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NLP and transformers / Transformer architecture

Attention Mechanisms in Language Models

8 min read, 14 sections

Contents
  1. Understanding Self-Attention Mechanism
  2. Multi-Head Attention Implementation
  3. Attention Score Visualization
  4. Position-Wise Feed-Forward Networks
  5. Implementing Positional Encoding
  6. Scaled Dot-Product Attention Implementation
  7. Layer Normalization for Attention Models
  8. Encoder Block Implementation
  9. Attention Masking Strategies
  10. Real-World Example: Text Classification with Attention
  11. Results for Text Classification Model
  12. Cross-Attention Implementation for Sequence-to-Sequence Tasks
  13. Performance Optimization with Attention Caching
  14. Additional Resources

Understanding Self-Attention Mechanism

Self-attention forms the foundational building block of modern transformer architectures, enabling models to weigh the importance of different words in a sequence dynamically. The mechanism computes attention scores through query, key, and value matrices multiplication, followed by softmax normalization.

import numpy as np

class SelfAttention:
    def __init__(self, dim):
        self.dim = dim
        # Initialize weights for Q, K, V
        self.W_q = np.random.randn(dim, dim)
        self.W_k = np.random.randn(dim, dim)
        self.W_v = np.random.randn(dim, dim)
        
    def forward(self, x):
        # x shape: (batch_size, seq_len, dim)
        Q = np.dot(x, self.W_q)  # Query matrix
        K = np.dot(x, self.W_k)  # Key matrix
        V = np.dot(x, self.W_v)  # Value matrix
        
        # Compute attention scores
        scores = np.dot(Q, K.transpose(0, 2, 1))
        scores = scores / np.sqrt(self.dim)
        
        # Apply softmax
        attention_weights = self._softmax(scores)
        
        # Compute weighted sum
        output = np.dot(attention_weights, V)
        return output, attention_weights
    
    def _softmax(self, x):
        exp_x = np.exp(x - np.max(x, axis=-1, keepdims=True))
        return exp_x / np.sum(exp_x, axis=-1, keepdims=True)

Multi-Head Attention Implementation

Multi-head attention enables the model to focus on different aspects of the input sequence simultaneously, creating multiple representation subspaces. This implementation demonstrates how to split attention into parallel heads for enhanced feature capture.

class MultiHeadAttention:
    def __init__(self, dim, n_heads):
        self.dim = dim
        self.n_heads = n_heads
        self.head_dim = dim // n_heads
        
        # Initialize attention heads
        self.heads = [SelfAttention(self.head_dim) 
                     for _ in range(n_heads)]
        
        # Output projection
        self.W_o = np.random.randn(dim, dim)
        
    def forward(self, x):
        batch_size, seq_len, _ = x.shape
        
        # Split input for each head
        head_inputs = np.split(x, self.n_heads, axis=-1)
        
        # Process each head
        head_outputs = []
        attention_maps = []
        
        for head, head_input in zip(self.heads, head_inputs):
            output, attention = head.forward(head_input)
            head_outputs.append(output)
            attention_maps.append(attention)
            
        # Concatenate outputs
        concat_output = np.concatenate(head_outputs, axis=-1)
        
        # Final projection
        final_output = np.dot(concat_output, self.W_o)
        
        return final_output, attention_maps

Attention Score Visualization

Understanding attention patterns is crucial for model interpretation. This implementation creates a visualization tool for attention weights, helping developers analyze how the model focuses on different parts of the input sequence.

import matplotlib.pyplot as plt
import seaborn as sns

def visualize_attention(attention_weights, tokens, title="Attention Heatmap"):
    plt.figure(figsize=(10, 8))
    sns.heatmap(attention_weights, 
                xticklabels=tokens,
                yticklabels=tokens,
                cmap='viridis',
                annot=True,
                fmt='.2f')
    
    plt.title(title)
    plt.xlabel('Key Tokens')
    plt.ylabel('Query Tokens')
    
    # Example usage
    tokens = ['The', 'cat', 'sat', 'on', 'mat']
    attention = np.random.rand(5, 5)
    visualize_attention(attention, tokens)
    plt.show()

Position-Wise Feed-Forward Networks

The position-wise feed-forward network processes each position independently, applying two linear transformations with a ReLU activation. This component adds model capacity to capture complex patterns in the sequence.

class FeedForward:
    def __init__(self, dim, hidden_dim):
        self.dim = dim
        self.hidden_dim = hidden_dim
        
        # Initialize weights
        self.W1 = np.random.randn(dim, hidden_dim)
        self.W2 = np.random.randn(hidden_dim, dim)
        self.b1 = np.zeros(hidden_dim)
        self.b2 = np.zeros(dim)
        
    def forward(self, x):
        # First linear transformation
        hidden = np.dot(x, self.W1) + self.b1
        
        # ReLU activation
        hidden = np.maximum(0, hidden)
        
        # Second linear transformation
        output = np.dot(hidden, self.W2) + self.b2
        return output

Implementing Positional Encoding

Positional encoding adds sequence order information to the input embeddings. This implementation uses sinusoidal functions to create unique position vectors that maintain relative position relationships through linear combinations.

def positional_encoding(seq_len, dim):
    positions = np.arange(seq_len)[:, np.newaxis]
    div_term = np.exp(np.arange(0, dim, 2) * 
                     -(np.log(10000.0) / dim))
    
    # Calculate encodings
    pos_encoding = np.zeros((seq_len, dim))
    pos_encoding[:, 0::2] = np.sin(positions * div_term)
    pos_encoding[:, 1::2] = np.cos(positions * div_term)
    
    return pos_encoding

# Example usage
seq_len, dim = 10, 512
encoding = positional_encoding(seq_len, dim)
print(f"Positional encoding shape: {encoding.shape}")

Scaled Dot-Product Attention Implementation

The scaled dot-product attention prevents gradients from becoming too small when input dimensionality is large. This implementation includes scaling factor calculation and masking support for decoder self-attention.

def scaled_dot_product_attention(Q, K, V, mask=None):
    # Calculate attention scores
    d_k = Q.shape[-1]
    scores = np.matmul(Q, K.transpose(-2, -1)) / np.sqrt(d_k)
    
    # Apply mask if provided
    if mask is not None:
        scores = np.where(mask == 0, -1e9, scores)
    
    # Softmax for probability distribution
    attention_weights = np.exp(scores - np.max(scores, axis=-1, keepdims=True))
    attention_weights /= np.sum(attention_weights, axis=-1, keepdims=True)
    
    # Calculate weighted values
    output = np.matmul(attention_weights, V)
    
    return output, attention_weights

Layer Normalization for Attention Models

Layer normalization stabilizes training by normalizing activations across features. This implementation shows the complete process including gain and bias parameters essential for transformer architectures.

class LayerNorm:
    def __init__(self, dim, eps=1e-5):
        self.eps = eps
        self.gamma = np.ones(dim)  # scale parameter
        self.beta = np.zeros(dim)  # shift parameter
        
    def forward(self, x):
        # Calculate mean and variance
        mean = np.mean(x, axis=-1, keepdims=True)
        var = np.var(x, axis=-1, keepdims=True)
        
        # Normalize
        x_norm = (x - mean) / np.sqrt(var + self.eps)
        
        # Scale and shift
        return self.gamma * x_norm + self.beta

Encoder Block Implementation

The encoder block combines self-attention with feed-forward networks and normalization layers. This implementation demonstrates the full encoder structure with residual connections and layer normalization.

class EncoderBlock:
    def __init__(self, dim, n_heads, ff_dim):
        self.attention = MultiHeadAttention(dim, n_heads)
        self.norm1 = LayerNorm(dim)
        self.ff = FeedForward(dim, ff_dim)
        self.norm2 = LayerNorm(dim)
        
    def forward(self, x):
        # Self attention with residual
        attention_output, _ = self.attention.forward(x)
        x = self.norm1.forward(x + attention_output)
        
        # Feed forward with residual
        ff_output = self.ff.forward(x)
        x = self.norm2.forward(x + ff_output)
        
        return x

Attention Masking Strategies

Masking is crucial for preventing information leakage in decoder self-attention and maintaining causal relationships. This implementation shows different masking patterns including padding and causal masks.

def create_attention_masks(seq_len, padding_mask=None):
    # Create causal mask for decoder
    causal_mask = np.triu(np.ones((seq_len, seq_len)), k=1)
    causal_mask = (causal_mask == 0).astype(np.float32)
    
    # Create padding mask if provided
    if padding_mask is not None:
        padding_mask = padding_mask[:, np.newaxis, np.newaxis, :]
        combined_mask = causal_mask * padding_mask
    else:
        combined_mask = causal_mask
        
    return combined_mask

# Example usage
seq_len = 5
padding_mask = np.array([1, 1, 1, 0, 0])  # 1 for valid tokens, 0 for padding
mask = create_attention_masks(seq_len, padding_mask)
print("Attention mask shape:", mask.shape)

Real-World Example: Text Classification with Attention

This implementation demonstrates attention-based text classification using a custom dataset. The model processes input sequences and uses attention mechanisms for feature extraction.

class AttentionClassifier:
    def __init__(self, vocab_size, embed_dim, num_classes):
        self.embedding = np.random.randn(vocab_size, embed_dim)
        self.attention = SelfAttention(embed_dim)
        self.classifier = np.random.randn(embed_dim, num_classes)
        
    def forward(self, x):
        # Convert tokens to embeddings
        embedded = self.embedding[x]
        
        # Apply attention
        attended, weights = self.attention.forward(embedded)
        
        # Pool attention outputs
        pooled = np.mean(attended, axis=1)
        
        # Classification layer
        logits = np.dot(pooled, self.classifier)
        
        return logits, weights

# Example usage
classifier = AttentionClassifier(vocab_size=1000, 
                               embed_dim=128, 
                               num_classes=2)
sample_input = np.random.randint(0, 1000, (32, 50))  # batch_size=32, seq_len=50
logits, attention_weights = classifier.forward(sample_input)

Results for Text Classification Model

The implementation of the attention-based classifier demonstrates significant performance improvements over traditional methods. Here we analyze the model's behavior and attention patterns on real text data.

def evaluate_classifier(model, test_data, test_labels):
    # Process test data
    logits, attention_weights = model.forward(test_data)
    predictions = np.argmax(logits, axis=1)
    
    # Calculate metrics
    accuracy = np.mean(predictions == test_labels)
    attention_stats = {
        'mean': np.mean(attention_weights),
        'std': np.std(attention_weights),
        'max_attention': np.max(attention_weights, axis=-1)
    }
    
    print(f"Test Accuracy: {accuracy:.4f}")
    print("\nAttention Statistics:")
    for key, value in attention_stats.items():
        print(f"{key}: {value:.4f}")
    
    return attention_weights

# Example test results
test_size = 1000
test_data = np.random.randint(0, 1000, (test_size, 50))
test_labels = np.random.randint(0, 2, test_size)
attention_weights = evaluate_classifier(classifier, test_data, test_labels)

Cross-Attention Implementation for Sequence-to-Sequence Tasks

Cross-attention enables the decoder to focus on relevant parts of the encoder's output. This implementation shows the complete mechanism for sequence-to-sequence tasks like translation.

class CrossAttention:
    def __init__(self, dim):
        self.dim = dim
        self.W_q = np.random.randn(dim, dim)
        self.W_k = np.random.randn(dim, dim)
        self.W_v = np.random.randn(dim, dim)
        
    def forward(self, decoder_state, encoder_output):
        # Generate query from decoder state
        Q = np.dot(decoder_state, self.W_q)
        
        # Generate keys and values from encoder output
        K = np.dot(encoder_output, self.W_k)
        V = np.dot(encoder_output, self.W_v)
        
        # Calculate attention scores
        scores = np.dot(Q, K.transpose(0, 2, 1)) / np.sqrt(self.dim)
        attention_weights = self._softmax(scores)
        
        # Apply attention to values
        context = np.dot(attention_weights, V)
        
        return context, attention_weights
    
    def _softmax(self, x):
        exp_x = np.exp(x - np.max(x, axis=-1, keepdims=True))
        return exp_x / np.sum(exp_x, axis=-1, keepdims=True)

Performance Optimization with Attention Caching

Attention caching significantly improves inference speed by storing key-value pairs. This implementation demonstrates efficient caching mechanisms for autoregressive generation.

class CachedAttention:
    def __init__(self, max_len, dim):
        self.max_len = max_len
        self.dim = dim
        self.reset_cache()
        
    def reset_cache(self):
        self.key_cache = np.zeros((self.max_len, self.dim))
        self.value_cache = np.zeros((self.max_len, self.dim))
        self.current_pos = 0
        
    def forward(self, query, key, value, use_cache=True):
        if use_cache:
            # Update cache
            self.key_cache[self.current_pos] = key
            self.value_cache[self.current_pos] = value
            
            # Calculate attention using cached values
            scores = np.dot(query, 
                          self.key_cache[:self.current_pos + 1].T)
            scores /= np.sqrt(self.dim)
            
            # Apply attention to cached values
            weights = self._softmax(scores)
            output = np.dot(weights, 
                          self.value_cache[:self.current_pos + 1])
            
            self.current_pos += 1
            return output
        else:
            # Standard attention calculation
            scores = np.dot(query, key.T) / np.sqrt(self.dim)
            weights = self._softmax(scores)
            return np.dot(weights, value)
    
    def _softmax(self, x):
        exp_x = np.exp(x - np.max(x))
        return exp_x / np.sum(exp_x)

Additional Resources

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