FeedForward Neural Networks: Layers, Functions, and Importance

Prashant Sharma 22 Jun, 2024
7 min read

Introduction

Feed-forward Neural Networks, also known as Deep feedforward Networks or Multi-layer Perceptrons, are the focus of this article. For example, Convolutional and Recurrent Neural Networks (used extensively in computer vision applications) are based on these networks. We’ll do our best to grasp the key ideas in an engaging and hands-on manner without having to delve too deeply into mathematics.

Search engines, machine translation, and mobile applications rely on deep learning technologies. These technologies stimulate the human brain to identify and create patterns from various types of input.

A feedforward neural network is a key component of this fantastic technology since it aids software developers with pattern recognition and classification, non-linear regression, and function approximation.

Let’s look at this fundamental aspect of the neural network’s construction.

Feedforward Neural Network

This article was published as a part of the Data Science Blogathon.

What is Feed-forward Neural Networks?

A feedforward neural network is an artificial neural network in which nodes’ connections do not form a loop. Often referred to as a multi-layered network of neurons, feedforward neural networks are so named because all information flows forward only.

Data enters the input nodes, travels through the hidden layers, and exits the output nodes. The network lacks links, allowing the information leaving the output node to be sent back into the network.

The purpose of feedforward neural networks is to approximate functions.

Here’s how it works

A classifier uses the formula y = f* (x).

This assigns the value of input x to the category y.

The feedfоrwаrd netwоrk will mар y = f (x; θ). It then memorizes the value of θ that most closely approximates the function.

The Google Photos app shows that a feedforward neural network is the foundation for photo object detection.

Types of Neural Network’s Layers

The following are the components of a feedforward neural network:

Layer of input

It contains the neurons that receive input. The data is subsequently passed on to the next tier. The input layer’s total number of neurons equals the number of variables in the dataset.

Hidden layer

This is the intermediate layer, which is concealed between the input and output layers. It has many neurons that alter the inputs and then communicate with the output layer.

Output layer

It is the last layer and depends on the model’s construction. The output layer is the expected feature, as you know the desired outcome.

Neurons weights

Weights describe the strength of a connection between neurons. A weight’s value ranges from 0 to 1.

Cost Function in Feedforward Neural Network

The cost function is an important factor of a feedforward neural network. Generally, minor adjustments to weights and biases have little effect on the categorized data points. Thus, a method for improving performance can be determined by making minor adjustments to weights and biases using a smooth cost function.

The mean square error cost function is defined as follows:

Feedforward Neural Network Formula

 Where,

w = weights collected in the network

b = biases

a = output vectors

x = input

‖v‖ = usual length of vector v

Loss Function in Feedforward Neural Network

Loss function in Feedforward Neural Network

The cross-entropy loss associated with multi-class categorization is as follows:

Cross Entropy loss

Also Read: Understanding Loss Function in Deep Learning

Gradient Learning Algorithm

The Gradient Descent Algorithm repeatedly calculates the next point using gradient at the current location, then scales it (by a learning rate) and subtracts the achieved value from the current position (makes a step) (makes a step). It subtracts the value since we want to decrease the function (to increase it would be adding) (and to maximize it would be adding). This procedure may be written as:

There’s a crucial parameter η, which adjusts the gradient and hence affects the step size. In machine learning, it is termed learning rate and substantially affects performance.

  • The smaller the learning rate, the longer GD converges or may approach maximum iteration before finding the optimal point
  • If the learning rate is too great, the algorithm may not converge to the ideal point (jump around) or diverge altogether.

The Gradient Descent method’s steps are:

  1. Pick a beginning point (initialization)
  2. Compute the gradient at this spot
  3. Produce a scaled step in the opposite direction to the gradient (objective: minimize) (objective: minimize)
  4. Repeat points 2 and 3 until one of the conditions is met:
  • maximum number of repetitions reached
  • step size is smaller than the tolerance.

The following is an example of how to construct the Gradient Descent algorithm (with steps tracking):

The function accepts the following five parameters:

  1. Starting point: In our example, we specify it manually, but it is frequently determined randomly.
  2. Gradient function – must be defined in advance
  3. Learning rate – factor used to scale step sizes
  4. Maximum iterations
  5. Tolerance for the algorithm to be stopped on a conditional basis (in this case, a default value is 0.01)

Example- A quadratic function

Consider the following elementary quadratic function:

Because it is a univariate function, a gradient function is as follows:

Let us now write the following methods in Python:def func1(x): return x**2-4*x+1 def gradient_func1(x):

  return 2*x – 4

With a learning rate of 0.1 and a starting point of x=9, we can compute each step manually for this function. Let us begin with the first three steps:

The python function is invoked as follows:history, result = gradient_descent(9, gradient_func1, 0.1, 100)

The animation below illustrates the GD algorithm’s steps at 0.1 and 0.8 learning rates. As the algorithm approaches the minimum, the steps become steadily smaller. Jumping from one side to the other is necessary for a faster learning rate before convergence.

Gradient Leaning
The first ten stages were conducted by GD to determine the learning rate for small and large groups. 

The following diagram illustrates the trajectory, number of iterations, and ultimate converged output (within tolerance) for various learning rates:

Feedforward Neural Network | Graph

The Need for a Neuron Model

Suppose the inputs to the network are pixel data from a character scan. There are a few things you need to keep in mind while designing a network to classify a digit appropriately:

You must experiment with the weights to see how the network learns. To reach perfection, weight variations of just a few grams should have a negligible effect on production.

On the other hand, what if a minor change in the weight results in a large change in the output? The sigmoid neuron model can resolve this issue.

Sigmoid Function

Applications of Feedforward Neural Network

These neural networks are utilized in a wide variety of applications. The following are units denote several of them:

  • Physiological feedforward system: Feedforward management is exemplified by the central involuntary system’s usual preventative control of heartbeat before exercise.
  • Gene regulation and feedforward: A theme predominates throughout the famous networks, and this motif has been demonstrated to be a feedforward system for detecting non-temporary atmospheric alteration.
  • Parallel feedforward compensation with derivative: This is a relatively recent approach for converting the non-minimum component of an open-loop transfer system into the minimum part.

Conclusion

Deep learning is a field of software engineering that has accumulated a massive amount of study over the years. Researchers have developed several neural network designs for use with diverse data types. Applying neural networks to large datasets requires enormous computing power and equipment acceleration. Designers achieve this by arranging a Graphics Processing Units (GPUs) system in a cluster.

New GPU users can find free customized settings on the Internet, which they can download and use without charge. They most commonly use Kaggle Notebooks and Google Colab Notebooks. To build a good feedforward neural network, you must test the network design several times.

Also Read: How to Load Kaggle Datasets Directly Into Google Colab?

Frequently Asked Questions

Q1. What is the difference between feedforward and deep neural networks?

A. Feedforward neural networks have a simple, direct connection from input to output without looping back. In contrast, deep neural networks have multiple hidden layers, making them more complex and capable of learning higher-level features from data.

Q2. Is CNN a Feedforward Network?

A. Yes, Convolutional Neural Networks (CNNs) are feedforward networks. They process input data through layers in a single forward pass, applying convolutional filters to detect patterns and features, particularly effective for image and spatial data.

Q3. What is the difference between feedforward and feedbackward neural networks?

A. Feedforward neural networks move data in one direction from input to output, without loops. In contrast, feedback (or recurrent) neural networks allow connections to cycle back, enabling the network to maintain a state and process sequences or temporal data.

Q4. What is the main difference between a feedforward neural network and a recurrent neural network?

A. Feedforward neural networks process data in a single pass from input to output without considering temporal dynamics. However, recurrent neural networks (RNNs) have loops that allow them to maintain a memory of previous inputs, making them suitable for sequential and time-dependent tasks.

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Prashant Sharma 22 Jun, 2024

Currently, I Am pursuing my Bachelors of Technology( B.Tech) from Vellore Institute of Technology. I am very enthusiastic about programming and its real applications including software development, machine learning and data science.

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