+---------+ +---------+ +---------+ +---------------------------------------+
| Query |------>| Key |------>| Value |------>| Raw Attn Scores for Token1 |
+---------+ +---------+ +---------+ | (dot product of Query1 & Key vectors) |
+---------------------------------------+
|
v
+---------------------------------------+
| Raw Attn Scores for Token2 |
| (dot product of Query2 & Key vectors) |
+---------------------------------------+
|
v
+---------------------------------------+
| Raw Attn Scores for Token3 |
| (dot product of Query3 & Key vectors) |
+---------------------------------------+
|
v
+---------------------------------------+
| Raw Attn Scores for Token4 |
| (dot product of Query4 & Key vectors) |
+---------------------------------------+
|
v
+---------------------------------------+
| Softmax Function to Normalize Attn |
| Scores & Obtain Attention Weights |
+---------------------------------------+
|
v
+---------------------------------------+
| Weighted Sum of Value Vectors of All |
| Tokens Using Attn Weights as Weights |
+---------------------------------------+
|
v
+---------------------------------------+
| Context Vector for Token1 |
+---------------------------------------+
|
v
+---------------------------------------+
| Context Vector for Token2 |
+---------------------------------------+
|
v
+---------------------------------------+
| Context Vector for Token3 |
+---------------------------------------+
|
v
+---------------------------------------+
| Context Vector for Token4 |
+---------------------------------------+
|
v
+---------------------------------------+
| Output for the Entire Sequence |
+---------------------------------------+
Here's a simple wire diagram of the attention mechanism:
+-----------------------+
| |
| v
+-----+-----+ +------+------+
| | | |
+---+ Encoder +---------> Attention |
| | | | |
| +-----+-----+ +------+------+
| ^ |
| | |
| +-----+-----+ |
| | | |
+---+ Input <-----------------+
| |
+-----+-----+
In the context of the attention mechanism in transformers, the dot product of Query1 and Key vectors is a raw attention score that measures the compatibility between the query and key vectors for a given token in the sequence. Specifically, the dot product involves taking the element-wise product of the Query1 and Key vectors, and then summing up the resulting values. This produces a scalar value that represents the strength of the relationship between the query and key vectors. This process is repeated for each token in the sequence to compute a raw attention score for each token.
What is a dot product?
a = [1, 2, 3]
b = [4, 5, 6]
dot_product = sum([a[i]*b[i] for i in range(len(a))])
In this example, we have two lists of numbers a and b, each with three elements. To calculate the dot product of these two vectors, we first multiply the corresponding elements of the two lists (1 and 4, 2 and 5, and 3 and 6), and then sum the resulting products. The dot product of a and b is therefore 32.
The attention mechanism is used to calculate the relevance of each input element to the current output element. It then uses these relevance scores to create a context vector that is a weighted sum of the input elements. It is widely used in natural language processing tasks such as machine translation and text summarization.
What are tensflow dense layers?
In TensorFlow, dense layers, also known as fully connected layers or linear layers, are a type of artificial neural network layer that connects each neuron in the layer to every neuron in the previous layer. Dense layers are implemented in TensorFlow using the tf.keras.layers.Dense class.
A dense layer performs a linear operation on the input data, followed by an optional activation function. The linear operation is a weighted sum of the input features, with each weight representing the strength of the connection between neurons. In mathematical terms, given an input vector x, the output y of a dense layer can be written as:
y = Wx + b
Where W is a weight matrix, x is the input vector, and b is a bias vector. After this linear operation, an optional activation function f can be applied element-wise to the result:
y = f(Wx + b)
Some common activation functions used in neural networks are ReLU (Rectified Linear Unit), sigmoid, and tanh.
When creating a dense layer in TensorFlow, you need to specify the number of output units (neurons) and, optionally, an activation function. For example:
python
dense_layer = tf.keras.layers.Dense(units=128, activation='relu')
In this example, we create a dense layer with 128 output units and the ReLU activation function. During the forward pass of the neural network, this dense layer will perform the linear operation followed by the ReLU activation on its input data.
Let's create a simple code diagram to demonstrate a neural network with two dense layers. The input has 4 features, the first dense layer has 3 units, and the second dense layer has 2 units.
Input: Dense Layer 1: Dense Layer 2:
[ x1 ] --> [ N1_1 ] --> [ N2_1 ]
[ x2 ] --> [ N1_2 ] --> [ N2_2 ]
[ x3 ] --> [ N1_3 ]
[ x4 ]
In this example:
x1, x2, x3, and x4 are the input features. N1_1, N1_2, and N1_3 are the neurons in the first dense layer with the ReLU activation function. N2_1 and N2_2 are the neurons in the second dense layer with the ReLU activation function. Each neuron in the dense layers is fully connected to all neurons in the previous layer. For example, neuron N1_1 receives input from all input features (x1, x2, x3, and x4), and neuron N2_1 receives input from all neurons in the first dense layer (N1_1, N1_2, and N1_3).
Here's the code to create this neural network using TensorFlow:
python
import tensorflow as tf
# Define the neural network model
model = tf.keras.Sequential([
tf.keras.layers.Input(shape=(4,)),
tf.keras.layers.Dense(units=3, activation='relu'),
tf.keras.layers.Dense(units=2, activation='relu')
])
# Print the model summary
model.summary()
Putting it all together in this script:
import tensorflow as tf
class Attention(tf.keras.layers.Layer):
"""
This class implements the attention mechanism
"""
def __init__(self, units):
super(Attention, self).__init__()
self.W1 = tf.keras.layers.Dense(units)
self.W2 = tf.keras.layers.Dense(units)
self.V = tf.keras.layers.Dense(1)
def call(self, features, hidden):
"""
This function calculates the attention scores and returns the context vector
"""
hidden_with_time_axis = tf.expand_dims(hidden, 1)
score = tf.nn.tanh(self.W1(features) + self.W2(hidden_with_time_axis))
attention_weights = tf.nn.softmax(self.V(score), axis=1)
context_vector = attention_weights * features
context_vector = tf.reduce_sum(context_vector, axis=1)
return context_vector, attention_weights
This code defines a custom TensorFlow layer that implements an attention mechanism. Attention mechanisms are used in deep learning models, especially in sequence-to-sequence tasks, to weigh the importance of different parts of the input when generating the output.
what is "self.W1" in the example you just gave?
In the attention mechanism code I provide next, self.W1 is an instance of a dense layer (tf.keras.layers.Dense) with a specified number of units. In the context of the attention mechanism, self.W1 is used as a learnable weight matrix to project the input features into a new space, which is then combined with the hidden state projection to compute the attention scores.
Here's the relevant code snippet from the Attention class:
python
class Attention(tf.keras.layers.Layer):
def __init__(self, units):
super(Attention, self).__init__()
self.W1 = tf.keras.layers.Dense(units)
...
self.W1 is created during the initialization of the Attention layer with a specified number of units. This dense layer does not have an activation function, so it performs only a linear transformation on its input.
In the call method of the Attention class, self.W1 is applied to the input features (features) as follows:
python
score = tf.nn.tanh(self.W1(features) + self.W2(hidden_with_time_axis))
self.W1(features) computes the weighted sum of the input features using the learned weights of the dense layer, and this result is combined with the hidden state projection (self.W2(hidden_with_time_axis)) before passing through the tanh activation function. The output of this operation is the attention score, which is used to compute the attention weights and the context vector.
In summary, self.W1 is a dense layer used as a part of the attention mechanism to project the input features and compute the attention scores. In the attention mechanism code, the hidden state projection is performed using self.W2(hidden_with_time_axis). The purpose of this operation is to transform the hidden state into a new space that is compatible with the input features, so that they can be combined effectively to compute the attention scores. Let's break down this operation step by step:
hidden is the hidden state of the model, which contains information about the input sequence up to a certain point. The hidden state is usually generated by a Recurrent Neural Network (RNN) or another type of sequential model.
Here's an example of how to create a simple RNN model using TensorFlow that generates a hidden state based on an input sequence. In this example, we use the tf.keras.layers.SimpleRNN layer, which is a basic RNN layer provided by TensorFlow:
python
import tensorflow as tf
# Define the RNN model
model = tf.keras.Sequential([
tf.keras.layers.Input(shape=(None, 4)), # Input shape: (batch_size, sequence_length, num_features)
tf.keras.layers.SimpleRNN(units=32), # RNN layer with 32 hidden units
])
# Print the model summary
model.summary()
In this example, the input shape is defined as (None, 4), which means that the model can accept input sequences of variable length (None) with 4 features at each time step. The model consists of a single SimpleRNN layer with 32 hidden units. When the model processes the input sequence, it generates a hidden state at each time step based on the input data and the previous hidden state.
To use the hidden state generated by the RNN in the attention mechanism, you can create a custom model that combines the RNN layer and the Attention layer. Here's an example:
python
import tensorflow as tf
class RNNWithAttention(tf.keras.Model):
def __init__(self, units):
super(RNNWithAttention, self).__init__()
self.rnn = tf.keras.layers.SimpleRNN(units, return_sequences=True, return_state=True)
self.attention = Attention(units)
def call(self, inputs):
rnn_output, hidden_state = self.rnn(inputs)
context_vector, attention_weights = self.attention(rnn_output, hidden_state)
return context_vector, attention_weights
# Create the model with 32 hidden units
model = RNNWithAttention(units=32)
# Example input sequence: (batch_size=1, sequence_length=5, num_features=4)
input_sequence = tf.random.normal(shape=(1, 5, 4))
# Get the context vector and attention weights
context_vector, attention_weights = model(input_sequence)
In this custom model, the SimpleRNN layer is used to generate the hidden state based on the input sequence, and the Attention layer is used to compute the context vector and attention weights using the RNN output and the hidden state. The model can be extended further to generate an output sequence or perform a specific task, such as sequence classification or sequence-to-sequence prediction.
Input Layer Hidden Layer Output Layer
(3 features) (4 neurons) (2 neurons)
x1 ----- H1_1 ----- O1
\--- W1 ----/ \--- W2 ----/
x2 ----- | H1_2 ----- O2
/--- W1 ----\ /--- W2 ----/
x3 ----- H1_3 -----
H1_4 -----
Here is an ASCII art representation of the same feedforward neural network with an input layer, one hidden layer (dense layer), and an output layer. The input layer has 3 input features, the hidden layer has 4 neurons, and the output layer has 2 neurons:
x1, x2, and x3 are the input features. H1_1, H1_2, H1_3, and H1_4 are the neurons in the hidden layer. O1 and O2 are the neurons in the output layer. W1 and W2 are the weight matrices connecting the input layer to the hidden layer and the hidden layer to the output layer, respectively. Each neuron in the hidden layer is fully connected to all the neurons in the previous layer. Similarly, each neuron in the output layer is fully connected to all the neurons in the hidden layer. The connections are represented by the weight matrices W1 and W2.
But to continue:
hidden_with_time_axis = tf.expand_dims(hidden, 1) adds an additional dimension to the hidden state tensor to make its shape compatible with the input features tensor. This is done using the tf.expand_dims function, which inserts a new dimension at the specified axis (in this case, axis 1). This operation does not change the data in the tensor; it only adjusts the shape.
self.W2 is a dense layer defined in the Attention class. It is used to project the hidden state into a new space by applying a linear transformation (a weighted sum of the hidden state elements) with learned weights.
self.W2(hidden_with_time_axis) computes the weighted sum of the hidden state tensor (with the expanded shape) using the learned weights of the dense layer. This result is the hidden state projection.
After the hidden state projection is computed, it is combined with the input features projection (self.W1(features)) by element-wise addition:
python
score = tf.nn.tanh(self.W1(features) + self.W2(hidden_with_time_axis))```
The tanh activation function is then applied to the sum, resulting in the attention score. The attention score is used to compute the attention weights and the context vector, which helps the model focus on the most relevant parts of the input sequence when generating the output.
In summary, the hidden state projection (self.W2(hidden_with_time_axis)) is a linear transformation of the hidden state that makes it compatible with the input features so that they can be combined effectively to compute the attention scores in the attention mechanism.
Here's a breakdown of the code:
Import the TensorFlow library:
import tensorflow as tf
Define a custom layer class called Attention that inherits from tf.keras.layers.Layer:
class Attention(tf.keras.layers.Layer):
The __init__ method initializes the layer with a given number of units and creates three dense layers (fully connected layers) with the specified number of units:
def __init__(self, units):
super(Attention, self).__init__()
self.W1 = tf.keras.layers.Dense(units)
self.W2 = tf.keras.layers.Dense(units)
self.V = tf.keras.layers.Dense(1)
```
The call method is the core function of the layer, which is invoked when the layer is called during the forward pass of the model. It takes two arguments: features, which is the input data, and hidden, which is the hidden state of the model:
def call(self, features, hidden):
The hidden state is expanded along a new dimension to match the shape of the input features:
hidden_with_time_axis = tf.expand_dims(hidden, 1
The attention score is computed using the input features and the expanded hidden state. This is done by applying the dense layers W1 and W2 to the features and hidden state, respectively, and then summing the two results. The tanh activation function is applied to the sum:
```
score = tf.nn.tanh(self.W1(features) + self.W2(hidden_with_time_axis))
```
The attention weights are computed by applying the V dense layer to the score and then applying the softmax function along the time axis (axis 1). Softmax normalizes the weights so that they sum up to 1:
```
attention_weights = tf.nn.softmax(self.V(score), axis=1)
```
The context vector is computed by element-wise multiplication of the attention weights and the input features. Then, the weighted features are summed along the time axis:
context_vector = attention_weights * features
context_vector = tf.reduce_sum(context_vector, axis=1)
The call method returns the context vector and the attention weights. The context vector represents the input features weighted by their attention scores, which can be used by the model to focus on the most relevant parts of the input:
return context_vector, attention_weights
This attention mechanism can be used in various sequence-to-sequence models, such as Recurrent Neural Networks (RNNs) or Transformers, to improve their performance in tasks like machine translation, text summarization, and more.