Ideal Chaotic Pattern Recognition is achievable: The Ideal-M-AdNN - its design and properties

This paper deals with the relatively new field of designing a Chaotic Pattern Recognition (PR) system. The benchmark of such a system is the following: First of all, one must be able to train the system with a set of “training” patterns. Subsequently, as long as there is no testing pattern, the system must be chaotic. However, if the system is, thereafter, presented with an unknown testing pattern, the behavior must ideally be as follows. If the testing pattern is not one of the trained patterns, the system must continue to be chaotic. As opposed to this, if the testing pattern is truly one of the trained patterns (or a noisy version of a trained pattern), the system must switch to being periodic, with the specific trained pattern appearing periodically at the output. This is truly an ambitious goal, with the requirement of switching from chaos to periodicity being the most demanding. Some related work has been done in this regard. The Adachi Neural Network (AdNN) [1-5] has properties which are pseudo-chaotic, but it also possesses limited PR characteristics. As opposed to this, the Modified Adachi Neural Network (M-AdNN) proposed by Calitoiu et al [6], is a fascinating NN which has been shown to possess the required periodicity property desirable for PR applications. However, in this paper, we shall demonstrate that the PR properties claimed in [6] are not as powerful as originally reported. Indeed, the claim of the authors of [6] is true, in that it resonates periodically for trained input patterns. But unfortunately, the M-AdNN also resonates for unknown patterns and produces these unknown patterns at the output periodically. However, we describe how the parameters of the M-AdNN for its weights, steepness and external inputs, can be specified so as to yield a new NN, which we shall refer to as the Ideal-M-AdNN. Using a rigorous Lyapunov analysis, we shall analyze the chaotic properties of the Ideal-M-AdNN, and demonstrate its chaotic characteristics. Thereafter, we shall verify that the system is also truly chaotic for untrained patterns. But most importantly, we demonstrate that it is able to switch to being periodic whenever it encounters patterns with which it was trained. Apart from being quite fascinating, as far as we know, the theoretical and experimental results presented here are both unreported and novel. Indeed, we are not aware of any NN that possesses these properties