Artificial Neural Networks: A Mathematical Model

Artificial neural networks

Artificial neural network is a mathematical model, based on the principle of the organization and functioning of biological neural networks - networks of nerve cells of a living organism. This model is biologically inspired and enables a computer to learn from the data. In other words, the neural network is a machine interpretation of the human brain, which contains millions of neurons that transmit information in the form of electrical impulses.

A neuron is a cell in the brain whose function is to collect, process and propagate electrical signals. Neuron has a wide structure of input data (dendrites), kernel and branching output (the axon). Axons of the cells connect to other cells of dendrites via synapses. When

The possibility of training - one of the major advantages of neural networks over conventional algorithms. Technical training is to find the coefficients of the connections between neurons. In the process of training the neural network is able to identify complex relationships between inputs and outputs, as well as to carry out a generalization. This means that in case of successful learning network, it will be able to return the correct result on the basis of data that were missing in the training set, or incomplete and "noisy" data that is partially

Suppose that n discrete samples {y (t1), y (t2), ..., y (tn)} at successive time points t1, t2, ..., tn. The challenge is to anticipate the values y (tn + 1) in the next time tn + 1. Foresight / prognosis are important for decision-making in business, science and technology (foresight prices on the stock exchange, weather forecast).

Optimization. Many problems in mathematics, statistics, engineering, science, medicine and economics can be viewed as an optimization problem. The objective of the optimization algorithm is to find a solution that satisfies the system constraints and maximizes or minimizes the objective function.

Memory addressable by meaning. In traditional computers, memory access is only available via the address that is independent of memory content. Moreover, if you make a mistake in calculating the address, it can be found other information at all. Associative memory is addressable by implication, is available at the direction of a given content. The contents of memory can be caused by even a partial entry or damaged content.

But despite the advantages of neural networks in some areas over traditional computing, the existing neural networks are not perfect solutions. They are trained and