尽管如此，我们仍然可以快速运行一个实验来找出这种方法的影响。我们将使用由以下公式给出的 CosineEmbeddingLoss

../_static/img/knowledge_distillation/cosine_embedding_loss.png — CosineEmbeddingLoss 公式#

显然，有一件事我们需要先解决。当我们对输出层应用蒸馏时，我们提到两个网络具有相同数量的神经元，等于类别的数量。然而，在卷积层之后的层并非如此。在这里，教师在展平最终卷积层后拥有的神经元比学生多。我们的损失函数接受两个维度相同的向量作为输入，因此我们需要以某种方式匹配它们。我们将通过在教师的卷积层之后加入一个平均池化层来减少其维度，以匹配学生。

为了继续，我们将修改我们的模型类，或创建新的类。现在，前向函数不仅返回网络的 logits，还返回卷积层之后的展平隐藏表征。我们在修改后的教师模型中包含了上述池化层。

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())

Norm of 1st layer for deep_nn: 7.480082988739014
Norm of 1st layer for modified_deep_nn: 7.480082988739014
Norm of 1st layer: 2.327361822128296

自然，我们需要更改训练循环，因为现在模型返回一个元组 (logits, hidden_representation)。使用一个示例输入张量，我们可以打印它们的形状。

# Create a sample input tensor
sample_input = torch.randn(128, 3, 32, 32).to(device) # Batch size: 128, Filters: 3, Image size: 32x32

# Pass the input through the student
logits, hidden_representation = modified_nn_light(sample_input)

# Print the shapes of the tensors
print("Student logits shape:", logits.shape) # batch_size x total_classes
print("Student hidden representation shape:", hidden_representation.shape) # batch_size x hidden_representation_size

# Pass the input through the teacher
logits, hidden_representation = modified_nn_deep(sample_input)

# Print the shapes of the tensors
print("Teacher logits shape:", logits.shape) # batch_size x total_classes
print("Teacher hidden representation shape:", hidden_representation.shape) # batch_size x hidden_representation_size

Student logits shape: torch.Size([128, 10])
Student hidden representation shape: torch.Size([128, 1024])
Teacher logits shape: torch.Size([128, 10])
Teacher hidden representation shape: torch.Size([128, 1024])

在我们的例子中，hidden_representation_size 是 1024。这是学生模型最终卷积层的展平特征图，如你所见，它是其分类器的输入。对于教师模型，这也是 1024，因为我们通过 avg_pool1d 将其从 2048 调整到了该数值。这里应用的损失仅在损失计算前影响学生的权重。换句话说，它不影响学生的分类器。修改后的训练循环如下

../_static/img/knowledge_distillation/cosine_loss_distillation.png — 在余弦损失最小化中，我们希望通过将梯度返回给学生来最大化两个表征的余弦相似度：#

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 mode
    student.train() # Student to train mode

    for epoch in range(epochs):
        running_loss = 0.0
        for 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 representation
            with torch.no_grad():
                _, teacher_hidden_representation = teacher(inputs)

            # Forward pass with the student model
            student_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 loss
            label_loss = ce_loss(student_logits, labels)

            # Weighted sum of the two losses
            loss = hidden_rep_loss_weight * hidden_rep_loss + ce_loss_weight * label_loss

            loss.backward()
            optimizer.step()

            running_loss += loss.item()

        print(f"Epoch {epoch+1}/{epochs}, Loss: {running_loss / len(train_loader)}")

由于同样的原因，我们需要修改测试函数。在这里，我们忽略模型返回的隐藏表征。

def test_multiple_outputs(model, test_loader, device):
    model.to(device)
    model.eval()

    correct = 0
    total = 0

    with 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 / total
    print(f"Test Accuracy: {accuracy:.2f}%")
    return accuracy

在这种情况下，我们可以很容易地在同一个函数中同时包含知识蒸馏和余弦损失最小化。结合多种方法以在师生范式中获得更好的性能是很常见的。目前，我们可以运行一个简单的训练-测试会话。

# 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)

Epoch 1/10, Loss: 1.3019725261137003
Epoch 2/10, Loss: 1.0716999337801238
Epoch 3/10, Loss: 0.9702405371629369
Epoch 4/10, Loss: 0.8952659559066948
Epoch 5/10, Loss: 0.8415537168607687
Epoch 6/10, Loss: 0.7984531910523124
Epoch 7/10, Loss: 0.7552351041523087
Epoch 8/10, Loss: 0.7218984947789966
Epoch 9/10, Loss: 0.6841177859574633
Epoch 10/10, Loss: 0.6567412945620544
Test Accuracy: 70.21%

中间回归器运行#

我们的朴素最小化并不能保证更好的结果，原因有很多，其中之一就是向量的维度。余弦相似度通常比欧几里得距离更适合高维向量，但我们处理的是各有 1024 个分量的向量，因此提取有意义的相似性难度更大。此外，如前所述，推动教师和学生隐藏表征的匹配并没有理论支持。我们没有充分的理由去追求这些向量的 1:1 匹配。我们将通过包含一个名为回归器的额外网络来提供训练干预的最终示例。目标是首先在卷积层之后提取教师的特征图，然后在卷积层之后提取学生的特征图，最后尝试匹配这些图。但是，这次我们将在网络之间引入一个回归器来促进匹配过程。回归器将是可训练的，理想情况下它会比我们的朴素余弦损失最小化方案表现得更好。它的主要工作是匹配这些特征图的维度，以便我们可以正确定义教师和学生之间的损失函数。定义这样的损失函数提供了一条教学“路径”，本质上就是流动反向传播梯度，这将改变学生的权重。针对我们原始网络中每个分类器之前的卷积层输出，我们有以下形状

# Pass the sample input only from the convolutional feature extractor
convolutional_fe_output_student = nn_light.features(sample_input)
convolutional_fe_output_teacher = nn_deep.features(sample_input)

# Print their shapes
print("Student's feature extractor output shape: ", convolutional_fe_output_student.shape)
print("Teacher's feature extractor output shape: ", convolutional_fe_output_teacher.shape)

Student's feature extractor output shape:  torch.Size([128, 16, 8, 8])
Teacher's feature extractor output shape:  torch.Size([128, 32, 8, 8])

我们有 32 个教师卷积核和 16 个学生卷积核。我们将包含一个可训练层，将学生的特征图转换为教师特征图的形状。实际上，我们修改了轻量级类以返回中间回归器之后的隐藏状态（该回归器匹配卷积特征图的大小），并修改了教师类以返回最终卷积层的输出，而不进行池化或展平。

../_static/img/knowledge_distillation/fitnets_knowledge_distill.png — 可训练层匹配中间张量的形状，且均方误差 (MSE) 定义得当：#

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 = x
        x = torch.flatten(x, 1)
        x = self.classifier(x)
        return x, conv_feature_map

class 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

此后，我们必须再次更新我们的训练循环。这次，我们提取学生的回归器输出和教师的特征图，我们在这些张量上计算 MSE（它们具有完全相同的形状，因此定义正确），并在分类任务的常规交叉熵损失之外，根据该损失反向传播梯度。

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 mode
    student.train() # Student to train mode

    for epoch in range(epochs):
        running_loss = 0.0
        for inputs, labels in train_loader:
            inputs, labels = inputs.to(device), labels.to(device)

            optimizer.zero_grad()

            # Again ignore teacher logits
            with torch.no_grad():
                _, teacher_feature_map = teacher(inputs)

            # Forward pass with the student model
            student_logits, regressor_feature_map = student(inputs)

            # Calculate the loss
            hidden_rep_loss = mse_loss(regressor_feature_map, teacher_feature_map)

            # Calculate the true label loss
            label_loss = ce_loss(student_logits, labels)

            # Weighted sum of the two losses
            loss = feature_map_weight * hidden_rep_loss + ce_loss_weight * label_loss

            loss.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)

Epoch 1/10, Loss: 1.7173191882155436
Epoch 2/10, Loss: 1.3418747204953752
Epoch 3/10, Loss: 1.1985273663040317
Epoch 4/10, Loss: 1.1054756199307454
Epoch 5/10, Loss: 1.0291845158237936
Epoch 6/10, Loss: 0.9663464654132229
Epoch 7/10, Loss: 0.9111720988207765
Epoch 8/10, Loss: 0.8608896627145655
Epoch 9/10, Loss: 0.8222318250504906
Epoch 10/10, Loss: 0.7858180063764763
Test Accuracy: 70.97%

预期最终方法会比 CosineLoss 工作得更好，因为现在我们在教师和学生之间设置了一个可训练层，这在学习方面给了学生一定的灵活性，而不是强迫学生复制教师的表征。包含额外网络是基于提示（Hint-based）的蒸馏背后的思想。

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: 74.93%
Student accuracy without teacher: 70.48%
Student accuracy with CE + KD: 70.56%
Student accuracy with CE + CosineLoss: 70.21%
Student accuracy with CE + RegressorMSE: 70.97%

结论#

以上任何一种方法都不会增加网络的参数数量或推理时间，因此性能提升只是以训练期间计算梯度的微小成本为代价。在机器学习应用中，我们主要关心推理时间，因为训练发生在模型部署之前。如果我们的轻量级模型对于部署来说仍然太重，我们可以应用不同的思路，例如训练后量化。额外的损失可以应用于许多任务，而不仅仅是分类，你可以尝试系数、温度或神经元数量等数值。请随意调整上述教程中的任何数字，但请记住，如果你更改了神经元/卷积核的数量，很可能会发生形状不匹配。

更多信息，请参阅

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