The Attention Mechanism is a transformative component in deep learning, designed to enable models to focus on relevant parts of input data when making predictions—mimicking how humans selectively focus on key information (e.g., emphasizing a specific word in a sentence to understand context). First introduced in 2014 for neural machine translation, attention has become the foundation of modern models like Transformers (used in GPT, BERT, and Vision Transformers), revolutionizing natural language processing (NLP), computer vision, and speech recognition.

Core Motivation: Limitations of RNNs/LSTMs/GRUs

Recurrent models (RNNs, LSTMs, GRUs) process sequential data step-by-step and rely on a single hidden state to encode all past information. This leads to two critical flaws:

1. Lost Context in Long Sequences: The hidden state becomes saturated with information, so early tokens (e.g., words in a long sentence) have little impact on later predictions (vanishing gradient problem).
2. Fixed Context Vector: For sequence-to-sequence tasks (e.g., translation), the encoder outputs a single fixed-length context vector to represent the entire input—insufficient for capturing nuanced relationships between input and output tokens.

The attention mechanism solves these issues by allowing the decoder to dynamically weigh the importance of each input token for every output token, instead of relying on a single context vector.

How Attention Works: Intuition and Math

At its core, attention computes a set of attention weights that quantify how much each input token should contribute to the current output token. The process can be broken into three key steps: score calculation, weight normalization, and context vector computation.

1. Key Definitions (for Sequence-to-Sequence Tasks)

To formalize attention, we define three vectors for each token:

2. Step 1: Calculate Attention Scores

Scores measure the similarity between the query and each key. Common scoring functions:

3. Step 2: Normalize Scores to Weights

Scores are converted to attention weights (values between 0 and 1 that sum to 1) using the softmax function:

\(\alpha_i = \text{softmax}(\text{score}(q, k_i)) = \frac{e^{\text{score}(q, k_i)}}{\sum_{j=1}^n e^{\text{score}(q, k_j)}}\)

A weight \(\alpha_i\) close to 1 means the decoder focuses heavily on the i-th input token; a weight close to 0 means it ignores that token.

4. Step 3: Compute Context Vector

The context vector is a weighted sum of the values using the attention weights:

\(c = \sum_{i=1}^n \alpha_i v_i\)

This vector contains the most relevant input information for generating the current output token.

5. Full Attention Formula (Scaled Dot-Product)

For a query matrix Q, key matrix K, and value matrix V (batched for efficiency), scaled dot-product attention is:

\(\text{Attention}(Q, K, V) = \text{softmax}\left( \frac{Q K^T}{\sqrt{d_k}} \right) V\)

Visualizing Attention Weights

A classic example is machine translation (e.g., English → French). For the input sentence “The cat sits on the mat” and output word “chat” (French for “cat”), the attention weights would be:

The model focuses 80% of its attention on the token “cat” when generating “chat”—exactly the relevant input token.

Types of Attention Mechanisms

Attention has evolved into multiple variants tailored to different tasks:

1. Encoder-Decoder Attention (Bahdanau Attention)

• Use Case: Sequence-to-sequence tasks (translation, summarization).
• How it works: The decoder’s query attends to the encoder’s keys/values (cross-attention between input and output sequences).

2. Self-Attention (Intra-Attention)

• Use Case: Understanding relationships within a single sequence (e.g., NLP: “it” refers to “cat”; computer vision: “this pixel is part of a dog”).
• How it works: Queries, keys, and values are all generated from the same sequence. Each token attends to other tokens in the sequence.
• Critical for Transformers: Self-attention allows parallel processing of sequences (unlike RNNs, which process tokens sequentially).

3. Multi-Head Attention

• Use Case: Capturing multiple types of relationships (e.g., syntax and semantics in text).
• How it works: Splits queries, keys, values into h “heads” (subspaces), computes attention independently for each head, then concatenates the results.
• Formula:\(\text{MultiHead}(Q, K, V) = \text{Concat}(\text{head}_1, …, \text{head}_h) W^O\)where \(\text{head}_i = \text{Attention}(Q W_i^Q, K W_i^K, V W_i^V)\) and \(W^O\) is a projection matrix.

4. Masked Attention

• Use Case: Autoregressive tasks (text generation, e.g., GPT).
• How it works: Masks future tokens (sets their attention scores to \(-\infty\)) so the model only attends to past tokens (prevents cheating by looking ahead).

Attention Implementation (Python with TensorFlow/Keras)

We’ll implement scaled dot-product attention and use it in a simple Transformer block for text classification.

Step 1: Implement Scaled Dot-Product Attention

python

运行

import tensorflow as tf
from tensorflow.keras import layers

class ScaledDotProductAttention(layers.Layer):
    def call(self, query, key, value, mask=None):
        # Calculate dot product: Q · K^T (batch_size, num_heads, seq_len_q, seq_len_k)
        matmul_qk = tf.matmul(query, key, transpose_b=True)
        
        # Scale by sqrt(d_k) to avoid large values saturating softmax
        d_k = tf.cast(tf.shape(key)[-1], tf.float32)
        scaled_attention_logits = matmul_qk / tf.math.sqrt(d_k)
        
        # Apply mask (if provided): mask future tokens for autoregressive tasks
        if mask is not None:
            scaled_attention_logits += (mask * -1e9)  # Masked positions → -infinity
        
        # Compute attention weights via softmax
        attention_weights = tf.nn.softmax(scaled_attention_logits, axis=-1)
        
        # Compute context vector: attention weights · V
        output = tf.matmul(attention_weights, value)
        
        return output, attention_weights

Step 2: Implement Multi-Head Attention

python

运行

class MultiHeadAttention(layers.Layer):
    def __init__(self, d_model, num_heads):
        super(MultiHeadAttention, self).__init__()
        self.num_heads = num_heads
        self.d_model = d_model
        
        # d_model must be divisible by num_heads
        assert d_model % num_heads == 0
        self.depth = d_model // num_heads
        
        # Projection matrices for Q, K, V
        self.wq = layers.Dense(d_model)
        self.wk = layers.Dense(d_model)
        self.wv = layers.Dense(d_model)
        
        # Output projection matrix
        self.dense = layers.Dense(d_model)
        self.attention = ScaledDotProductAttention()
    
    def split_heads(self, x, batch_size):
        # Split d_model into num_heads × depth (batch_size, seq_len, num_heads, depth)
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.depth))
        # Transpose to (batch_size, num_heads, seq_len, depth) for attention computation
        return tf.transpose(x, perm=[0, 2, 1, 3])
    
    def call(self, v, k, q, mask=None):
        batch_size = tf.shape(q)[0]
        
        # Project Q, K, V to d_model dimensions
        q = self.wq(q)
        k = self.wk(k)
        v = self.wv(v)
        
        # Split into multiple heads
        q = self.split_heads(q, batch_size)
        k = self.split_heads(k, batch_size)
        v = self.split_heads(v, batch_size)
        
        # Compute scaled dot-product attention for each head
        scaled_attention, attention_weights = self.attention(q, k, v, mask)
        
        # Concatenate heads back to original shape
        scaled_attention = tf.transpose(scaled_attention, perm=[0, 2, 1, 3])
        concat_attention = tf.reshape(scaled_attention, (batch_size, -1, self.d_model))
        
        # Project concatenated attention to d_model
        output = self.dense(concat_attention)
        return output, attention_weights

Step 3: Use Multi-Head Attention in a Transformer Block

python

运行

class TransformerBlock(layers.Layer):
    def __init__(self, d_model, num_heads, dff, rate=0.1):
        super(TransformerBlock, self).__init__()
        self.mha = MultiHeadAttention(d_model, num_heads)
        self.ffn = tf.keras.Sequential([
            layers.Dense(dff, activation='relu'),
            layers.Dense(d_model)
        ])
        # Layer normalization and dropout for regularization
        self.layernorm1 = layers.LayerNormalization(epsilon=1e-6)
        self.layernorm2 = layers.LayerNormalization(epsilon=1e-6)
        self.dropout1 = layers.Dropout(rate)
        self.dropout2 = layers.Dropout(rate)
    
    def call(self, x, training, mask=None):
        # Multi-head self-attention + residual connection + layer norm
        attn_output, _ = self.mha(x, x, x, mask)  # Self-attention: Q=K=V=x
        attn_output = self.dropout1(attn_output, training=training)
        out1 = self.layernorm1(x + attn_output)  # Residual connection
        
        # Feed-forward network + residual connection + layer norm
        ffn_output = self.ffn(out1)
        ffn_output = self.dropout2(ffn_output, training=training)
        out2 = self.layernorm2(out1 + ffn_output)  # Residual connection
        return out2

Step 4: Test the Transformer Block

python

运行

# Hyperparameters
d_model = 128  # Embedding dimension
num_heads = 4  # Number of attention heads
dff = 512      # Feed-forward network dimension

# Create a Transformer block
transformer_block = TransformerBlock(d_model, num_heads, dff)

# Dummy input: batch_size=2, seq_len=10, d_model=128
x = tf.random.uniform((2, 10, d_model))

# Forward pass
output = transformer_block(x, training=False)
print(f"Transformer Block Output Shape: {output.shape}")  # Output: (2, 10, 128)

Time and Space Complexity

Attention complexity depends on the sequence length (L) and embedding dimension (d):

Key Tradeoff

• Attention is slower than RNNs for short sequences (\(L < 100\)).
• Attention is faster than RNNs for long sequences (\(L > 1000\)) because it can be parallelized (unlike RNNs, which are sequential).

Pros and Cons of Attention Mechanisms

Pros

1. Captures Long-Term Dependencies: Eliminates the vanishing gradient problem by directly connecting all tokens (no reliance on hidden states).
2. Interpretability: Attention weights provide insight into which input tokens the model uses for predictions (e.g., why a translation chose a specific word).
3. Parallelization: Self-attention processes all tokens simultaneously (unlike RNNs, which process tokens one by one)—critical for training large models.
4. Universal Applicability: Works for NLP (text), computer vision (images as sequences of patches), speech (audio waveforms), and time series.

Cons

1. High Memory Usage for Long Sequences: \(O(L^2)\) complexity makes self-attention infeasible for very long sequences (e.g., \(L > 10,000\))—mitigated by sparse attention (e.g., Reformer, Longformer).
2. Computationally Expensive: Training large Transformer models (e.g., GPT-3) requires massive GPU/TPU resources.
3. No Inherent Order Information: Attention is permutation-invariant (ignores token order)—requires positional encoding to add sequence order information.

Real-World Applications

1. Natural Language Processing (NLP):
   • Machine translation (Google Translate uses Transformers).
   • Text generation (GPT, Llama).
   • Sentiment analysis, named entity recognition (BERT).
   • Question answering (T5).
2. Computer Vision:
   • Image classification (Vision Transformer, ViT).
   • Object detection (DETR).
   • Image captioning (Transformer encoder-decoder).
3. Speech Recognition:
   • Converting audio to text (Whisper uses Transformers).
   • Speech translation (direct audio-to-text translation).
4. Time Series Forecasting:
   • Predicting stock prices, weather, and energy consumption (attention captures long-range temporal dependencies).

Attention vs. RNNs/LSTMs/GRUs

Summary

1. The Attention Mechanism enables models to focus on relevant input tokens by computing attention weights, context vectors, and (in Transformers) multi-head self-attention.
2. It solves the long-term dependency problem of RNNs and enables parallel training of sequence models.
3. Core variants: Encoder-decoder attention, self-attention, multi-head attention, masked attention.
4. Foundation of modern AI models: GPT, BERT, ViT, and Whisper all rely on attention for state-of-the-art performance.

Would you like me to implement positional encoding (critical for Transformers to understand sequence order)? Or build a full Transformer model for text classification using the blocks we created?编辑分享

Multi-Head Attention

Multi-Head Attention

Multi-Head Attention is a key extension of the basic attention mechanism, designed to capture multiple distinct types of relationships between tokens in a sequence. Introduced in the seminal Attention Is All You Need paper (2017), it is the core component of Transformer models (used in GPT, BERT, and Vision Transformers) and enables state-of-the-art performance in NLP, computer vision, and sequential data tasks.

Core Motivation: Limitations of Single-Head Attention

A single attention head can only learn one type of relationship between tokens (e.g., grammatical dependencies in text, or spatial correlations in images). For complex tasks like machine translation or text summarization, models need to:

• Focus on syntax (e.g., subject-verb agreement).
• Focus on semantics (e.g., how a pronoun refers to a noun).
• Focus on context (e.g., the meaning of a word based on its neighbors).

Multi-Head Attention solves this by splitting the attention computation into multiple parallel “heads”, each specializing in a different type of relationship. The results from all heads are then combined to form a richer, more comprehensive representation of the sequence.

How Multi-Head Attention Works

Multi-Head Attention extends the scaled dot-product attention framework by splitting queries (Q), keys (K), and values (V) into h independent subspaces, computing attention for each subspace, and concatenating the outputs. The process has 5 key steps:

1. Key Definitions

We start with the same three vectors as basic attention:

• Query (Q): Shape = \((batch\_size, seq\_len\_q, d_{model})\) — represents the “question” for each target token.
• Key (K): Shape = \((batch\_size, seq\_len\_k, d_{model})\) — represents the “answer” for each source token.
• Value (V): Shape = \((batch\_size, seq\_len\_v, d_{model})\) — contains the content to be weighted by attention scores.

Where:

• \(d_{model}\): The embedding dimension of the model (e.g., 512 for BERT-base).
• \(seq\_len\_q = seq\_len\_k = seq\_len\_v\) for self-attention (all vectors come from the same sequence).

2. Step 1: Linear Projections (Splitting into Heads)

We project Q, K, and V into h smaller subspaces using learnable weight matrices:

\(\begin{align*} Q_i &= Q W_i^Q, \quad W_i^Q \in \mathbb{R}^{d_{model} \times d_k} \\ K_i &= K W_i^K, \quad W_i^K \in \mathbb{R}^{d_{model} \times d_k} \\ V_i &= V W_i^V, \quad W_i^V \in \mathbb{R}^{d_{model} \times d_v} \end{align*}\)

For simplicity, we set \(d_k = d_v = d_{model}/h\) (ensures the total dimension remains the same after concatenation).

Each projection \(Q_i, K_i, V_i\) has shape \((batch\_size, seq\_len, d_k)\) — smaller than the original \(d_{model}\).

3. Step 2: Scaled Dot-Product Attention per Head

For each head i, compute scaled dot-product attention independently:

\(\text{head}_i = \text{Attention}(Q_i, K_i, V_i) = \text{softmax}\left( \frac{Q_i K_i^T}{\sqrt{d_k}} \right) V_i\)

Each head learns to focus on a different aspect of the sequence (e.g., head 1 focuses on syntax, head 2 on semantics).

4. Step 3: Concatenate Heads

Combine the outputs of all h heads into a single vector by concatenation:

\(\text{Concat} = \text{head}_1 \oplus \text{head}_2 \oplus \dots \oplus \text{head}_h\)

Where \(\oplus\) denotes concatenation along the last dimension. The shape of Concat is \((batch\_size, seq\_len\_q, d_{model})\) (since \(h \times d_k = d_{model}\)).

5. Step 4: Final Linear Projection

Apply a final learnable weight matrix \(W^O\) to the concatenated output to produce the final multi-head attention result:

\(\text{MultiHead}(Q, K, V) = \text{Concat} W^O, \quad W^O \in \mathbb{R}^{d_{model} \times d_{model}}\)

Full Formula for Multi-Head Attention

\(\text{MultiHead}(Q, K, V) = \text{Concat}\left( \text{head}_1, \dots, \text{head}_h \right) W^O\)

\(\text{where } \text{head}_i = \text{Attention}(Q W_i^Q, K W_i^K, V W_i^V)\)

Visualization of Multi-Head Attention

For a sentence like “The cat sits on the mat”, different heads will focus on different token relationships:

Key Properties of Multi-Head Attention

1. Parallelism: All heads are computed in parallel, making the process efficient on GPUs/TPUs.
2. Dimension Preservation: The input and output dimensions are both \(d_{model}\), so multi-head attention can be seamlessly integrated into Transformer blocks.
3. Flexibility: The number of heads h is a hyperparameter (e.g., 8 for BERT-base, 16 for BERT-large). More heads capture more relationships but increase computational cost.
4. Interpretability: We can visualize attention weights for each head to understand what the model is focusing on (e.g., which words are important for a translation).

Multi-Head Attention Implementation (Python with TensorFlow/Keras)

Below is a production-ready implementation of multi-head attention, compatible with Transformer models. We include masking to handle padding tokens and autoregressive tasks (e.g., text generation).

Step 1: Scaled Dot-Product Attention (Helper Function)

python

运行

import tensorflow as tf
from tensorflow.keras import layers

def scaled_dot_product_attention(query, key, value, mask=None):
    """
    Compute scaled dot-product attention.
    Args:
        query: Tensor of shape (batch_size, num_heads, seq_len_q, d_k)
        key: Tensor of shape (batch_size, num_heads, seq_len_k, d_k)
        value: Tensor of shape (batch_size, num_heads, seq_len_v, d_v)
        mask: Tensor of shape (batch_size, 1, seq_len_q, seq_len_k) (optional)
    Returns:
        output: Attention output (batch_size, num_heads, seq_len_q, d_v)
        attention_weights: Attention weights (batch_size, num_heads, seq_len_q, seq_len_k)
    """
    # Compute Q · K^T
    matmul_qk = tf.matmul(query, key, transpose_b=True)  # (batch_size, num_heads, seq_len_q, seq_len_k)
    
    # Scale by sqrt(d_k)
    d_k = tf.cast(tf.shape(key)[-1], tf.float32)
    scaled_attention_logits = matmul_qk / tf.math.sqrt(d_k)
    
    # Apply mask (if provided): mask → -infinity before softmax
    if mask is not None:
        scaled_attention_logits += (mask * -1e9)
    
    # Compute attention weights (softmax)
    attention_weights = tf.nn.softmax(scaled_attention_logits, axis=-1)  # (batch_size, num_heads, seq_len_q, seq_len_k)
    
    # Compute attention output (weights · value)
    output = tf.matmul(attention_weights, value)  # (batch_size, num_heads, seq_len_q, d_v)
    
    return output, attention_weights

Step 2: Multi-Head Attention Layer

python

运行

class MultiHeadAttention(layers.Layer):
    def __init__(self, d_model, num_heads):
        super(MultiHeadAttention, self).__init__()
        self.num_heads = num_heads
        self.d_model = d_model
        
        # Ensure d_model is divisible by num_heads
        assert d_model % self.num_heads == 0, "d_model must be divisible by num_heads"
        
        self.d_k = d_model // self.num_heads  # Dimension per head
        
        # Linear projection layers for Q, K, V
        self.wq = layers.Dense(d_model)
        self.wk = layers.Dense(d_model)
        self.wv = layers.Dense(d_model)
        
        # Final linear projection layer for concatenated heads
        self.dense = layers.Dense(d_model)
    
    def split_heads(self, x, batch_size):
        """
        Split the last dimension of x into (num_heads, d_k), then transpose to (batch_size, num_heads, seq_len, d_k).
        Args:
            x: Tensor of shape (batch_size, seq_len, d_model)
            batch_size: Integer, batch size
        Returns:
            x: Tensor of shape (batch_size, num_heads, seq_len, d_k)
        """
        x = tf.reshape(x, (batch_size, -1, self.num_heads, self.d_k))
        return tf.transpose(x, perm=[0, 2, 1, 3])
    
    def call(self, v, k, q, mask=None):
        batch_size = tf.shape(q)[0]
        
        # Step 1: Linear projections for Q, K, V
        q = self.wq(q)  # (batch_size, seq_len_q, d_model)
        k = self.wk(k)  # (batch_size, seq_len_k, d_model)
        v = self.wv(v)  # (batch_size, seq_len_v, d_model)
        
        # Step 2: Split into multiple heads
        q = self.split_heads(q, batch_size)  # (batch_size, num_heads, seq_len_q, d_k)
        k = self.split_heads(k, batch_size)  # (batch_size, num_heads, seq_len_k, d_k)
        v = self.split_heads(v, batch_size)  # (batch_size, num_heads, seq_len_v, d_k)
        
        # Step 3: Scaled dot-product attention per head
        scaled_attention, attention_weights = scaled_dot_product_attention(q, k, v, mask)
        
        # Step 4: Concatenate heads back to original shape
        scaled_attention = tf.transpose(scaled_attention, perm=[0, 2, 1, 3])  # (batch_size, seq_len_q, num_heads, d_k)
        concat_attention = tf.reshape(scaled_attention, (batch_size, -1, self.d_model))  # (batch_size, seq_len_q, d_model)
        
        # Step 5: Final linear projection
        output = self.dense(concat_attention)  # (batch_size, seq_len_q, d_model)
        
        return output, attention_weights

Step 3: Test the Multi-Head Attention Layer

python

运行

# Hyperparameters (matching BERT-base)
d_model = 512
num_heads = 8

# Create multi-head attention layer
mha = MultiHeadAttention(d_model, num_heads)

# Dummy input (batch_size=2, seq_len=10, d_model=512)
x = tf.random.uniform((2, 10, d_model))

# Compute self-attention (Q=K=V=x)
output, attn_weights = mha(x, x, x)

print(f"Input Shape: {x.shape}")  # (2, 10, 512)
print(f"Output Shape: {output.shape}")  # (2, 10, 512) → dimension preserved
print(f"Attention Weights Shape: {attn_weights.shape}")  # (2, 8, 10, 10) → (batch, heads, seq_len_q, seq_len_k)

Time and Space Complexity

Multi-Head Attention has the same asymptotic complexity as single-head attention, but with a constant factor increase due to h heads:

Where:

• L: Sequence length.
• \(d_{model}\): Model embedding dimension.
• h: Number of heads.

This means multi-head attention is no more complex than single-head attention—a critical insight that made Transformers feasible.

Multi-Head Attention vs. Single-Head Attention

Real-World Applications

Multi-Head Attention is the backbone of all modern Transformer-based models:

1. Natural Language Processing:
   • GPT: Uses masked multi-head self-attention for autoregressive text generation.
   • BERT: Uses bidirectional multi-head self-attention for pre-training on text.
   • T5: Uses encoder-decoder multi-head attention for translation and summarization.
2. Computer Vision:
   • Vision Transformer (ViT): Treats images as sequences of patches and uses multi-head self-attention to capture spatial relationships.
   • DETR: Uses multi-head attention for object detection (no need for handcrafted anchors).
3. Speech Recognition:
   • Whisper: Uses multi-head attention to convert audio waveforms to text.

Summary

It is the core component of Transformers, powering state-of-the-art AI models in NLP, computer vision, and speech.

Multi-Head Attention splits queries, keys, and values into h parallel heads, computes attention for each head, and concatenates the results.

It captures multiple distinct relationships between tokens, outperforming single-head attention on complex tasks.

It has the same asymptotic complexity as single-head attention, making it efficient for large models.

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