Publication

Bounds on the Degree of High Order Binary Perceptrons

1996
Conference Papers

Abstract

High order perceptrons are often used in order to reduce the size of neural networks. The complexity of the architecture of a usual multilayer network is then turned into the complexity of the functions performed by each high order unit and in particular by the degree of their polynomials. The main result of this paper provides a bound on the degree of the polynomial of a high order perceptron, when the binary training data result from the encoding of an arrangement of hyperplanes in the Euclidian space. Such a situation occurs naturally in the case of a feedforward network with a single hidden layer of first order perceptrons and an output layer of high order perceptrons. In this case, the result says that the degree of the high order perceptrons can be bounded by the minimum of the number of inputs and the number of hidden units.

Official source

https://infoscience.epfl.ch/entities/publication/f9bdd137-3758-4d54-afcb-5fd05d1eadce

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1996
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/f9bdd137-3758-4d54-afcb-5fd05d1eadce

About this result

Related concepts (32)

Types of artificial neural networks

There are many types of artificial neural networks (ANN). Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown. Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat). The way neurons semantically communicate is an area of ongoing research.

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

Perceptron

In machine learning, the perceptron (or McCulloch-Pitts neuron) is an algorithm for supervised learning of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.

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Bounds on the Degree of High Order Binary Perceptrons

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