Keras serves as TensorFlow’s high-level API, pioneering a user-friendly, modular deep learning framework. Here are the key features:

Key Features and Advantages

• High-Level Abstraction: Keras simplifies model construction, making it accessible even to novices in deep learning.

• Fast Prototyping: The API allows rapid building and testing of neural network architectures.

• Compatibility: It’s compatible with TensorFlow, Theano, and Microsoft Cognitive Toolkit (CNTK).

• Support for Multiple Backends: Enables users to move between different computation engines seamlessly.

• Modularity and Flexibility: Layers, models, and optimizers in Keras are modular and customizable.

• Integrated Utilities: Offers a built-in toolset for tasks like data preprocessing, model evaluation, and visualization.

• Wide Range of Applications: Keras is customizable and adaptable, catering to various machine learning tasks.

• Huge Community: Due to its user-friendly yet powerful nature, Keras has a large and active community of users.

  Keras serves as an abstraction layer, offering a high-level, user-friendly interface for building and training neural network models in TensorFlow.

Keras vs Pure TensorFlow

When should you use Keras over pure TensorFlow, and vice versa?

Keras

• Advantages:

  • User-Friendly: Keras is easier to learn and use for beginners.
  • Faster Prototyping: Its simplicity and mode of use aid in rapid model creation and testing.
  • Clear and Concise Code: Keras’s high-level abstraction means code is often more easy to read and follow.

• When to Use It:

  • For quick, small to medium-sized projects
  • When you prize simplicity and “rapid proof of concept”
  • If you’re starting out in deep learning

TensorFlow with tf.keras

• Advantages:

  • Seamless Integration: As TensorFlow’s high-level API, it integrates smoothly with lower-level TensorFlow operations and workflows.
  • Greater Control: Offers more flexibility and control over the model and training process.
  • Real-World Applications: Suits larger, more complex projects and customized models.

• When to Use It:

  • For projects requiring advanced or highly specialized models
  • If you prioritize control and scalability
  • In production-grade applications

Code Example: CIFAR-10 Classification with Keras

Here is the Python code:

import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Conv2D, MaxPooling2D, Flatten, Dense

# Load and prepare the CIFAR-10 dataset
(train_images, train_labels), (test_images, test_labels) = tf.keras.datasets.cifar10.load_data()
train_images, test_images = train_images / 255.0, test_images / 255.0

# Model definition
model = Sequential([
  Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)),
  MaxPooling2D((2, 2)),
  Conv2D(64, (3, 3), activation='relu'),
  MaxPooling2D((2, 2)),
  Conv2D(64, (3, 3), activation='relu'),
  Flatten(),
  Dense(64, activation='relu'),
  Dense(10, activation='softmax')
])

# Compile the model
model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy'])

# Train the model
model.fit(train_images, train_labels, epochs=10, validation_data=(test_images, test_labels))

A Deep Learning Framework acts as a vital foundation for designing and training neural networks. It facilitates numerous tasks such as data preprocessing, model specification, optimization settings, and model evaluation.

Purpose of a Deep Learning Framework

• Abstraction: Hides intricate math behind user-friendly interfaces.
• Performance Optimizations: Often uses GPU acceleration to expedite computations.
• Versatility: Allows for both high-level and low-level model architecture design, catering to novice and experienced users.
• Scalability: Streamlines deployment, enabling the transition from small-scale experiments to large-scale industrial applications.

Core Components

1. Model Library: Offers a variety of network architectures, such as CNNs, RNNs, and GANs, along with pre-trained models for transfer learning.
2. Layers & Modules: Building blocks for constructing models, ranging from simple ones like dense layers to more intricate ones like LSTM cells.
3. Loss Functions: Metrics quantifying model performance during training.
4. Optimizers: Algorithms guiding the model’s learning process.
5. Data Utilities: Accommodates data pre-processing, augmentation, and pipelines for seamless feeding of data to models.

Common Deep Learning Frameworks

• TensorFlow (Google): Its distinctive feature is its data flow graph mechanism.

• Keras (Community-Maintained Lens on TensorFlow): An API designed for user-friendliness, acting as the go-to choice for beginners and rapid prototypers.

• PyTorch (Facebook): Based on a dynamic computation graph paradigm, it has gained traction for its intuitive nature and has become the tool of choice for numerous machine learning researchers.

• Caffe (UC Berkeley): This framework shines in its capacity to efficiently handle computer vision tasks and deep learning networks.

• Theano (University of Montreal): One of the earlier frameworks, it offered functionalities for defining, optimizing, and evaluating mathematical expressions.

• MXNet (Apache): Known for its speed and efficiency, MXNet supports various front-ends (including Keras) and has embedded support for a range of high-level languages.

• Chainer (Preferred by RIKEN and Preferred Networks Co., Ltd.): Standing out with its ease-of-use and straightforwardness, it is appreciated for its flexibility in network design and its dynamic graph mechanism.

A Keras model is built around its core components, the Input and Output Layers, and is structured through its Architecture and Training Configurations.

Key Components of a Keras Model

1. Input Layer: Passes data directly to the first hidden layer. It includes shape information for the data.

2. Output Layer: The final layer that produces predictions. The type of Model (Sequential or Functional) determines its shape.

3. Architecture: The arrangement of layers. Keras offers two main types: the straightforward Sequential model and the more flexible Functional model.

4. Training Configurations: Define how the model learns from data using optimizers, loss functions, and evaluation metrics.

Code Example: Keras Model Building (Sequential and Functional)

Here is the Python code:

# Sequential model
import keras
from keras.models import Sequential
from keras.layers import Dense

model = Sequential()
model.add(Dense(units=64, activation='relu', input_dim=100))
model.add(Dense(units=1, activation='sigmoid'))

# Functional model
inputs = keras.Input(shape=(100,))
x = Dense(units=64, activation='relu')(inputs)
outputs = Dense(units=1, activation='sigmoid')(x)
model = keras.Model(inputs=inputs, outputs=outputs)

Flexibility of Keras Functional Model

The Functional API can effectively handle complex architectures like multi-input and multi-output models, shared layers, and more intricate network topologies, making it an ideal choice for sophisticated model designs. This aspect provides more versatility compared to the straightforward Sequential model.

For instance, in the case of an image model which processes images from two taps, we can split the input into two branches and then combine those branches’ output. Here is the code, in Python, for it:

from keras.layers import Input, Embedding, LSTM, concatenate, Dense
from keras.models import Model

input_1 = Input(shape=(28, 28))
input_2 = Input(shape=(28, 28))

shared_embedding = Embedding(1000, 64)
x1 = shared_embedding(input_1)
x2 = shared_embedding(input_2)

lstm_out = LSTM(32)

out_1 = lstm_out(x1)
out_2 = lstm_out(x2)

concatenated = concatenate([out_1, out_2])

output = Dense(1, activation='sigmoid')(concatenated)

model = Model(inputs=[input_1, input_2], outputs=output)

In Keras, you can configure a neural network through two approaches:

01. Sequential Model Configuration

This method is suitable for simple network architectures characterized by a linear, one-input-one-output stacking of layers.

Code Example: Sequential Model

Here is the Python code:

import keras
from keras import layers

# Initialize a sequential model
model = keras.Sequential()

# Add layers one by one
model.add(layers.Dense(64, activation='relu', input_shape=(784,)))
model.add(layers.Dense(10, activation='softmax'))

02. Functional API Model Configuration

This method is the recommended choice for more complex architecture designs such as multi-input and multi-output models, layer sharing, and non-linear topologies.

Code Example: Functional API Model

Here is the Python code:

import keras
from keras import layers

# Input tensor placeholder
inputs = keras.Input(shape=(784,))

# Hidden layers
x = layers.Dense(64, activation='relu')(inputs)
x = layers.Dense(64, activation='relu')(x)

# Output layer for 10-class classification
outputs = layers.Dense(10, activation='softmax')(x)

# Define the model
model = keras.Model(inputs=inputs, outputs=outputs)

While Sequential and Functional APIs in Keras both facilitate the creation of neural networks, they differ in flexibility, complexity of models that can be built, and the way each API is used.

Key Distinctions

• Control Flow:

  • Sequential: Fixed.
  • Functional: Arbitrary, using Keras layers.

• Model Complexity:

  • Sequential: Suited for straight, linear stacks of layers where each layer has one input and one output.
  • Functional: For complex, multi-input, multi-output architectures, including shared layers and branches.

• Use Case:

  • Sequential: Ideal for beginners and linear networks.
  • Functional: Better for advanced architectures and research.

• Evaluation and Inference:

  • Sequential: Simple.

    • For evaluation, use model.evaluate().
    • For prediction, use model.predict().

  • Functional: Potentially complex, with custom feedback mechanisms.

    • For evaluation, use model.evaluate() and possibly custom measures.
    • For prediction, typically model.predict(), but can involve multi-input or multi-output structures.

Benefits of Using the Functional API

• Multi-Modal Inputs and Multi-Output Structures:

  • Models can process different types of data through the use of multiple input layers.
  • Useful for tasks like joint sentiment analysis and emotion recognition from text and images in social media data.

• Model Branching:

  • Encourages the creation of ‘branching’ or ‘dual pathway’ models where different inputs may follow separate paths before being combined.

• Model Sharing with Multiple Inputs and Outputs:

  • Supports models where multiple output layers could be predicted simultaneously using the same internal state from the shared layers.

• Non-Sequential Connectivity:

  • Non-linear connections can exist between layers.

• Custom Loss Functions and Model Metrics:

  • Allows for the computation of more complicated loss functions to handle the multiple outputs or inputs.

• Layer Sharing and Resue:

  • Layers can be reused across different parts of the model, making it easier to work with complex architectures.

Code Example: Multi-Input/Output Model using Functional API

Here is the Python code:

import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers

# Define input for numerical data
numerical_input = keras.Input(shape=(2,), name="numerical_input")

# Define input for categorical data
categorical_input = keras.Input(shape=(3,), name="categorical_input")

# Multi-modal input concatenation
concatenation = layers.Concatenate()([numerical_input, categorical_input])

# Hidden layer
hidden1 = layers.Dense(3, activation='relu')(concatenation)

# Define two output branches from the hidden layer
output1 = layers.Dense(1, name="output1")(hidden1)
output2 = layers.Dense(1, name="output2")(hidden1)

# Create the model
model = keras.Model(inputs=[numerical_input, categorical_input], outputs=[output1, output2])

# Compile the model
model.compile(optimizer=keras.optimizers.Adam(learning_rate=0.01), 
              loss={"output1": "mse", "output2": "mse"},
              metrics={"output1": "mae", "output2": "mae"})

Keras can be installed using pip or conda. Before installation, make sure you have Python $>= 3.5$, as Keras does not support Python 2.

Installing Keras

Using pip:

pip install tensorflow   # Install TensorFlow backend as Keras may not work without TensorFlow.
pip install keras

Using conda (recommended with Anaconda distribution):

conda install -c conda-forge keras
conda install -c conda-forge tensorflow

If using TensorFlow as the Keras backend, it is recommended to install Keras with TensorFlow as it is incorporated better.

Setting Keras Backend

After the installation, you may need to configure the Keras backend. If using TensorFlow and installed it separately, you typically don’t need to set it up; otherwise, to link Keras to TensorFlow, run the following Python code:

import os
os.environ['KERAS_BACKEND'] = 'tensorflow'

Verifying the Installation

To check if Keras is installed and set up correctly, import Keras and verify the configuration using the following Python code:

import keras
from keras import backend as K

print(keras.__version__)  # Display Keras version.
print(K.backend())        # Display the current backend (e.g., 'tensorflow').

Keras offers several distinct advantages as a library for building neural networks over other frameworks like TensorFlow or PyTorch.

Key Advantages of Keras

1. Intuitive Interface: Keras is designed with simplicity in mind – making it ideal for both beginners and experts. Its API is clear and concise, providing a smooth learning curve.

2. Modularity and Flexibility: Keras models are created by stacking layers making them highly intuitive. It allows easy model reusability, modular architecture, models’ customization, and experiment management.

3. Back-end Agnosticism: Although originally built on top of TensorFlow, Keras is now integrated with TensorFlow, Theano, and CNTK. It’s especially useful when one framework has an edge for specific tasks or hardware.

4. Multiple Compute Platforms: Keras supports CPU and GPU computation, and its compatibility with Google’s TPU (Tensor Processing Unit) through TensorFlow makes it highly versatile.

5. Clean and Lightweight: With relatively fewer lines of code, Keras is less verbose than other deep learning frameworks, enhancing readability and speed of model prototyping.

6. Increased Performance in Data Parallel Jobs: Data-parallel jobs (like training on multisocket CPUs and multiple GPUs) see performance gains as tensors get split at computation boundaries.

7. Package Delivery and Resource-efficiency with Tensors: It facilitates the sharing, command sequences, and eliminates redundant memory copying.

Contextual Comparison

• TensorFlow alone offers in-depth control. However, the trade-off is added complexity and a steeper learning curve.

• PyTorch, especially favored by researchers, boasts dynamic computation graphs and imperative programming, but the trade-off is increased code complexity.

• Keras balances a focus on user-friendliness, efficient experimentation, and deployment-ready models.

Incorporating higher-level libraries, such as tf.keras and keras-tuner, adds streamlined model optimization, auto-ML capability, and improved compatibility with TensorFlow features like TF Records, Estimators, and TPUs.

Keras provides straightforward methods to save and load trained models.

Save and Load Model with Keras

You can save or load two types of Keras models:

1. Architecture-Only Models: Saved as JSON or YAML files. These files contain the model’s architecture but not its weights or training configuration.
2. Stateful Models: Saved as Hierarchical Data Format (HDF5) files. They store the model’s architecture, weights, and training configuration. This is the preferred way for saving trained models.

Here is the Keras code that demonstrates how to do that:

Code: Save and Load Models in Keras

Here is the Python code:

from keras.models import model_from_json

# Save model in JSON format (architecture-only)
model_json = model.to_json()
with open("model.json", "w") as json_file:
    json_file.write(model_json)

# Load model from JSON
json_file = open('model.json', 'r')
loaded_model_json = json_file.read()
json_file.close()
loaded_model = model_from_json(loaded_model_json)

# Save model in HDF5 format (stateful model)
model.save("model.h5")

# Load model from HDF5
loaded_model_h5 = load_model('model.h5')

Additional Considerations

• Historical Data: The HDF5 format does not save the training metrics. This means that the loaded model will not include the training and validation histories. If you need those, you’ll have to save them separately.

• Custom Objects: If your model uses custom layers or other custom objects, you need to pass them to the loading mechanism using the custom_objects parameter. This is particularly crucial when loading pre-trained models.

The Dense layer in Keras is a standard, fully-connected neural network layer. It is essential in most network architectures, serving as the primary mechanism for training model parameters. This layer ensures a structured, efficient data flow in both forward and backward propagation.

Key Components

• Dense Layer: Each neuron in this layer is connected to every neuron in the preceding and succeeding layers. Mathematically, it multiplies the input data by a weight matrix and adds a bias vector.
• Activation Function: This non-linear function introduces complexity and adaptability to the network.

Mathematical Representation

The output $y$ from a single neuron in a dense layer with $n$ input features is calculated as:

$$y = \sigma \left( \sum_{i=1}^{n} (w_i \cdot x_i) + b \right)$$

where:

• $\sigma$ is the activation function.
• $w_i$ are the weights associated with each input feature $x_i$.
• $b$ is the bias term.

Code Example: Single Neuron in a Dense Layer

Here is the Python code:

# Import relevant libraries
from keras.models import Sequential
from keras.layers import Dense

# Initialize neural network model
model = Sequential()

# Add a dense layer with one neuron and sigmoid activation
model.add(Dense(units=1, input_dim=1, activation='sigmoid'))

# Compile the model
model.compile(optimizer='adam', loss='binary_crossentropy')

In Keras, you can create a Convolutional Neural Network (CNN) using the Sequential model. This model requires you to add layers in a sequential pattern.

To build a CNN, you would use Conv2D, MaxPooling2D, and other layers as well as flatten and dense layers.

Key Keras Modules

• Layers: Define the layers, such as Dense for fully connected layers and Conv2D for convolutional layers.
• Model: Combines layers to build the neural network.
• Optimizers: Configures the model for training, e.g., Adam.
• Loss Functions: Indicate the goal of the learning task, e.g., categorical_crossentropy for classification.
• Metrics: Measure performance, e.g., accuracy for classification tasks.

Step-by-Step with Code Example

Here is the Python code:

  from keras.models import Sequential
  from keras.layers import Conv2D, MaxPooling2D, Flatten, Dense

  # Create a Sequential model
  model = Sequential()

  # Add Convolutional layers
  model.add(Conv2D(32, (3, 3), input_shape=(64, 64, 3), activation='relu'))
  model.add(MaxPooling2D(pool_size=(2, 2)))

  # Flatten the output from preceding layers
  model.add(Flatten())

  # Add a Dense layer for final classification
  model.add(Dense(units=128, activation='relu'))  # Optional intermediate layer
  model.add(Dense(units=1, activation='sigmoid'))  # Output layer for binary classification

  # Compile the model before fitting it to data
  model.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy'])

A Recurrent Neural Network (RNN) processes sequential data by maintaining a hidden state that encapsulates the network’s knowledge up to a certain point in the sequence.

For instance, if our input sequence is $(x_1, x_2, x_3, \ldots, x_T)$, the RNN updates its hidden state at each time step $t$ using the input at that time step $x_t$ and the previous hidden state $h_{t-1}$. Mathematically, this is represented as:

$$h_t = \text{RNN}(x_t, h_{t-1})$$

Key Distinctive Features of RNNs

Concept of Hidden State

RNNs leverage a notion called the hidden state, $h_t$, to maintain a contextual understanding of all the preceding elements in the sequence. The hidden state is recursively updated at each time step using both the current input element and the previous hidden state.

Shared Parameters

In an RNN, the transformation that maps the input and the previous hidden state to the next hidden state uses the same set of parameters for every time step. This feature enables the RNN to generalize across the sequence.

Mathematically:

$$h_t = \text{tanh}(W_{hh}h_{t-1} + W_{xh}x_t + b_h)$$

Here, $W_{hh}$ and $W_{xh}$ are the shared weight matrices, and $b_h$ is the shared bias vector.

How to Implement an RNN in Keras

Keras provides a high-level API for building RNNs. Specifically, you can use the SimpleRNN layer to construct basic RNN models.

Here is the Python code:

from keras.models import Sequential
from keras.layers import SimpleRNN, Embedding
from keras.layers import Dense

model = Sequential()

# SimpleRNN with 32 hidden neurons
model.add(SimpleRNN(32, input_shape=(None, 100))) # Input shape: (num_timesteps, input_dim)

# A final Dense layer for prediction
model.add(Dense(1, activation='sigmoid'))

model.summary()

In the example above:

• We define a Sequential model.
• We add a SimpleRNN layer with 32 hidden neurons. The layer infers the input shape, (num_timesteps, input_dim), from the shape of its input.
• We add a final Dense layer with a sigmoid activation for binary classification tasks.

Dropout layers are a powerful tool designed to prevent overfitting in deep learning models.

Purpose of Dropout Layers

• Regularization: Dropout discourages overfitting, enhancing a model’s ability to generalize.
• Ensemble Learning: It simulates training and testing on multiple different thinned-out (or “dropped-out”) networks, which can boost robustness.

Dropout Mechanism

During training, each neuron in the dropout layer has a probability $p$ of being “dropped out” or temporarily removed. The remaining neurons are then “scaled up” by a factor of $1/(1-p)$ to maintain model expectation.

At inference, all neurons are active, but their outputs are divided by $1-p$ to ensure consistency with the training phase.

Code Example: Using Dropout in Keras

Here is the Python code:

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, Dropout

model = Sequential([
    Dense(64, input_shape=(10,), activation='relu'),
    Dropout(0.2),  # 20% dropout rate
    Dense(64, activation='relu'),
    Dropout(0.3),  # 30% dropout rate
    Dense(1, activation='sigmoid')
])

model.compile(optimizer='sgd', loss='binary_crossentropy')
model.fit(X_train, y_train, epochs=20, batch_size=32, validation_data=(X_val, y_val))

Batch Normalization is key to faster and more stable training in neural networks.

In Keras, you can incorporate Batch Normalization via the BatchNormalization layer and also via the use_bias argument with layers like Dense and Conv2D.

Code Example: Keras Model with Batch Normalization

Here is the Python code:

from keras.models import Sequential
from keras.layers import Dense, Activation, BatchNormalization

model = Sequential()

# First hidden layer with Batch Normalization
model.add(Dense(64, input_dim=100))  # Assuming 100 input dimensions
model.add(BatchNormalization())
model.add(Activation('relu'))

# Second hidden layer with Batch Normalization(Python Module)
model.add(Dense(64))
model.add(BatchNormalization())

# Third hidden layer with Batch Normalization AND no bias term
model.add(Dense(64, use_bias=False))
model.add(BatchNormalization())

# Final output layer without Batch Normalization
model.add(Dense(10))
model.add(Activation('softmax'))

model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])

Custom layers in Keras enable you to create proprietary operations or architectures not pre-defined in the standard libraries.

Implementing a custom layer typically involves handling input and output shapes, as well as the layer’s core logic.

Code Example: Custom Layer in Keras

Here is the Python code:

import tensorflow as tf

class MyCustomLayer(tf.keras.layers.Layer):
    def __init__(self, output_dim, activation=None):
        super(MyCustomLayer, self).__init__()
        self.output_dim = output_dim
        self.activation = tf.keras.activations.get(activation)

    def build(self, input_shape):
        self.kernel = self.add_weight("kernel", 
                                      shape=[int(input_shape[-1]), self.output_dim])

    def call(self, inputs):
        return self.activation(tf.matmul(inputs, self.kernel))

# Instantiate the layer
my_layer = MyCustomLayer(32, activation='relu')

# Test the layer
output = my_layer(tf.zeros([10, 5]))
assert output.shape == (10, 32)

In this code:

• MyCustomLayer inherits from tf.keras.layers.Layer.
• The constructor __init__ sets layer attributes. Here, output_dim and activation. The activation parameter is optional. If you do not need or want to specify an activation function, set the default value to None and use the tf.keras.activations.get method as shown in the code.
• The method build is where layer weights are defined. Here, a 2D kernel weight shared by all inputs is created.
• The call method describes the layer’s computation - in this case, a matrix multiplication followed by an activation function.

Sequential vs. Functional API

You can instantiate this custom layer using both the Sequential and Functional API. The code below illustrates both:

Sequential API

model = tf.keras.Sequential([MyCustomLayer(32, activation='relu')])

Functional API

inputs = tf.keras.Input(shape=(5,))
x = MyCustomLayer(32, activation='relu')(inputs)
model = tf.keras.Model(inputs=inputs, outputs=x)

In Keras, the implementation of Residual Networks (ResNets) is straightforward, primarily due to the framework’s modularity.

ResNets introduced a novel concept with the identity shortcut connection, or skip-connection, to ease training and enable the building of deeper networks. Keras simplifies the implementation of these connections using, for example, Add layers.

Key Components of a ResNet Model

1. Convolutional Blocks: A sequence of convolutional and activation layers.
2. Identity Blocks: These contain at least three layers with a skip-connection to maintain the same feature map size.

Code Example: ResNet Identity Block in Keras

Here is the Keras compatible Python code:

from keras.layers import Input, Conv2D, BatchNormalization, Activation, Add
from keras.models import Model

def identity_block(X, f, filters):
    """
    Implementation of the identity block as defined by the ResNet architecture in Keras.
    
    Arguments:
    X -- input to the block
    f -- integer, specifying the shape of the CONV's window for the main path
    filters -- python list of integers, defining the number of filters in the CONV layers
    
    Returns:
    X -- output of the identity block
    """
    
    # Retrieve Filters
    F1, F2, F3 = filters
    
    # Save the input value:
    X_shortcut = X
    
    # First component of main path
    X = Conv2D(filters = F1, kernel_size = (1, 1), strides = (1,1), padding = 'valid')(X)
    X = BatchNormalization(axis = 3)(X)
    X = Activation('relu')(X)

    # Second component of main path
    X = Conv2D(filters = F2, kernel_size = (f, f), strides = (1,1), padding = 'same')(X)
    X = BatchNormalization(axis = 3)(X)
    X = Activation('relu')(X)

    # Third component of main path
    X = Conv2D(filters = F3, kernel_size = (1, 1), strides = (1,1), padding = 'valid')(X)
    X = BatchNormalization(axis = 3)(X)

    # Add shortcut value to main path, and pass it through a RELU activation
    X = Add()([X, X_shortcut])
    X = Activation('relu')(X)
    
    return X

# To test the implementation
input_shape = (3, 256, 256)  # for RGB images
X_input = Input(input_shape)
X = identity_block(X_input, f=3, filters=[64, 64, 256])
model = Model(inputs = X_input, outputs = X)
model.summary()