Information theory, complexity and neural networks

Some of the main results in the mathematical evaluation of neural networks as information processing systems are discussed. The basic operation of feedback and feed-forward neural networks is described. Their memory capacity and computing power are considered. The concept of learning by example as it applies to neural networks is examined

Secure exchange of information by synchronization of neural networks

A connection between the theory of neural networks and cryptography is presented. A new phenomenon, namely synchronization of neural networks is leading to a new method of exchange of secret messages. Numerical simulations show that two artificial networks being trained by Hebbian learning rule on their mutual outputs develop an antiparallel state of their synaptic weights. The synchronized weights are used to construct an ephemeral key exchange protocol for a secure transmission of secret data. It is shown that an opponent who knows the protocol and all details of any transmission of the data has no chance to decrypt the secret message, since tracking the weights is a hard problem compared to synchronization. The complexity of the generation of the secure channel is linear with the size of the network.Comment: 11 pages, 5 figure

Nonlinear Combination of Financial Forecast with Genetic Algorithm

Complexity in the financial markets requires intelligent forecasting models for return volatility. In this paper, historical simulation, GARCH, GARCH with skewed student-t distribution and asymmetric normal mixture GRJ-GARCH models are combined with Extreme Value Theory Hill by using artificial neural networks with genetic algorithm as the combination platform. By employing daily closing values of the Istanbul Stock Exchange from 01/10/1996 to 11/07/2006, Kupiec and Christoffersen tests as the back-testing mechanisms are performed for forecast comparison of the models. Empirical findings show that the fat-tails are more properly captured by the combination of GARCH with skewed student-t distribution and Extreme Value Theory Hill. Modeling return volatility in the emerging markets needs “intelligent” combinations of Value-at-Risk models to capture the extreme movements in the markets rather than individual model forecast.Forecast combination; Artificial neural networks; GARCH models; Extreme value theory; Christoffersen test