Neural Networks

Internal

• Machine Learning

Overview

A neural network consists of several layers of activation units ("individual neurons"), where one layer's activation unit output is connected to the inputs of all activation units of the successive layer. The behavior of an individual activation unit is described in the "Individual Unit" section. A neural network's topology, along with conventions and notations - which are essential to get right if you want to follow the linear algebra equations - are discussed in the "Topology" section. A neural network produces predictions by forward propagating input, then activations across its layers from left to right, until the output layer computes the hypothesis function, for a specific input sample. The forward propagation process is described in the "Forward Propagation" section. Forward propagation computations are performed based on a set of parameters (or weights) that are obtained by training the network. Training the network, or "fitting the parameters", is performed by a backpropagation algorithm, which is described in the "Backpropagation" section.

Individual Unit

Individual neural network units are computational units that read input features, represented as an unidimensional vector x₁ ... x_n in the diagram below, and calculate the hypothesis function as output of the unit. In most cases, an additional constant value x₀ is added to the feature vector. x₀ is not part of the feature vector, but it represents a bias value for the unit. The output value of the hypothesis function is also called the "activation" of the unit.

Input Feature

In context of an individual processing unit, the input feature refers to an individual value fed to a single input of the unit. For units in the first layer, the features are individual elements of the input matrix, while for units in the hidden layers or the output layers, the features are the activation values of the computational units from the previous layer.

Activation

The output value of the hypothesis function is also called the "activation" of the unit and it is conventionally named a_i^(j), where j is the layer the unit belongs to, and i is the index of the unit in the layer. For more details see Topology section below. The activation value is calculated by applying the logistic function to a linear combination of input features and parameters, thus the unit is referred to as a logistic unit with a sigmoid (logistic) activation function.