Read Online The Numbers Behind NUMB3RS by Keith Devlin - Free Book Online

function of the signal at the start node and the transmission strength of the connection. Every time a signal is transmitted along a connection, the strength of that connection (also often called its “weight”) is increased or decreased proportional to the signal strength, according to a preset formula. (This corresponds to the way that, in a living brain, life experiences result in changes to the strengths of the synaptic connections between neurons in the brain.) Thus, the overall connection-strength configuration of the network changes with each operational cycle.
    To use the network to carry out a particular computational task, the input(s) to the computation must be encoded as a set of input signals to the input layer and the corresponding output signal(s) interpreted as a result of the computation. The behavior of the network—what it does to the input(s)—is dependent on the weights of the various network connections. Essentially, the patterns of those weights constitute the network’s “memory.” The ability of a neural network to perform a particular task at any moment in time depends upon the actual architecture of the network and its current memory.
    TRAINING A NEURAL NETWORK
    Neural networks are not programmed in the usual sense of programming a computer. In the majority of cases, particularly neural networks used for classification, the application of a network must be preceded by a process of “training” to set the various connection weights.
    By way of an example, suppose a bank wanted to train a neural network to recognize unauthorized credit card use. The bank first presents the network with a large number of previous credit card transactions (recorded in terms of user’s home address, credit history, spending limit, expenditure, date, amount, location, etc.), each known to be either authentic or fraudulent. For each one, the network has to make a prediction concerning the transaction’s authenticity. If the connection weights in the network are initially set randomly or in some neutral way, then some of its predictions will be correct and others wrong. During the training process, the network is “rewarded” each time its prediction is correct and “punished” each time it is wrong. (That is to say, the network is constructed so that a “correct grade”—i.e., positive feedback on its prediction—causes it to continue adjusting the connection weights as before, whereas a “wrong grade” causes it to adjust them differently.) After many cycles (thousands or more), the connection weights will adjust so that on the majority of occasions (generally the vast majority) the decision made by the network is correct. What happens is that, over the course of many training cycles, the connection weights in the network will adjust in a way that corresponds to the profiles of legitimate and fraudulent credit card use, whatever those profiles may be (and, of great significance, without the programmer having to know them).
    Some skill is required to turn these general ideas into a workable system, and many different network architectures have been developed to build systems that are suited to particular classification tasks.
    After completion of a successful training cycle, it can be impossible for a human operator to figure out just what patterns of features (to continue with our current example) of credit card transactions the network has learned to identify as indicative of fraud. All that the operator can know is that the system is accurate to a certain degree of error, giving a correct prediction perhaps 95 percent of the time.
    A similar phenomenon can occur with highly trained, highly experienced human experts in a particular domain, such as physicians. An experienced doctor will sometimes examine a patient and say with some certainty what she believes is wrong with the individual, and yet be unable to explain exactly just what