In a feed forward network information at a later level, never backpropagates to a previous level

A feedforward neural network is an artificial neural network where connections between the units do not form a directed cycle. This is different from recurrent neural networks. An artificial neural network (ANN), often just called a neural network (NN), is an interconnected group of artificial neurons that uses a mathematical model or computational model for information processing based on a connectionist approach to computation. ... In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. ... A recurrent neural network is a neural network where the connections between the units form a directed cycle. ...

The feedforward neural network was the first and arguably simplest type of artificial neural network devised. In this network, the information moves in only one direction, forward, from the input nodes, through the hidden nodes (if any) and to the output nodes. There are no cycles or loops in the network.

Single-layer perceptron

The earliest kind of neural network is a single-layer perceptron network, which consists of a single layer of output nodes; the inputs are fed directly to the outputs via a series of weights. In this way it can be considered the simplest kind of feed-forward network. The sum of the products of the weights and the inputs is calculated in each node, and if the value is above some threshold (typically 0) the neuron fires and takes the activated value (typically 1); otherwise it takes the deactivated value (typically -1). Neurons with this kind of activation function are also called McCulloch-Pitts neurons or threshold neurons. In the literature the term perceptron often refers to networks consisting of just one of these units. They were described by Warren McCulloch and Walter Pitts in the 1940s. An artificial neuron (also called a node or Nv neuron or Binary neuron or McCulloch-Pitts neuron) is an abstraction of biological neurons and the basic unit in an artificial neural network. ... The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt. ... Warren McCulloch (November 16, 1899 - September 24, 1969) was an American neurophysiologist and cybernetician. ... Walter Pitts (1923? - 1969) was a logician who worked in the field of cognitive psychology. ... This article or section does not cite any references or sources. ...

A perceptron can be created using any values for the activated and deactivated states as long as the threshold value lies between the two. Most perceptrons have outputs of 1 or -1 with a threshold of 0 and there is some evidence that such networks can be trained more quickly than networks created from nodes with different activation and deactivation values.

Perceptrons can be trained by a simple learning algorithm that is usually called the delta rule. It calculates the errors between calculated output and sample output data, and uses this to create an adjustment to the weights, thus implementing a form of gradient descent. The delta rule is a rule for updating the weights of the neurons in a single-layer perceptron. ... Gradient descent is an optimization algorithm that approaches a local minimum of a function by taking steps proportional to the negative of the gradient (or the approximate gradient) of the function at the current point. ...

Single-unit perceptrons are only capable of learning linearly separable patterns; in 1969 in a famous monograph entitled Perceptrons Marvin Minsky and Seymour Papert showed that it was impossible for a single-layer perceptron network to learn an XOR function. They conjectured (incorrectly) that a similar result would hold for a multi-layer perceptron network. Although a single threshold unit is quite limited in its computational power, it has been shown that networks of parallel threshold units can approximate any continuous function from a compact interval of the real numbers into the interval [-1,1]. This very recent result can be found in [Auer, Burgsteiner, Maass: The p-delta learning rule for parallel perceptrons, 2001 (state Jan 2003: submitted for publication)]. For the Stargate SG-1 episode, see 1969 (Stargate SG-1). ... A monograph is a scholarly book or a treatise on a single subject or a group of related subjects. ... The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt. ... Marvin Lee Minsky (born August 9, 1927), sometimes affectionately known as Old Man Minsky, is an American cognitive scientist in the field of artificial intelligence (AI), co-founder of MITs AI laboratory, and author of several texts on AI and philosophy. ... Seymour Papert Seymour Papert (born March 1, 1928 Pretoria, South Africa) is an MIT mathematician, computer scientist, and prominent educator. ... Exclusive disjunction (usual symbol xor) is a logical operator that results in true if one of the operands (not both) is true. ...

A single-layer neural network can compute a continuous output instead of a step function. A common choice is the so-called logistic function: In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of half-open intervals. ... Logistic curve, specifically the sigmoid function A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops. ...

(In general form, f(X) is in place of x, where f(X) is an analytic function in set of x's.) With this choice, the single-layer network is identical to the logistic regression model, widely used in statistical modelling. The logistic function is also known as the sigmoid function. It has a continuous derivative, which allows it to be used in backpropagation. This function is also preferred because its derivative is easily calculated: In mathematics, an analytic function is a function that is locally given by a convergent power series. ... Logistic regression is a statistical regression model for Bernoulli-distributed dependent variables. ... A statistical model is used in applied statistics. ... Logistic curve, specifically the sigmoid function A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops. ... The logistic curve A sigmoid function is a mathematical function that produces a sigmoid curve — a curve having an S shape. ...

y' = y(1 − y) (times df / dX, in general form, according to the Chain Rule)

In calculus, the chain rule is a formula for the derivative of the composite of two functions. ...

Multi-layer perceptron

A two-layer neural network capable of calculating XOR. The numbers within the neurons represent each neuron's explicit threshold (which can be factored out so that all neurons have the same threshold, usually 1). The numbers that annotate arrows represent the weight of the inputs. This net assumes that if the threshold is not reached, zero (not -1) is output. Note that the bottom layer of inputs is not always considered a real neural network layer

This class of networks consists of multiple layers of computational units, usually interconnected in a feed-forward way. Each neuron in one layer has directed connections to the neurons of the subsequent layer. In many applications the units of these networks apply a sigmoid function as an activation function. Image File history File links XOR_perceptron_net. ... Image File history File links XOR_perceptron_net. ...

The universal approximation theorem for neural networks states that every continuous function that maps intervals of real numbers to some output interval of real numbers can be approximated arbitrarily closely by a multi-layer perceptron with just one hidden layer. This result holds only for restricted classes of activation functions, e.g. for the sigmoidal functions.

Multi-layer networks use a variety of learning techniques, the most popular being back-propagation. Here the output values are compared with the correct answer to compute the value of some predefined error-function. By various techniques the error is then fed back through the network. Using this information, the algorithm adjusts the weights of each connection in order to reduce the value of the error function by some small amount. After repeating this process for a sufficiently large number of training cycles the network will usually converge to some state where the error of the calculations is small. In this case one says that the network has learned a certain target function. To adjust weights properly one applies a general method for non-linear optimization that is called gradient descent. For this, the derivative of the error function with respect to the network weights is calculated and the weights are then changed such that the error decreases (thus going downhill on the surface of the error function). For this reason back-propagation can only be applied on networks with differentiable activation functions. Backpropagation is a technique used for training neural networks. ... In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. ... Gradient descent is an optimization algorithm that approaches a local minimum of a function by taking steps proportional to the negative of the gradient (or the approximate gradient) of the function at the current point. ...

In general the problem of teaching a network to perform well, even on samples that were not used as training samples, is a quite subtle issue that requires additional techniques. This is especially important for cases where only very limited numbers of training samples are available. The danger is that the network overfits the training data and fails to capture the true statistical process generating the data. Computational learning theory is concerned with training classifiers on a limited amount of data. In the context of neural networks a simple heuristic, called early stopping, often ensures that the network will generalize well to examples not in the training set. Noisy (roughly linear) data is fit to both linear and polynomial functions. ... In statistics, computational learning theory is a mathematical field related to the analysis of machine learning algorithms. ... Look up Heuristic in Wiktionary, the free dictionary. ... In machine learning, early stopping is a form of regularization used when a machine learning model (such as a neural network) is trained by on-line gradient descent. ...

Other typical problems of the back-propagation algorithm are the speed of convergence and the possibility of ending up in a local minimum of the error function. Today there are practical solutions that make back-propagation in multi-layer perceptrons the solution of choice for many machine learning tasks. A graph illustrating local min/max and global min/max points In mathematics, a point x* is a local maximum of a function f if there exists some &#949; > 0 such that f(x*) &#8805; f(x) for all x with |x-x*| < &#949;. Stated less formally, a local maximum... As a broad subfield of artificial intelligence, machine learning is concerned with the design and development of algorithms and techniques that allow computers to learn. At a general level, there are two types of learning: inductive, and deductive. ...

ADALINE

ADALINE stands for Adaptive Linear Neuron. or later called Adaptive Linear Element. It was developed by Professor Bernard Widrow and his graduate student Ted Hoff at Stanford University in 1960. It's based on the McCulloch-Pitts model. It consists of a weight, a bias and a summation function. Bernard Widrow (born December 24, 1929) is a U.S. professor of electrical engineering at Stanford University. ... Dr. Marcian Edward Ted Hoff Jr. ... Leland Stanford Junior University, commonly known as Stanford University (or simply Stanford), is a private university located approximately 37 miles (60 kilometers) southeast of San Francisco and approximately 20 miles northwest of San José in Stanford, California. ...

Operation: y_i = wx_i + b

Its adaptation is defined through a cost function (error metric) of the residual e = d_i − (b + wx_i) where d_i is the desired input. With the MSE error metric the adapted weight and bias become: and In statistics the mean squared error of an estimator T of an unobservable parameter θ is i. ...

The Adaline has practical applications in the controls area. A single neuron with 5 to 10 tapped inputs can be used to determine the higher order transfer function of a physical system via the bi-linear z-transform. This is done as the Adaline is, functionally, an adaptive FIR filter. Like the single-layer perceptron, ADALINE has a counterpart in statistical modelling, in this case least squares regression. In regression analysis, least squares, also known as ordinary least squares analysis is a method for linear regression that determines the values of unknown quantities in a statistical model by minimizing the sum of the residuals (difference between the predicted and observed values) squared. ... Generally, regression is related to moving backwards, and the opposite of progression. ...

There is an extension of the Adaline, called the Multiple Adaline (MADALINE) that consists of two or more adalines serially connected.

See also

• Feed-forward
• Artificial neural network