Notes on Deep Feedforward Network (MLP) (original) (raw)

Multilayer perceptron and neural networks

Wseas Transactions on Circuits and Systems, 2009

The attempts for solving linear inseparable problems have led to different variations on the number of layers of neurons and activation functions used. The backpropagation algorithm is the most known and used supervised learning algorithm. Also called the generalized delta algorithm because it expands the training way of the adaline network, it is based on minimizing the difference between the desired output and the actual output, through the downward gradient method (the gradient tells us how a function varies in different directions). Training a multilayer perceptron is often quite slow, requiring thousands or tens of thousands of epochs for complex problems. The best known methods to accelerate learning are: the momentum method and applying a variable learning rate. The paper presents the possibility to control the induction driving using neural systems.

An Analysis of the Perceptron-Multilayer Algorithm and its Applications

Perceptron Multilayer, 2024

This paper provides a comprehensive examination of the perceptron and multilayer perceptron (MLP) models, em- phasizing their historical significance and practical applications in artificial intelligence and machine learning. It begins with an overview of the perceptron, introduced by Frank Rosenblatt in 1958, as a foundational element in neural network research, capable of solving linear classification problems. The paper discusses the limitations of single-layer perceptrons, particularly their inability to address non-linear problems like the XOR problem, which led to the development of multilayer perceptrons and the backpropagation algorithm in the 1980s. The study details the implementation of a simple neural network with one hidden layer using C++, focusing on key com- ponents such as activation functions, weight updates, and training methods. It also explores the integration of the perceptron model with hardware components, specifically using the ESP32 microcontroller to demonstrate real-world applications, including controlling LEDs based on model predictions. Furthermore, the paper evaluates the performance and generalization capabilities of both perceptron and multilayer perceptron models through training and validation datasets. In addition to practical implementations, the paper discusses the evolution of neural network architectures, including convo- lutional and recurrent neural networks, and their relevance in solving complex problems beyond the scope of simpler models. The findings underscore the importance of understanding the perceptron as a stepping stone in the broader context of neural network research and its implications for future advancements in artificial intelligence.

General Model of the Perceptron

Models of Neurons and Perceptrons: Selected Problems and Challenges, 2018

The general model of the perceptron is presented in this chapter. The model consists of two parts. The first one is a mathematical description of structure of the artificial neural network. The description is based on graph theory and it is very general. It is valid for each type of neural networks, not only for the perceptron. The formal basis of training process of the perceptron is presented in Sect. 8.2. Next, in Sect. 8.3, the training process of the perceptron is discussed in the context of dynamical systems theory. 8.1 Model of a Structure of a Neural Network As it has been aforementioned, the general approach to a mathematical description of artificial neural networks structure is proposed in this section. Since it is based on graph theory, let us recall some very basic definitions that concern oriented graphsso called orgraphs. In this type of graphs the edges are oriented. Definition 8.1 Let a finite set A be given. An orgraph G is an ordered pair G := (A, Ed), where Ed ⊂ A × A. The set A is the set of the nodes of the graph G, whereas the set Ed is a set of its edges. Let us set that (a i , a j), ∈ Ed is the edge from the node a i to the node a j. Let us notice that, according to the above definition, at most one edge (a i , a j) belongs to the set Ed. The oriented graphs in which this condition is not satisfied are called multigraphs. They are not considered in this monograph. If graphs are used to description of artificial neural network structures, then the nodes denote neurons whereas the edges define connections between them. Let # A denotes the power (the number of elements) of the finite set A.

Strict Generalization in Multilayered Perceptron Networks

Lecture Notes in Computer Science, 2007

Typically the response of a multilayered perceptron (MLP) network on points which are far away from the boundary of its training data is not very reliable. When test data points are far away from the boundary of its training data, the network should not make any decision on these points. We propose a training scheme for MLPs which tries to achieve this. Our methodology trains a composite network consisting of two subnetworks : a mapping network and a vigilance network. The mapping network learns the usual input-output relation present in the data and the vigilance network learns a decision boundary and decides on which points the mapping network should respond. Though here we propose the methodology for multilayered perceptrons, the philosophy is quite general and can be used with other learning machines also.

Multilayer perceptron trained with numerical gradient

Proceedings of International Conference. on …, 2003

An application of numerical gradient (NG) to training of MLP networks is presented. Several versions of the algorithm and the influence of various parameters on the training process are discussed. Optimization of network parameters based on global search with numerical gradient is presented. Examples of two-dimensional projection of the error surface are shown and the influence of various numerical gradient parameters on the error surface is presented. The speed and accuracy of this method is compared with the search-based MLP training algorithm.

Nature of the learning algorithms for feedforward neural networks

1996

The neural network model (NN) comprised of relatively simple computing elements, operat¬ ing in parallel, offers an attractive and versatile framework for exploring a variety of learning structures and processes for intelligent systems. Due to the amount of research developed in the area many types of networks have been defined. The one of interest here is the multi-layer perceptron as it is one of the simplest and it is considered a powerful representation tool whose complete potential has not been adequately exploited and whose limitations need yet to be specified in a formal and coherent framework. This dissertation addresses the theory of gen¬ eralisation performance and architecture selection for the multi-layer perceptron; a subsidiary aim is to compare and integrate this model with existing data analysis techniques and exploit its potential by combining it with certain constructs from computational geometry creating a reliable, coherent network design process which conforms t...

The Backpropagation Algorithm Functions for the Multilayer Perceptron

The attempts for solving linear unseparable problems have led to different variations on the number of layers of neurons and activation functions used. The backpropagation algorithm is the most known and used supervised learning algorithm. Also called the generalized delta algorithm because it expands the training way of the adaline network, it is based on minimizing the difference between the desired output and the actual output, through the downward gradient method (the gradient tells us how a function varies in different directions). Training a multilayer perceptron is often quite slow, requiring thousands or tens of thousands of epochs for complex problems. The best known methods to accelerate learning are: the momentum method and applying a variable learning rate.