# Chapter 6: Self-Attention and Multi-Head Attention in Transformers

## 6.3 Multi-Head Attention in Transformers

Multi-head attention allows for even greater flexibility in the model's focus on different words in the input sequence. This technique not only computes the self-attention multiple times in parallel, but also allows for the model to learn different relationships between words by using different attention heads.

Each parallel operation corresponds to an attention head, and the overall result is a more fine-grained understanding of how each word in the sequence relates to the others. Therefore, multi-head attention is a powerful tool for improving the performance of neural machine translation and other natural language processing tasks that depend on modeling complex relationships between words.

### 6.3.1 Definition and Intuition of Multi-Head Attention

Multi-head attention is a novel technique in deep learning that has been shown to improve the performance of many natural language processing models. The basic idea behind multi-head attention is that it allows the model to focus on different parts of the input for each head. This means that one head could pay attention to the grammatical structure of the sentence, while another head focuses on the sentiment of the words. By having multiple heads, the model can potentially learn more complex and nuanced relationships between words, resulting in more accurate predictions.

But how exactly does multi-head attention work? Well, in a typical attention mechanism, we compute a set of attention weights that tell us how much each input element should contribute to the final output. In multi-head attention, we instead compute multiple sets of attention weights, one for each head. These attention weights are then combined to produce a single set of output weights that are used to compute the final output.

This approach has several benefits. First, it allows the model to attend to different parts of the input simultaneously, which can be especially useful for complex tasks like machine translation or summarization. Second, it enables the model to capture more nuanced relationships between words, which can lead to better performance on tasks that require a deep understanding of language. Finally, by incorporating multiple heads, the model can be more robust to noisy or ambiguous input, since each head can focus on a different aspect of the input and help filter out irrelevant information.

In summary, multi-head attention is a powerful technique that has been shown to improve the performance of many natural language processing models. By allowing the model to focus on different parts of the input for each head, it can learn more complex and nuanced relationships between words, resulting in more accurate predictions and better performance on a wide range of tasks.

### 6.3.2 Calculating Multi-Head Attention

The calculation of multi-head attention is similar to self-attention, but with the added step of being done multiple times. This allows for the input to be transformed into Query, Key, and Value spaces using different learned weight matrices for each head. Once this is done, self-attention is then computed for each head, allowing for a more nuanced understanding of the input data.

The outputs of all the heads are then concatenated and linearly transformed to produce the final output, which has been refined through the multi-head attention process. Overall, the use of multi-head attention allows for a more comprehensive understanding of the input, which can lead to better performance in natural language processing tasks.

**Example:**

Here's a Python function that demonstrates the computation of multi-head attention:

`def multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads):`

# Split the weight matrices for each head

Wq_split = np.split(Wq, num_heads, axis=-1)

Wk_split = np.split(Wk, num_heads, axis=-1)

Wv_split = np.split(Wv, num_heads, axis=-1)

outputs = []

for i in range(num_heads):

output, _ = self_attention(X, Wq_split[i], Wk_split[i], Wv_split[i])

outputs.append(output)

# Concatenate the outputs and apply the final linear transformation

output_concat = np.concatenate(outputs, axis=-1)

output = np.dot(output_concat, Wo)

return output

# Test the function with random data

X = np.random.rand(2, 3) # Input sequence

Wq = np.random.rand(3, 6) # Weight matrix for Query

Wk = np.random.rand(3, 6) # Weight matrix for Key

Wv = np.random.rand(3, 6) # Weight matrix for Value

Wo = np.random.rand(6, 3) # Weight matrix for final linear transformation

num_heads = 2

output = multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads)

print("Output:", output)

In this code, `num_heads`

is the number of heads in the multi-head attention. The function `multi_head_attention`

first splits the weight matrices for each head, then computes the self-attention for each head using the `self_attention`

function defined earlier. The outputs of all the heads are concatenated and finally transformed by a learned weight matrix `Wo`

.

## 6.3 Multi-Head Attention in Transformers

Multi-head attention allows for even greater flexibility in the model's focus on different words in the input sequence. This technique not only computes the self-attention multiple times in parallel, but also allows for the model to learn different relationships between words by using different attention heads.

Each parallel operation corresponds to an attention head, and the overall result is a more fine-grained understanding of how each word in the sequence relates to the others. Therefore, multi-head attention is a powerful tool for improving the performance of neural machine translation and other natural language processing tasks that depend on modeling complex relationships between words.

### 6.3.1 Definition and Intuition of Multi-Head Attention

Multi-head attention is a novel technique in deep learning that has been shown to improve the performance of many natural language processing models. The basic idea behind multi-head attention is that it allows the model to focus on different parts of the input for each head. This means that one head could pay attention to the grammatical structure of the sentence, while another head focuses on the sentiment of the words. By having multiple heads, the model can potentially learn more complex and nuanced relationships between words, resulting in more accurate predictions.

But how exactly does multi-head attention work? Well, in a typical attention mechanism, we compute a set of attention weights that tell us how much each input element should contribute to the final output. In multi-head attention, we instead compute multiple sets of attention weights, one for each head. These attention weights are then combined to produce a single set of output weights that are used to compute the final output.

This approach has several benefits. First, it allows the model to attend to different parts of the input simultaneously, which can be especially useful for complex tasks like machine translation or summarization. Second, it enables the model to capture more nuanced relationships between words, which can lead to better performance on tasks that require a deep understanding of language. Finally, by incorporating multiple heads, the model can be more robust to noisy or ambiguous input, since each head can focus on a different aspect of the input and help filter out irrelevant information.

In summary, multi-head attention is a powerful technique that has been shown to improve the performance of many natural language processing models. By allowing the model to focus on different parts of the input for each head, it can learn more complex and nuanced relationships between words, resulting in more accurate predictions and better performance on a wide range of tasks.

### 6.3.2 Calculating Multi-Head Attention

The calculation of multi-head attention is similar to self-attention, but with the added step of being done multiple times. This allows for the input to be transformed into Query, Key, and Value spaces using different learned weight matrices for each head. Once this is done, self-attention is then computed for each head, allowing for a more nuanced understanding of the input data.

The outputs of all the heads are then concatenated and linearly transformed to produce the final output, which has been refined through the multi-head attention process. Overall, the use of multi-head attention allows for a more comprehensive understanding of the input, which can lead to better performance in natural language processing tasks.

**Example:**

Here's a Python function that demonstrates the computation of multi-head attention:

`def multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads):`

# Split the weight matrices for each head

Wq_split = np.split(Wq, num_heads, axis=-1)

Wk_split = np.split(Wk, num_heads, axis=-1)

Wv_split = np.split(Wv, num_heads, axis=-1)

outputs = []

for i in range(num_heads):

output, _ = self_attention(X, Wq_split[i], Wk_split[i], Wv_split[i])

outputs.append(output)

# Concatenate the outputs and apply the final linear transformation

output_concat = np.concatenate(outputs, axis=-1)

output = np.dot(output_concat, Wo)

return output

# Test the function with random data

X = np.random.rand(2, 3) # Input sequence

Wq = np.random.rand(3, 6) # Weight matrix for Query

Wk = np.random.rand(3, 6) # Weight matrix for Key

Wv = np.random.rand(3, 6) # Weight matrix for Value

Wo = np.random.rand(6, 3) # Weight matrix for final linear transformation

num_heads = 2

output = multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads)

print("Output:", output)

In this code, `num_heads`

is the number of heads in the multi-head attention. The function `multi_head_attention`

first splits the weight matrices for each head, then computes the self-attention for each head using the `self_attention`

function defined earlier. The outputs of all the heads are concatenated and finally transformed by a learned weight matrix `Wo`

.

## 6.3 Multi-Head Attention in Transformers

Multi-head attention allows for even greater flexibility in the model's focus on different words in the input sequence. This technique not only computes the self-attention multiple times in parallel, but also allows for the model to learn different relationships between words by using different attention heads.

Each parallel operation corresponds to an attention head, and the overall result is a more fine-grained understanding of how each word in the sequence relates to the others. Therefore, multi-head attention is a powerful tool for improving the performance of neural machine translation and other natural language processing tasks that depend on modeling complex relationships between words.

### 6.3.1 Definition and Intuition of Multi-Head Attention

Multi-head attention is a novel technique in deep learning that has been shown to improve the performance of many natural language processing models. The basic idea behind multi-head attention is that it allows the model to focus on different parts of the input for each head. This means that one head could pay attention to the grammatical structure of the sentence, while another head focuses on the sentiment of the words. By having multiple heads, the model can potentially learn more complex and nuanced relationships between words, resulting in more accurate predictions.

But how exactly does multi-head attention work? Well, in a typical attention mechanism, we compute a set of attention weights that tell us how much each input element should contribute to the final output. In multi-head attention, we instead compute multiple sets of attention weights, one for each head. These attention weights are then combined to produce a single set of output weights that are used to compute the final output.

This approach has several benefits. First, it allows the model to attend to different parts of the input simultaneously, which can be especially useful for complex tasks like machine translation or summarization. Second, it enables the model to capture more nuanced relationships between words, which can lead to better performance on tasks that require a deep understanding of language. Finally, by incorporating multiple heads, the model can be more robust to noisy or ambiguous input, since each head can focus on a different aspect of the input and help filter out irrelevant information.

In summary, multi-head attention is a powerful technique that has been shown to improve the performance of many natural language processing models. By allowing the model to focus on different parts of the input for each head, it can learn more complex and nuanced relationships between words, resulting in more accurate predictions and better performance on a wide range of tasks.

### 6.3.2 Calculating Multi-Head Attention

The calculation of multi-head attention is similar to self-attention, but with the added step of being done multiple times. This allows for the input to be transformed into Query, Key, and Value spaces using different learned weight matrices for each head. Once this is done, self-attention is then computed for each head, allowing for a more nuanced understanding of the input data.

The outputs of all the heads are then concatenated and linearly transformed to produce the final output, which has been refined through the multi-head attention process. Overall, the use of multi-head attention allows for a more comprehensive understanding of the input, which can lead to better performance in natural language processing tasks.

**Example:**

Here's a Python function that demonstrates the computation of multi-head attention:

`def multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads):`

# Split the weight matrices for each head

Wq_split = np.split(Wq, num_heads, axis=-1)

Wk_split = np.split(Wk, num_heads, axis=-1)

Wv_split = np.split(Wv, num_heads, axis=-1)

outputs = []

for i in range(num_heads):

output, _ = self_attention(X, Wq_split[i], Wk_split[i], Wv_split[i])

outputs.append(output)

# Concatenate the outputs and apply the final linear transformation

output_concat = np.concatenate(outputs, axis=-1)

output = np.dot(output_concat, Wo)

return output

# Test the function with random data

X = np.random.rand(2, 3) # Input sequence

Wq = np.random.rand(3, 6) # Weight matrix for Query

Wk = np.random.rand(3, 6) # Weight matrix for Key

Wv = np.random.rand(3, 6) # Weight matrix for Value

Wo = np.random.rand(6, 3) # Weight matrix for final linear transformation

num_heads = 2

output = multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads)

print("Output:", output)

In this code, `num_heads`

is the number of heads in the multi-head attention. The function `multi_head_attention`

first splits the weight matrices for each head, then computes the self-attention for each head using the `self_attention`

function defined earlier. The outputs of all the heads are concatenated and finally transformed by a learned weight matrix `Wo`

.

## 6.3 Multi-Head Attention in Transformers

### 6.3.1 Definition and Intuition of Multi-Head Attention

### 6.3.2 Calculating Multi-Head Attention

**Example:**

Here's a Python function that demonstrates the computation of multi-head attention:

`def multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads):`

# Split the weight matrices for each head

Wq_split = np.split(Wq, num_heads, axis=-1)

Wk_split = np.split(Wk, num_heads, axis=-1)

Wv_split = np.split(Wv, num_heads, axis=-1)

outputs = []

for i in range(num_heads):

output, _ = self_attention(X, Wq_split[i], Wk_split[i], Wv_split[i])

outputs.append(output)

# Concatenate the outputs and apply the final linear transformation

output_concat = np.concatenate(outputs, axis=-1)

output = np.dot(output_concat, Wo)

return output

# Test the function with random data

X = np.random.rand(2, 3) # Input sequence

Wq = np.random.rand(3, 6) # Weight matrix for Query

Wk = np.random.rand(3, 6) # Weight matrix for Key

Wv = np.random.rand(3, 6) # Weight matrix for Value

Wo = np.random.rand(6, 3) # Weight matrix for final linear transformation

num_heads = 2

output = multi_head_attention(X, Wq, Wk, Wv, Wo, num_heads)

print("Output:", output)

`num_heads`

is the number of heads in the multi-head attention. The function `multi_head_attention`

first splits the weight matrices for each head, then computes the self-attention for each head using the `self_attention`

function defined earlier. The outputs of all the heads are concatenated and finally transformed by a learned weight matrix `Wo`

.