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Deep learning / Autoencoders and generative

Efficient Knowledge Distillation Techniques

12 min read, 15 sections

Contents
  1. Knowledge Distillation Fundamentals
  2. Teacher Assistant Knowledge Distillation
  3. Basic Student-Teacher Architecture
  4. Temperature Scaling Implementation
  5. Training Loop with Progressive Knowledge Transfer
  6. Teacher Assistant Selection Strategy
  7. Multi-teacher Knowledge Distillation
  8. Online Knowledge Distillation
  9. Feature-based Knowledge Distillation
  10. Attention-based Knowledge Distillation
  11. Knowledge Distillation with Data Augmentation
  12. Progressive Layer-wise Knowledge Distillation
  13. Real-world Implementation: Image Classification
  14. Real-world Implementation: Performance Metrics and Visualization
  15. Additional Resources

Knowledge Distillation Fundamentals

Knowledge distillation is a model compression technique where a smaller student model learns to mimic the behavior of a larger teacher model. The process involves training the student model to match the soft probability distributions produced by the teacher model rather than hard class labels.

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

class DistillationLoss(nn.Module):
    def __init__(self, temperature=2.0):
        super().__init__()
        self.temperature = temperature
        
    def forward(self, student_logits, teacher_logits, labels):
        # Soften probability distributions
        soft_targets = F.softmax(teacher_logits / self.temperature, dim=1)
        soft_prob = F.log_softmax(student_logits / self.temperature, dim=1)
        
        # Calculate distillation loss
        distillation_loss = F.kl_div(soft_prob, soft_targets, reduction='batchmean')
        
        # Calculate standard cross entropy with true labels
        student_loss = F.cross_entropy(student_logits, labels)
        
        # Combine losses (usually with a weighted sum)
        total_loss = (0.5 * student_loss) + (0.5 * distillation_loss)
        return total_loss

# Example usage
student_outputs = torch.randn(32, 10)  # batch_size=32, num_classes=10
teacher_outputs = torch.randn(32, 10)
labels = torch.randint(0, 10, (32,))

criterion = DistillationLoss()
loss = criterion(student_outputs, teacher_outputs, labels)

Teacher Assistant Knowledge Distillation

The Teacher Assistant (TA) approach introduces an intermediate model between the teacher and student. This model bridges the capacity gap, making knowledge transfer more effective. The TA model is trained first from the teacher, then transfers knowledge to the student.

class TeacherAssistantDistillation:
    def __init__(self, teacher, assistant, student, temperature=2.0):
        self.teacher = teacher
        self.assistant = assistant
        self.student = student
        self.temperature = temperature
        
    def train_assistant(self, dataloader, optimizer, epochs):
        criterion = DistillationLoss(self.temperature)
        self.teacher.eval()
        self.assistant.train()
        
        for epoch in range(epochs):
            for inputs, labels in dataloader:
                with torch.no_grad():
                    teacher_outputs = self.teacher(inputs)
                
                assistant_outputs = self.assistant(inputs)
                loss = criterion(assistant_outputs, teacher_outputs, labels)
                
                optimizer.zero_grad()
                loss.backward()
                optimizer.step()
                
    def train_student(self, dataloader, optimizer, epochs):
        criterion = DistillationLoss(self.temperature)
        self.assistant.eval()
        self.student.train()
        
        for epoch in range(epochs):
            for inputs, labels in dataloader:
                with torch.no_grad():
                    assistant_outputs = self.assistant(inputs)
                
                student_outputs = self.student(inputs)
                loss = criterion(student_outputs, assistant_outputs, labels)
                
                optimizer.zero_grad()
                loss.backward()
                optimizer.step()

Basic Student-Teacher Architecture

The fundamental architecture consists of a teacher network that is typically larger and pre-trained, and a student network that is smaller but architecturally similar. Both networks process the same input but produce different output distributions.

class TeacherNetwork(nn.Module):
    def __init__(self):
        super().__init__()
        self.features = nn.Sequential(
            nn.Conv2d(3, 64, 3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2),
            nn.Conv2d(64, 128, 3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2)
        )
        self.classifier = nn.Linear(128 * 8 * 8, 10)
    
    def forward(self, x):
        x = self.features(x)
        x = x.view(x.size(0), -1)
        return self.classifier(x)

class StudentNetwork(nn.Module):
    def __init__(self):
        super().__init__()
        self.features = nn.Sequential(
            nn.Conv2d(3, 32, 3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2),
            nn.Conv2d(32, 64, 3, padding=1),
            nn.ReLU(),
            nn.MaxPool2d(2)
        )
        self.classifier = nn.Linear(64 * 8 * 8, 10)
    
    def forward(self, x):
        x = self.features(x)
        x = x.view(x.size(0), -1)
        return self.classifier(x)

Temperature Scaling Implementation

Temperature scaling is crucial in knowledge distillation as it softens probability distributions, making it easier for the student to learn from the teacher's knowledge. Higher temperatures produce softer probability distributions, revealing more information about the teacher's learned patterns.

class TemperatureScaling:
    def __init__(self, temperature=2.0):
        self.temperature = temperature
        
    def scale_logits(self, logits):
        """Scale logits using temperature and return softened probabilities"""
        scaled_logits = logits / self.temperature
        return torch.softmax(scaled_logits, dim=1)
    
    def compare_distributions(self, original_logits):
        """Compare original and scaled probability distributions"""
        original_probs = torch.softmax(original_logits, dim=1)
        scaled_probs = self.scale_logits(original_logits)
        
        print(f"Original probabilities:\n{original_probs[0]}")
        print(f"Scaled probabilities (T={self.temperature}):\n{scaled_probs[0]}")

# Example usage
scaler = TemperatureScaling(temperature=3.0)
sample_logits = torch.tensor([[2.0, 1.0, 0.1, 0.01]])
scaler.compare_distributions(sample_logits)

Training Loop with Progressive Knowledge Transfer

This implementation showcases a progressive knowledge transfer approach where the student model gradually learns from both hard labels and teacher's soft targets. The balance between these two sources is controlled by a dynamically adjusted alpha parameter.

class ProgressiveDistillation:
    def __init__(self, teacher, student, temperature=2.0, max_epochs=100):
        self.teacher = teacher
        self.student = student
        self.temperature = temperature
        self.max_epochs = max_epochs
        
    def calculate_alpha(self, current_epoch):
        """Dynamic weighting between soft and hard targets"""
        return min(1.0, current_epoch / (self.max_epochs * 0.3))
    
    def train_epoch(self, dataloader, optimizer, epoch):
        total_loss = 0
        alpha = self.calculate_alpha(epoch)
        
        for inputs, labels in dataloader:
            # Get teacher's predictions
            with torch.no_grad():
                teacher_logits = self.teacher(inputs)
                teacher_probs = torch.softmax(teacher_logits / self.temperature, dim=1)
            
            # Get student's predictions
            student_logits = self.student(inputs)
            student_probs = torch.log_softmax(student_logits / self.temperature, dim=1)
            
            # Calculate losses
            distillation_loss = F.kl_div(student_probs, teacher_probs, reduction='batchmean')
            student_loss = F.cross_entropy(student_logits, labels)
            
            # Combine losses with dynamic alpha
            loss = (alpha * distillation_loss) + ((1 - alpha) * student_loss)
            
            optimizer.zero_grad()
            loss.backward()
            optimizer.step()
            
            total_loss += loss.item()
            
        return total_loss / len(dataloader)

Teacher Assistant Selection Strategy

The selection of an appropriate teacher assistant model is crucial for effective knowledge transfer. This implementation provides a strategy to automatically select the best TA architecture based on the capacity gap between teacher and student.

class TASelector:
    def __init__(self, teacher_params, student_params):
        self.teacher_size = teacher_params
        self.student_size = student_params
        
    def calculate_optimal_ta_size(self):
        """Calculate optimal TA model size using geometric mean"""
        return int(np.sqrt(self.teacher_size * self.student_size))
    
    def generate_ta_architecture(self):
        optimal_size = self.calculate_optimal_ta_size()
        
        class TeacherAssistant(nn.Module):
            def __init__(self, hidden_size):
                super().__init__()
                self.features = nn.Sequential(
                    nn.Conv2d(3, hidden_size, 3, padding=1),
                    nn.ReLU(),
                    nn.MaxPool2d(2),
                    nn.Conv2d(hidden_size, hidden_size*2, 3, padding=1),
                    nn.ReLU(),
                    nn.MaxPool2d(2)
                )
                self.classifier = nn.Linear(hidden_size*2 * 8 * 8, 10)
            
            def forward(self, x):
                x = self.features(x)
                x = x.view(x.size(0), -1)
                return self.classifier(x)
        
        return TeacherAssistant(optimal_size)

# Example usage
selector = TASelector(teacher_params=128, student_params=32)
ta_model = selector.generate_ta_architecture()

Multi-teacher Knowledge Distillation

Multi-teacher knowledge distillation leverages knowledge from multiple expert models simultaneously. This approach combines diverse knowledge sources to create a more robust student model, particularly useful when different teachers excel at different aspects of the task.

class MultiTeacherDistillation:
    def __init__(self, teachers, student, temperature=2.0):
        self.teachers = teachers  # List of teacher models
        self.student = student
        self.temperature = temperature
        self.teacher_weights = nn.Parameter(torch.ones(len(teachers)) / len(teachers))
    
    def ensemble_teacher_predictions(self, inputs):
        teacher_outputs = []
        for teacher in self.teachers:
            with torch.no_grad():
                logits = teacher(inputs)
                probs = F.softmax(logits / self.temperature, dim=1)
                teacher_outputs.append(probs)
        
        # Weighted average of teacher predictions
        weighted_probs = sum(w * p for w, p in zip(
            F.softmax(self.teacher_weights, dim=0),
            teacher_outputs
        ))
        return weighted_probs
    
    def train_step(self, inputs, labels, optimizer):
        # Get ensemble teacher predictions
        teacher_ensemble_probs = self.ensemble_teacher_predictions(inputs)
        
        # Student forward pass
        student_logits = self.student(inputs)
        student_probs = F.log_softmax(student_logits / self.temperature, dim=1)
        
        # Calculate losses
        distillation_loss = F.kl_div(student_probs, teacher_ensemble_probs)
        student_loss = F.cross_entropy(student_logits, labels)
        
        # Combined loss
        total_loss = 0.7 * distillation_loss + 0.3 * student_loss
        
        optimizer.zero_grad()
        total_loss.backward()
        optimizer.step()
        
        return total_loss.item()

Online Knowledge Distillation

Online knowledge distillation enables simultaneous training of both teacher and student networks. This approach is particularly efficient as it eliminates the need for pre-training the teacher model and allows for dynamic knowledge transfer during training.

class OnlineDistillation:
    def __init__(self, teacher_model, student_model, temperature=2.0):
        self.teacher = teacher_model
        self.student = student_model
        self.temperature = temperature
        
    def mutual_learning_step(self, inputs, labels, teacher_opt, student_opt):
        # Teacher forward pass
        teacher_logits = self.teacher(inputs)
        teacher_probs = F.softmax(teacher_logits / self.temperature, dim=1)
        
        # Student forward pass
        student_logits = self.student(inputs)
        student_probs = F.softmax(student_logits / self.temperature, dim=1)
        
        # Teacher learning from ground truth and student
        teacher_loss = (
            F.cross_entropy(teacher_logits, labels) +
            F.kl_div(F.log_softmax(teacher_logits / self.temperature, dim=1),
                     student_probs.detach(), reduction='batchmean')
        )
        
        # Student learning from ground truth and teacher
        student_loss = (
            F.cross_entropy(student_logits, labels) +
            F.kl_div(F.log_softmax(student_logits / self.temperature, dim=1),
                     teacher_probs.detach(), reduction='batchmean')
        )
        
        # Update both networks
        teacher_opt.zero_grad()
        teacher_loss.backward()
        teacher_opt.step()
        
        student_opt.zero_grad()
        student_loss.backward()
        student_opt.step()
        
        return teacher_loss.item(), student_loss.item()

Feature-based Knowledge Distillation

This implementation focuses on transferring knowledge through intermediate feature representations rather than just final outputs. This approach helps the student learn rich internal representations from the teacher's feature maps.

class FeatureDistillation(nn.Module):
    def __init__(self, teacher_channels, student_channels):
        super().__init__()
        self.transform = nn.Sequential(
            nn.Conv2d(student_channels, teacher_channels, 1),
            nn.BatchNorm2d(teacher_channels),
            nn.ReLU()
        )
        
    def forward(self, teacher_features, student_features):
        # Transform student features to match teacher dimensions
        adapted_student = self.transform(student_features)
        
        # Calculate feature similarity loss
        similarity_loss = F.mse_loss(
            self._normalize_features(adapted_student),
            self._normalize_features(teacher_features)
        )
        return similarity_loss
    
    def _normalize_features(self, features):
        return F.normalize(features.view(features.size(0), -1), dim=1)

# Usage in training loop
feature_distiller = FeatureDistillation(
    teacher_channels=256,
    student_channels=128
)

def train_with_features(inputs, labels, teacher, student, optimizer):
    teacher.eval()
    student.train()
    
    with torch.no_grad():
        t_features, t_output = teacher(inputs, return_features=True)
    
    s_features, s_output = student(inputs, return_features=True)
    
    # Combine feature and output distillation
    feature_loss = feature_distiller(t_features, s_features)
    output_loss = F.kl_div(
        F.log_softmax(s_output / 2.0, dim=1),
        F.softmax(t_output / 2.0, dim=1)
    )
    
    total_loss = feature_loss + output_loss
    
    optimizer.zero_grad()
    total_loss.backward()
    optimizer.step()

Attention-based Knowledge Distillation

Attention-based knowledge distillation transfers the teacher's attention patterns to the student model. This approach helps the student focus on important regions of the input data, similar to how the teacher model processes information.

class AttentionDistillation(nn.Module):
    def __init__(self):
        super().__init__()
        
    def compute_attention_map(self, features):
        """Compute spatial attention maps from feature maps"""
        batch_size, channels, height, width = features.size()
        attention = features.pow(2).mean(1, keepdim=True)
        attention = F.normalize(attention.view(batch_size, -1), dim=1)
        return attention.view(batch_size, 1, height, width)
    
    def attention_loss(self, teacher_features, student_features):
        """Calculate attention transfer loss"""
        teacher_attention = self.compute_attention_map(teacher_features)
        student_attention = self.compute_attention_map(student_features)
        
        return F.mse_loss(
            student_attention,
            teacher_attention,
            reduction='mean'
        )

class AttentionDistillationTrainer:
    def __init__(self, teacher, student, temperature=2.0):
        self.teacher = teacher
        self.student = student
        self.temperature = temperature
        self.attention_distiller = AttentionDistillation()
        
    def training_step(self, inputs, labels, optimizer):
        # Get teacher's features and predictions
        with torch.no_grad():
            t_features, t_logits = self.teacher(inputs, return_features=True)
            
        # Get student's features and predictions
        s_features, s_logits = self.student(inputs, return_features=True)
        
        # Calculate attention distillation loss
        attention_loss = self.attention_distiller.attention_loss(
            t_features, s_features
        )
        
        # Calculate standard distillation loss
        distill_loss = F.kl_div(
            F.log_softmax(s_logits / self.temperature, dim=1),
            F.softmax(t_logits / self.temperature, dim=1),
            reduction='batchmean'
        )
        
        # Combine losses
        total_loss = 0.7 * distill_loss + 0.3 * attention_loss
        
        optimizer.zero_grad()
        total_loss.backward()
        optimizer.step()
        
        return total_loss.item()

Knowledge Distillation with Data Augmentation

This implementation combines knowledge distillation with advanced data augmentation techniques to enhance the student model's learning process and improve generalization capabilities.

import torchvision.transforms as transforms
from torch.utils.data import Dataset

class AugmentedDistillationDataset(Dataset):
    def __init__(self, base_dataset, num_augmentations=2):
        self.dataset = base_dataset
        self.num_augmentations = num_augmentations
        self.augment = transforms.Compose([
            transforms.RandomHorizontalFlip(),
            transforms.RandomRotation(15),
            transforms.ColorJitter(
                brightness=0.2,
                contrast=0.2,
                saturation=0.2
            ),
            transforms.RandomResizedCrop(
                size=32,
                scale=(0.8, 1.0),
                ratio=(0.9, 1.1)
            )
        ])
    
    def __getitem__(self, idx):
        image, label = self.dataset[idx]
        augmented_images = [
            self.augment(image) for _ in range(self.num_augmentations)
        ]
        return augmented_images, label
    
    def __len__(self):
        return len(self.dataset)

class AugmentedDistillationTrainer:
    def __init__(self, teacher, student, temperature=2.0):
        self.teacher = teacher
        self.student = student
        self.temperature = temperature
        
    def train_step(self, augmented_inputs, labels, optimizer):
        teacher_outputs = []
        student_outputs = []
        
        # Process all augmented versions
        for aug_input in augmented_inputs:
            with torch.no_grad():
                teacher_logits = self.teacher(aug_input)
                teacher_outputs.append(
                    F.softmax(teacher_logits / self.temperature, dim=1)
                )
            
            student_logits = self.student(aug_input)
            student_outputs.append(
                F.log_softmax(student_logits / self.temperature, dim=1)
            )
        
        # Calculate consistency loss across augmentations
        distill_losses = [
            F.kl_div(s_out, t_out, reduction='batchmean')
            for s_out, t_out in zip(student_outputs, teacher_outputs)
        ]
        
        # Average losses
        avg_distill_loss = sum(distill_losses) / len(distill_losses)
        
        optimizer.zero_grad()
        avg_distill_loss.backward()
        optimizer.step()
        
        return avg_distill_loss.item()

Progressive Layer-wise Knowledge Distillation

This advanced implementation focuses on transferring knowledge layer by layer progressively, ensuring better feature alignment between teacher and student networks while maintaining computational efficiency.

class LayerwiseDistillation:
    def __init__(self, teacher_layers, student_layers):
        self.layer_pairs = list(zip(teacher_layers, student_layers))
        self.adaptation_layers = nn.ModuleList([
            nn.Sequential(
                nn.Conv2d(s.out_channels, t.out_channels, 1),
                nn.BatchNorm2d(t.out_channels)
            ) for t, s in self.layer_pairs
        ])
        
    def layer_loss(self, teacher_feat, student_feat, adapter):
        adapted_student = adapter(student_feat)
        return F.mse_loss(
            F.normalize(adapted_student, dim=1),
            F.normalize(teacher_feat, dim=1)
        )
    
    def progressive_training_step(self, inputs, current_layer_idx, optimizer):
        teacher_features = []
        student_features = []
        
        # Forward pass through teacher layers
        x_teacher = inputs
        for i, (t_layer, _) in enumerate(self.layer_pairs):
            x_teacher = t_layer(x_teacher)
            if i <= current_layer_idx:
                teacher_features.append(x_teacher.detach())
                
        # Forward pass through student layers
        x_student = inputs
        for i, (_, s_layer) in enumerate(self.layer_pairs):
            x_student = s_layer(x_student)
            if i <= current_layer_idx:
                student_features.append(x_student)
        
        # Calculate layer-wise losses
        layer_losses = []
        for i in range(current_layer_idx + 1):
            layer_loss = self.layer_loss(
                teacher_features[i],
                student_features[i],
                self.adaptation_layers[i]
            )
            layer_losses.append(layer_loss)
        
        total_loss = sum(layer_losses)
        
        optimizer.zero_grad()
        total_loss.backward()
        optimizer.step()
        
        return total_loss.item()

Real-world Implementation: Image Classification

Complete implementation of knowledge distillation for a practical image classification task, demonstrating the entire pipeline from data preprocessing to model evaluation.

class ImageClassificationDistillation:
    def __init__(self, num_classes, pretrained_teacher=True):
        # Initialize teacher (ResNet50) and student (ResNet18)
        self.teacher = models.resnet50(pretrained=pretrained_teacher)
        self.student = models.resnet18(pretrained=False)
        
        # Modify final layers for num_classes
        self.teacher.fc = nn.Linear(2048, num_classes)
        self.student.fc = nn.Linear(512, num_classes)
        
        self.temperature = 2.0
        self.alpha = 0.5  # Weight for distillation loss
        
    def preprocess_data(self, batch_size=32):
        transform = transforms.Compose([
            transforms.Resize(256),
            transforms.CenterCrop(224),
            transforms.ToTensor(),
            transforms.Normalize(
                mean=[0.485, 0.456, 0.406],
                std=[0.229, 0.224, 0.225]
            )
        ])
        
        # Load your dataset here
        trainset = datasets.ImageFolder('path/to/train', transform=transform)
        trainloader = DataLoader(trainset, batch_size=batch_size, shuffle=True)
        
        return trainloader
    
    def train_epoch(self, dataloader, optimizer, device):
        self.teacher.eval()
        self.student.train()
        
        running_loss = 0.0
        correct = 0
        total = 0
        
        for inputs, labels in dataloader:
            inputs, labels = inputs.to(device), labels.to(device)
            
            # Teacher predictions
            with torch.no_grad():
                teacher_logits = self.teacher(inputs)
            
            # Student predictions
            student_logits = self.student(inputs)
            
            # Calculate losses
            distillation_loss = F.kl_div(
                F.log_softmax(student_logits / self.temperature, dim=1),
                F.softmax(teacher_logits / self.temperature, dim=1),
                reduction='batchmean'
            ) * (self.temperature ** 2)
            
            student_loss = F.cross_entropy(student_logits, labels)
            
            # Combined loss
            loss = (self.alpha * distillation_loss + 
                   (1 - self.alpha) * student_loss)
            
            optimizer.zero_grad()
            loss.backward()
            optimizer.step()
            
            running_loss += loss.item()
            
            # Calculate accuracy
            _, predicted = student_logits.max(1)
            total += labels.size(0)
            correct += predicted.eq(labels).sum().item()
            
        epoch_loss = running_loss / len(dataloader)
        accuracy = 100. * correct / total
        
        return epoch_loss, accuracy

Real-world Implementation: Performance Metrics and Visualization

This implementation focuses on comprehensive evaluation metrics and visualization tools to analyze the effectiveness of knowledge distillation in practical scenarios.

class DistillationMetrics:
    def __init__(self, teacher, student):
        self.teacher = teacher
        self.student = student
        self.metrics_history = {
            'teacher_accuracy': [],
            'student_accuracy': [],
            'compression_ratio': self._calculate_compression_ratio(),
            'inference_speedup': None
        }
        
    def _calculate_compression_ratio(self):
        teacher_params = sum(p.numel() for p in self.teacher.parameters())
        student_params = sum(p.numel() for p in self.student.parameters())
        return teacher_params / student_params
    
    def measure_inference_time(self, sample_input, num_runs=100):
        self.teacher.eval()
        self.student.eval()
        
        # Measure teacher inference time
        torch.cuda.synchronize()
        teacher_start = time.time()
        for _ in range(num_runs):
            with torch.no_grad():
                _ = self.teacher(sample_input)
        torch.cuda.synchronize()
        teacher_time = (time.time() - teacher_start) / num_runs
        
        # Measure student inference time
        torch.cuda.synchronize()
        student_start = time.time()
        for _ in range(num_runs):
            with torch.no_grad():
                _ = self.student(sample_input)
        torch.cuda.synchronize()
        student_time = (time.time() - student_start) / num_runs
        
        self.metrics_history['inference_speedup'] = teacher_time / student_time
        return teacher_time, student_time
    
    def plot_learning_curves(self):
        plt.figure(figsize=(12, 6))
        plt.plot(self.metrics_history['teacher_accuracy'], 
                 label='Teacher Accuracy')
        plt.plot(self.metrics_history['student_accuracy'], 
                 label='Student Accuracy')
        plt.xlabel('Epoch')
        plt.ylabel('Accuracy (%)')
        plt.title('Knowledge Distillation Learning Curves')
        plt.legend()
        plt.grid(True)
        return plt.gcf()
    
    def generate_performance_report(self):
        report = {
            'compression_ratio': self.metrics_history['compression_ratio'],
            'inference_speedup': self.metrics_history['inference_speedup'],
            'final_accuracy_gap': (self.metrics_history['teacher_accuracy'][-1] - 
                                 self.metrics_history['student_accuracy'][-1])
        }
        return report

Additional Resources

For implementation details and practical examples, search for:

  • Pytorch knowledge distillation implementations
  • Hugging Face transformers distillation examples
  • TensorFlow model compression techniques

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  3. Graphical Neural Networks in Python:10 min

    Graphical Neural Networks (GNNs) are a powerful class of deep learning models designed to work with graph-structured data. They leverage the relationships...

  4. Constructing MaxOut Neural Networks in Python12 min

    MaxOut networks are a type of neural network architecture introduced by Ian Goodfellow et al. in 2013. They are designed to improve the performance of deep...

  5. How Autoencoders Work for Dimension Reduction9 min

    An autoencoder is a neural network architecture that learns to compress data into a lower-dimensional representation and then reconstruct it. The network...

  6. Compressing ML Models with Knowledge Distillation12 min

    Knowledge distillation is a technique used to compress large, complex machine learning models into smaller, more efficient ones while preserving their...