Python is a popular language for deep learning due to its versatility, simplicity, and broad support for libraries and frameworks. TensorFlow, Keras, scikit-learn and PyTorch are essential libraries used in deep learning, providing various tools and APIs for creating, training and deploying deep neural networks (DNNs).

Deep learning refers to the creating, and training of deep neural networks, which are computational models inspired by the structure and function of the human brain. Python is essential as a programming language for exploring deep neural networks and sigmoid functions.

But where to start? This article will cover the topic of deep learning for Python, including deep neural networks and sigmoid function, to understand the construction of deep neural networks.

What is Deep Learning?

Deep learning is a subfield of machine learning, which is a branch of AI (artificial intelligence) used to create algorithms that enable computers to learn independently and make decisions from data.

Deep learning focuses on building artificial neural networks that mimic how human brain neurons communicate and learn from data so the computer can solve complex problems automatically using pre-trained data. 

An artificial neural network consists of multiple interconnected layers or nodes to process and transform the input data to produce meaningful outputs.  

Deep learning has gained immense popularity and success in recent years due to several key factors:

• Data sufficiency
• Computational Power
• Architectural Innovations
• Transfer Learning

The application of deep learning is huge, and we can use it to handle massive datasets and complex tasks like image recognition, speech recognition, autonomous driving and many more. Its potential to automatically learn and extract relevant data from raw data has made it a game-changer and valuable technology in solving complex problems across various industries.

What is a Deep Neural Network?

Deep neural networks (DNNs), often called deep networks, are machine learning models consisting of multiple layers of interconnected nodes or neurons. Each layer works independently to achieve specific tasks by processing and transforming data hierarchically.  

The depth of multiple layers of nodes or neurons allows the model to learn and represent complex and abstract patterns within the given data.

The DNN nodes or neurons are organized into three types of layers:  

1. Input Layer: It is known as the initial or first layer of a Deep Neural Network (DNN), which is responsible for accepting the input data like images, text or numbers.
2. Hidden Layer: As the name suggests, this layer is located between the input and output layers of deep neural networks. Most DNNs contain one or more hidden layers. Hidden layers are directly responsible for learning and capturing hidden information from the input.
3. Output Layer: It is known as the last layer of Deep Neural Network (DNN), which is responsible for generating the desired output.

Each node or neuron in one layer is connected to every node or neuron in adjacent layers. Multiple layers of interconnected nodes or neurons characterize deep neural networks.

Activation Function

Activation functions are an important component of deep neural networks, which introduce non-linearity into computational models by allowing the network to learn complex patterns and relationships in the data.

Basically, it decides whether the neuron should be activated (i.e., “fired”) or not. And if the neuron will be activated, to what extent. More simply, it decides whether the neuron’s input to the neural network is important or not in the process of prediction or decision using mathematical operations.

There are a variety of activation functions available in a neural network, such as:

• Sigmoid Function
• Threshold Function
• Rectifier Function
• Hyperbolic Tangent Function

Let’s talk about the sigmoid function in detail to understand the workings of activation functions.

Sigmoid Function

The sigmoid function often called the logistic sigmoid function, is a mathematical function commonly used in deep learning and deep neural networks. The sigmoid function maps any real-valued number to a value between 0 and 1. Therefore, it is mainly used for computational models where we must predict the probability as an output. 

Graphing the sigmoid function looks like an S-shaped curve, which makes it helpful in predicting probabilities.

It demonstrates the larger the input (positive), the closer the output is to 1.0, while the smaller the input (negative), the closer the output is to 0.0.

The sigmoid function is defined as:

Where:

x is the input to the sigmoid function.

e is Euler's number (approximately 2.71828).

The sigmoid function is commonly used because it introduces non

linearity into the computational model. It is primarily used in the output layer, where deep neural networks are required to generate probabilities.

Deep Neural Network Example

We are going to build a simple neural network to demonstrate its ability to learn and predict the logical OR operation. We will go through the code step-by-step and then run it to predict the output from the given input.

Step 1: Import all the required library

First, we start by importing all the required libraries. In our case, we must import NumPy, TensorFlow and keras from TensorFlow.

import numpy as np
import tensorflow as tf
from tensorflow import keras

Where the NumPy is used for numerical operations, TensorFlow is used for building neural networks and the Keras module of TensorFlow is used for building and training neural networks.

Step 2: Generate synthetic data

We generate synthetic data using NumPy to represent the logical OR operation.

X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([0, 1, 1, 0])

Where the X variable contains the input data. 

The y variable contains the binary classification labels.

Step 3: Define the neural network

Then, we define a simple neural network using keras.Sequential.

model = keras.Sequential([
    keras.layers.Dense(2, activation='sigmoid', input_shape=(2,)),  # Input layer with 2 features and sigmoid activation
    keras.layers.Dense(1, activation='sigmoid') ])

The defined neural network consists of:

• Input layer with two neurons and a sigmoid function.
• Output layer with one neuron and a sigmoid activation function.

Step 4: Compile the model

We compile the model with the optimizer as “adam” and the loss as “binary_crossentropy”, and we specify that we want to track the model's accuracy during training.

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

Step 5: Train the model

After building and compiling the model, we need to train the model with data. So, we are using input data X and label y for 5000 epochs. Additionally, we define the argument verbose with the value 0 to suppress training updates.

model.fit(X, y, epochs=5000, verbose=0)

Step 6: Predictions

After completing the training part of the neural network, we go ahead and use the trained model to make some predictions on the same generated synthetic input data X.

predictions = model.predict(X)
print("Predictions:")
print(predictions)

Trained model predictions represent the predicted output for each input sample. Since this neural network uses the sigmoid function and is trained with the logical OR operation, the output will be between 0 and 1.

Expected Output

When we run the deep neural network, it starts predicting the output value between 0 and 1 based on the input value.

The output will look like this:

Predictions:

[[0.19620144]

[0.8595249 ]

[0.7904943 ]

[0.18041825]]

Conclusion

In this article, we’ve covered concepts like deep learning, deep neural networks, activation function, and sigmoid function, as well as deep neural network examples. We’ve also included a step-by-step guide to building your first deep neural network using the sigmoid function in Python. 

The created deep neural network has utilized the Python NumPy and TensorFlow libraries. We developed a neural network from scratch, which included defining the neural network with the sigmoid function, compiling and training the model, and finally predicting the values using the trained model. 

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