目录

• Transformer Network
  • Packages
  • 1 - Positional Encoding
    • 1.1 - Sine and Cosine Angles
    • Exercise 1 - get_angles
    • 1.2 - Sine and Cosine Positional Encodings
    • Exercise 2 - positional_encoding
      • Additional Hints
  • 2 - Masking
    • 2.1 - Padding Mask
    • 2.2 - Look-ahead Mask
  • 3 - Self-Attention
    • Exercise 3 - scaled_dot_product_attention
  • 4 - Encoder
    • 4.1 Encoder Layer
    • Exercise 4 - EncoderLayer
    • 4.2 - Full Encoder
    • Exercise 5 - Encoder
  • 5 - Decoder
    • 5.1 - Decoder Layer
    • Exercise 6 - DecoderLayer
    • 5.2 - Full Decoder
    • Exercise 7 - Decoder
  • 6 - Transformer
    • Exercise 8 - Transformer
  • Conclusion
• Congratulations on finishing the Deep Learning Specialization!!!!!!
  • 7 - References

Transformer Network

Welcome to Week 4's assignment, the last assignment of Course 5 of the Deep Learning Specialization! And congratulations on making it to the last assignment of the entire Deep Learning Specialization - you're almost done!

Ealier in the course, you've implemented sequential neural networks such as RNNs, GRUs, and LSTMs. In this notebook you'll explore the Transformer architecture, a neural network that takes advantage of parallel processing and allows you to substantially speed up the training process.

After this assignment you'll be able to:

• Create positional encodings to capture sequential relationships in data
• Calculate scaled dot-product self-attention with word embeddings
• Implement masked multi-head attention
• Build and train a Transformer model

For the last time, let's get started!

Run the following cell to load the packages you'll need.

import tensorflow as tf
import pandas as pd
import time
import numpy as np
import matplotlib.pyplot as plt

from tensorflow.keras.layers import Embedding, MultiHeadAttention, Dense, Input, Dropout, LayerNormalization
from transformers import DistilBertTokenizerFast #, TFDistilBertModel
from transformers import TFDistilBertForTokenClassification
from tqdm import tqdm_notebook as tqdm

In sequence to sequence tasks, the relative order of your data is extremely important to its meaning. When you were training sequential neural networks such as RNNs, you fed your inputs into the network in order. Information about the order of your data was automatically fed into your model. However, when you train a Transformer network using multi-head attention, you feed your data into the model all at once. While this dramatically reduces training time, there is no information about the order of your data. This is where positional encoding is useful - you can specifically encode the positions of your inputs and pass them into the network using these sine and cosine formulas:

\[PE_{(pos, 2i)}= sin\left(\frac{pos}{{10000}^{\frac{2i}{d}}}\right)
\tag{1}\]

$$
PE_{(pos, 2i+1)}= cos\left(\frac{pos}{{10000}^{\frac{2i}{d}}}\right)
\tag{2}$$

• \(d\) is the dimension of the word embedding and positional encoding
• \(pos\) is the position of the word.
• \(i\) refers to each of the different dimensions of the positional encoding.

To develop some intuition about positional encodings, you can think of them broadly as a feature that contains the information about the relative positions of words. The sum of the positional encoding and word embedding is ultimately what is fed into the model. If you just hard code the positions in, say by adding a matrix of 1's or whole numbers to the word embedding, the semantic meaning is distorted. Conversely, the values of the sine and cosine equations are small enough (between -1 and 1) that when you add the positional encoding to a word embedding, the word embedding is not significantly distorted, and is instead enriched with positional information. Using a combination of these two equations helps your Transformer network attend to the relative positions of your input data. This was a short discussion on positional encodings, but develop further intuition, check out the Positional Encoding Ungraded Lab.

Note: In the lectures Andrew uses vertical vectors, but in this assignment all vectors are horizontal. All matrix multiplications should be adjusted accordingly.

1.1 - Sine and Cosine Angles

Notice that even though the sine and cosine positional encoding equations take in different arguments (2i versus 2i+1, or even versus odd numbers) the inner terms for both equations are the same: $$\theta(pos, i, d) = \frac{pos}{10000^{\frac{2i}{d}}} \tag{3}$$

Consider the inner term as you calculate the positional encoding for a word in a sequence.

\(PE_{(pos, 0)}= sin\left(\frac{pos}{{10000}^{\frac{0}{d}}}\right)\), since solving 2i = 0 gives i = 0

\(PE_{(pos, 1)}= cos\left(\frac{pos}{{10000}^{\frac{0}{d}}}\right)\), since solving 2i + 1 = 1 gives i = 0

The angle is the same for both! The angles for \(PE_{(pos, 2)}\) and \(PE_{(pos, 3)}\) are the same as well, since for both, i = 1 and therefore the inner term is \(\left(\frac{pos}{{10000}^{\frac{1}{d}}}\right)\). This relationship holds true for all paired sine and cosine curves:

k

          0          

          1          

          2          

          3          

          ...

          d - 2          

          d - 1          

encoding(0) =

[\(sin(\theta(0, 0, d))\)

\(cos(\theta(0, 0, d))\)

\(sin(\theta(0, 1, d))\)

\(cos(\theta(0, 1, d))\)

…

\(sin(\theta(0, d//2, d))\)

\(cos(\theta(0, d//2, d))\)]

encoding(1) =

[\(sin(\theta(1, 0, d))\)

\(cos(\theta(1, 0, d))\)

\(sin(\theta(1, 1, d))\)

\(cos(\theta(1, 1, d))\)

…

\(sin(\theta(1, d//2, d))\)

\(cos(\theta(1, d//2, d))\)]

…

| encoding(pos) = | [\(sin(\theta(pos, 0, d))\)| \(cos(\theta(pos, 0, d))\)| \(sin(\theta(pos, 1, d))\)| \(cos(\theta(pos, 1, d))\)|… |\(sin(\theta(pos, d//2, d))\)| \(cos(\theta(pos, d//2, d))]\)|

Exercise 1 - get_angles

Implement the function get_angles() to calculate the possible angles for the sine and cosine positional encodings

Hints

• If k = [0, 1, 2, 3, 4, 5], then, i must be i = [0, 0, 1, 1, 2, 2]

• i = k//2

  UNQ_C1 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)

  GRADED FUNCTION get_angles

  def get_angles(pos, k, d):
  """
  Get the angles for the positional encoding

  Arguments:
      pos -- Column vector containing the positions [[0], [1], ...,[N-1]]
      k --   Row vector containing the dimension span [[0, 1, 2, ..., d-1]]
      d(integer) -- Encoding size
  
  Returns:
      angles -- (pos, d) numpy array
  """
  
  # START CODE HERE
  # Get i from dimension span k
  i =k//2
  # Calculate the angles using pos, i and d
  angles = pos/(np.power(10000,2*i/d))
  # END CODE HERE
  
  return angles

then

from public_tests import *

get_angles_test(get_angles)

# Example
position = 4
d_model = 8
pos_m = np.arange(position)[:, np.newaxis]
dims = np.arange(d_model)[np.newaxis, :]
get_angles(pos_m, dims, d_model)

1.2 - Sine and Cosine Positional Encodings

Now you can use the angles you computed to calculate the sine and cosine positional encodings.

\[PE_{(pos, 2i)}= sin\left(\frac{pos}{{10000}^{\frac{2i}{d}}}\right)
\]

$$
PE_{(pos, 2i+1)}= cos\left(\frac{pos}{{10000}^{\frac{2i}{d}}}\right)
$$

Exercise 2 - positional_encoding

Implement the function positional_encoding() to calculate the sine and cosine positional encodings

Reminder: Use the sine equation when \(i\) is an even number and the cosine equation when \(i\) is an odd number.

Additional Hints

• You may find

  np.newaxis useful depending on the implementation you choose.

  UNQ_C2 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)

  GRADED FUNCTION positional_encoding

  def positional_encoding(positions, d):
  """
  Precomputes a matrix with all the positional encodings

  Arguments:
      positions (int) -- Maximum number of positions to be encoded ，要编码的单词的数量
      d (int) -- Encoding size ，编码的维度
  
  Returns:
      pos_encoding -- (1, position, d_model) A matrix with the positional encodings
  """
  # START CODE HERE
  # initialize a matrix angle_rads of all the angles
  angle_rads = get_angles( np.arange(positions)[:, np.newaxis],#变为列向量，值为0~positions-1
                          np.arange(d)[np.newaxis, :],#同理
                          d)
  
  # apply sin to even indices in the array; 2i
  angle_rads[:, 0::2] = np.sin(angle_rads[:, 0::2])#语法为seq[start:end:step]，即从0开始步长为2,一定要注意左右两边的维度要相同
  
  # apply cos to odd indices in the array; 2i+1
  angle_rads[:, 1::2] = np.cos(angle_rads[:, 1::2])
  # END CODE HERE
  
  pos_encoding = angle_rads[np.newaxis, ...]
  
  return tf.cast(pos_encoding, dtype=tf.float32)

then

# UNIT TEST
positional_encoding_test(positional_encoding, get_angles)

Nice work calculating the positional encodings! Now you can visualize them.

pos_encoding = positional_encoding(50, 512)

print (pos_encoding.shape)

plt.pcolormesh(pos_encoding[0], cmap='RdBu')
plt.xlabel('d')
plt.xlim((0, 512))
plt.ylabel('Position')
plt.colorbar()
plt.show()

Each row represents a positional encoding - notice how none of the rows are identical! You have created a unique positional encoding for each of the words.

There are two types of masks that are useful when building your Transformer network: the padding mask and the look-ahead mask. Both help the softmax computation give the appropriate weights to the words in your input sentence.

2.1 - Padding Mask

Oftentimes your input sequence will exceed the maximum length of a sequence your network can process. Let's say the maximum length of your model is five, it is fed the following sequences:

[["Do", "you", "know", "when", "Jane", "is", "going", "to", "visit", "Africa"],
 ["Jane", "visits", "Africa", "in", "September" ],
 ["Exciting", "!"]
]

which might get vectorized as:

[[ 71, 121, 4, 56, 99, 2344, 345, 1284, 15],
 [ 56, 1285, 15, 181, 545],
 [ 87, 600]
]

When passing sequences into a transformer model, it is important that they are of uniform length. You can achieve this by padding the sequence with zeros, and truncating sentences that exceed the maximum length of your model:

[[ 71, 121, 4, 56, 99],
 [ 2344, 345, 1284, 15, 0],
 [ 56, 1285, 15, 181, 545],
 [ 87, 600, 0, 0, 0],
]

Sequences longer than the maximum length of five will be truncated, and zeros will be added to the truncated sequence to achieve uniform length. Similarly, for sequences shorter than the maximum length, they zeros will also be added for padding. However, these zeros will affect the softmax calculation - this is when a padding mask comes in handy! You will need to define a boolean mask that specifies which elements you must attend(1) and which elements you must ignore(0). Later you will use that mask to set all the zeros in the sequence to a value close to negative infinity (-1e9). We'll implement this for you so you can get to the fun of building the Transformer network! Just make sure you go through the code so you can correctly implement padding when building your model.

After masking, your input should go from [87, 600, 0, 0, 0] to [87, 600, -1e9, -1e9, -1e9], so that when you take the softmax, the zeros don't affect the score.

The MultiheadAttention layer implemented in Keras, use this masking logic.

def create_padding_mask(decoder_token_ids):
    """
    Creates a matrix mask for the padding cells

    Arguments:
        decoder_token_ids -- (n, m) matrix

    Returns:
        mask -- (n, 1, 1, m) binary tensor
    """
    seq = 1 - tf.cast(tf.math.equal(decoder_token_ids, 0), tf.float32)

    # add extra dimensions to add the padding
    # to the attention logits.
    return seq[:, tf.newaxis, :]

then

x = tf.constant([[7., 6., 0., 0., 1.], [1., 2., 3., 0., 0.], [0., 0., 0., 4., 5.]])
print(create_padding_mask(x))#可以看到，就是将非零的位置标为1，将数值为0的位置标为0

If we multiply (1 - mask) by -1e9 and add it to the sample input sequences, the zeros are essentially set to negative infinity. Notice the difference when taking the softmax of the original sequence and the masked sequence:

print(tf.keras.activations.softmax(x))
print(tf.keras.activations.softmax(x + (1 - create_padding_mask(x)) * -1.0e9))#将1-mask乘以一个极小值，那么表示0的掩码就变为一个极小值
#总体相当于在原始x的基础上，将为0的部分变为一个极小值而非零部分基本不做改变

2.2 - Look-ahead Mask

The look-ahead mask follows similar intuition. In training, you will have access to the complete correct output of your training example. The look-ahead mask helps your model pretend that it correctly predicted a part of the output and see if, without looking ahead, it can correctly predict the next output.

For example, if the expected correct output is [1, 2, 3] and you wanted to see if given that the model correctly predicted the first value it could predict the second value, you would mask out the second and third values. So you would input the masked sequence [1, -1e9, -1e9] and see if it could generate [1, 2, -1e9].

Just because you've worked so hard, we'll also implement this mask for you . Again, take a close look at the code so you can effictively implement it later.

def create_look_ahead_mask(sequence_length):
    """
    Returns an upper triangular matrix filled with ones

    Arguments:
        sequence_length -- matrix size

    Returns:
        mask -- (size, size) tensor
    """
    mask = tf.linalg.band_part(tf.ones((1, sequence_length, sequence_length)), -1, 0)
    return mask

then

x = tf.random.uniform((1, 3))
temp = create_look_ahead_mask(x.shape[1])
temp

As the authors of the Transformers paper state, "Attention is All You Need".

Figure 1: Self-Attention calculation visualization

**

The use of self-attention paired with traditional convolutional networks allows for the parallization which speeds up training. You will implement scaled dot product attention which takes in a query, key, value, and a mask as inputs to returns rich, attention-based vector representations of the words in your sequence. This type of self-attention can be mathematically expressed as:

\[\text { Attention }(Q, K, V)=\operatorname{softmax}\left(\frac{Q K^{T}}{\sqrt{d_{k}}}+{M}\right) V\tag{4}\
\]

• \(Q\) is the matrix of queries
• \(K\) is the matrix of keys
• \(V\) is the matrix of values
• \(M\) is the optional mask you choose to apply
• \({d_k}\) is the dimension of the keys, which is used to scale everything down so the softmax doesn't explode

Exercise 3 - scaled_dot_product_attention

Implement the function `scaled_dot_product_attention()` to create attention-based representations

Reminder: The boolean mask parameter can be passed in as none or as either padding or look-ahead.

Multiply (1. - mask) by -1e9 before applying the softmax.

Additional Hints

• You may find tf.matmul useful for matrix multiplication.

  UNQ_C3 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)

  GRADED FUNCTION scaled_dot_product_attention

  def scaled_dot_product_attention(q, k, v, mask):
  """
  Calculate the attention weights.
  q, k, v must have matching leading dimensions.
  k, v must have matching penultimate dimension, i.e.: seq_len_k = seq_len_v.
  The mask has different shapes depending on its type(padding or look ahead)
  but it must be broadcastable for addition.

  Arguments:
      q -- query shape == (..., seq_len_q, depth)
      k -- key shape == (..., seq_len_k, depth)
      v -- value shape == (..., seq_len_v, depth_v)
      mask: Float tensor with shape broadcastable
            to (..., seq_len_q, seq_len_k). Defaults to None.
  
  Returns:
      output -- attention_weights
  """
  # START CODE HERE
  
  matmul_qk = tf.matmul(q,k,transpose_b=True)  # (..., seq_len_q, seq_len_k)
  
  # scale matmul_qk
  dk = float(k.shape[1])#一定要注意要将dk换为float型，否则在下一步会出现格式错误，
  #这里k的维度到底是哪个我也不确定，因为这里k.shape为(4，4)
  scaled_attention_logits = matmul_qk/tf.sqrt(dk)
  
  # add the mask to the scaled tensor.
  if mask is not None: # Don't replace this None
      scaled_attention_logits += (1.-mask)* -1e9
  
  # softmax is normalized on the last axis (seq_len_k) so that the scores
  # add up to 1.
  attention_weights = tf.keras.activations.softmax(scaled_attention_logits,axis=-1 )  # (..., seq_len_q, seq_len_k)
  
  output = tf.matmul(attention_weights,v)  # (..., seq_len_q, depth_v)
  
  # END CODE HERE
  
  return output, attention_weights

then

# UNIT TEST
scaled_dot_product_attention_test(scaled_dot_product_attention

Excellent work! You can now implement self-attention. With that, you can start building the encoder block!

The Transformer Encoder layer pairs self-attention and convolutional neural network style of processing to improve the speed of training and passes K and V matrices to the Decoder, which you'll build later in the assignment. In this section of the assignment, you will implement the Encoder by pairing multi-head attention and a feed forward neural network (Figure 2a).

Figure 2a: Transformer encoder layer

**

• MultiHeadAttention you can think of as computing the self-attention several times to detect different features.
• Feed forward neural network contains two Dense layers which we'll implement as the function FullyConnected

Your input sentence first passes through a multi-head attention layer, where the encoder looks at other words in the input sentence as it encodes a specific word. The outputs of the multi-head attention layer are then fed to a feed forward neural network. The exact same feed forward network is independently applied to each position.

• For the MultiHeadAttention layer, you will use the Keras implementation. If you're curious about how to split the query matrix Q, key matrix K, and value matrix V into different heads, you can look through the implementation.

• You will also use the Sequential API with two dense layers to built the feed forward neural network layers.

  def FullyConnected(embedding_dim, fully_connected_dim):
  return tf.keras.Sequential([
  tf.keras.layers.Dense(fully_connected_dim, activation='relu'), # (batch_size, seq_len, dff)
  tf.keras.layers.Dense(embedding_dim) # (batch_size, seq_len, d_model)
  ])

4.1 Encoder Layer

Now you can pair multi-head attention and feed forward neural network together in an encoder layer! You will also use residual connections and layer normalization to help speed up training (Figure 2a).

Exercise 4 - EncoderLayer

Implement EncoderLayer() using the call() method

In this exercise, you will implement one encoder block (Figure 2) using the call() method. The function should perform the following steps:

1. You will pass the Q, V, K matrices and a boolean mask to a multi-head attention layer. Remember that to compute self-attention Q, V and K should be the same. Let the default values for return_attention_scores and training. You will also perform Dropout in this multi-head attention layer during training.
2. Now add a skip connection by adding your original input x and the output of the your multi-head attention layer.
3. After adding the skip connection, pass the output through the first normalization layer.
4. Finally, repeat steps 1-3 but with the feed forward neural network with a dropout layer instead of the multi-head attention layer.

Additional Hints (Click to expand)

• The __init__ method creates all the layers that will be accesed by the the call method. Wherever you want to use a layer defined inside the __init__ method you will have to use the syntax self.[insert layer name].

• You will find the documentation of MultiHeadAttention helpful. Note that if query, key and value are the same, then this function performs self-attention.

• The call arguments for self.mha are (Where B is for batch_size, T is for target sequence shapes, and S is output_shape):

• query: Query Tensor of shape (B, T, dim).

• value: Value Tensor of shape (B, S, dim).

• key: Optional key Tensor of shape (B, S, dim). If not given, will use value for both key and value, which is the most common case.

• attention_mask: a boolean mask of shape (B, T, S), that prevents attention to certain positions. The boolean mask specifies which query elements can attend to which key elements, 1 indicates attention and 0 indicates no attention. Broadcasting can happen for the missing batch dimensions and the head dimension.

• return_attention_scores: A boolean to indicate whether the output should be attention output if True, or (attention_output, attention_scores) if False. Defaults to False.

• training: Python boolean indicating whether the layer should behave in training mode (adding dropout) or in inference mode (no dropout). Defaults to either using the training mode of the parent layer/model, or False (inference) if there is no parent layer.

  UNQ_C4 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)

  GRADED FUNCTION EncoderLayer

  class EncoderLayer(tf.keras.layers.Layer):
  """
  The encoder layer is composed by a multi-head self-attention mechanism,
  followed by a simple, positionwise fully connected feed-forward network.
  This archirecture includes a residual connection around each of the two
  sub-layers, followed by layer normalization.
  """
  def init(self, embedding_dim, num_heads, fully_connected_dim,
  dropout_rate=0.1, layernorm_eps=1e-6):
  super(EncoderLayer, self).init()

      self.mha = MultiHeadAttention(num_heads=num_heads,
                                    key_dim=embedding_dim,
                                    dropout=dropout_rate)
  self.ffn = FullyConnected(embedding_dim=embedding_dim,
                            fully_connected_dim=fully_connected_dim)#实现两个dense层，见上面实现代码
  
  self.layernorm1 = LayerNormalization(epsilon=layernorm_eps)#用作对不同时间步进行标准化
  self.layernorm2 = LayerNormalization(epsilon=layernorm_eps)
  
  self.dropout_ffn = Dropout(dropout_rate)
  def call(self, x, training, mask):
      """
      Forward pass for the Encoder Layer
  Arguments:
      x -- Tensor of shape (batch_size, input_seq_len, fully_connected_dim)，要注意x已经是tensor（张量）了，不需要在转换
      training -- Boolean, set to true to activate
                  the training mode for dropout layers
      mask -- Boolean mask to ensure that the padding is not
              treated as part of the input
  Returns:
      encoder_layer_out -- Tensor of shape (batch_size, input_seq_len, fully_connected_dim)
  """
  # START CODE HERE
  # calculate self-attention using mha(~1 line). Dropout will be applied during training
  attn_output = self.mha(query=x,
                         value=x,
                         key=x,
                         attention_mask=mask,training=training) # Self attention (batch_size, input_seq_len, fully_connected_dim)
  #前面的hints里又说training为默认值，默认值即为true所以这里删去training也可以，所以这里实际已经droupout了不需要单独的dense层在执行
  # apply layer normalization on sum of the input and the attention output to get the
  # output of the multi-head attention layer (~1 line)
  out1 = self.layernorm1(x+attn_output)  # (batch_size, input_seq_len, fully_connected_dim)
  
  # pass the output of the multi-head attention layer through a ffn (~1 line)
  ffn_output =  self.ffn(out1)  # (batch_size, input_seq_len, fully_connected_dim)
  
  # apply dropout layer to ffn output during training (~1 line)
  ffn_output =  self.dropout_ffn(ffn_output,training)
  
  # apply layer normalization on sum of the output from multi-head attention and ffn output to get the
  # output of the encoder layer (~1 line)
  encoder_layer_out = self.layernorm2(out1+ffn_output)  # (batch_size, input_seq_len, fully_connected_dim)
  # END CODE HERE
  
  return encoder_layer_out</code></pre></li>

# UNIT TEST
EncoderLayer_test(EncoderLayer)

# UNIT TEST
Encoder_test(Encoder)

# UNIT TEST
DecoderLayer_test(DecoderLayer, create_look_ahead_mask)

# UNIT TEST
Transformer_test(Transformer, create_look_ahead_mask, create_padding_mask)