Chaotic Pattern Recognition: The Spectrum of Properties of the Adachi Neural Network

Abstract

Abstract. Chaotic Pattern Recognition (PR) is a relatively new subfield of PR in which a system, which demonstrates chaotic behavior under normal conditions, resonates when it is presented with a pattern that it is trained with. The Adachi Neural Network (AdNN) is a classic neural structure which has been proven to demonstrate the phenomenon of Associative Memory (AM). In their pioneering paper [1,2], Adachi and his co-authors showed that the AdNN also emanates periodic outputs on being exposed to trained patterns. This was later utilized by Calitoiu et al [4,5] to design systems which possibly possessed PR capabilities. In this paper, we show that the previously reported properties of the AdNN do not adequately describe the dynamics of the system. Rather, although it possesses far more powerful PR and AM properties than was earlier known, it goes through a spectrum of characteristics as one of its crucial parameters, α, changes. As α increases, the AdNN which is first an AM become quasi-chaotic 1 . The system is then distinguished by two phases which really do not have clear boundaries of demarcation. In the former of these phases it is quasi-chaotic for some patterns and periodic for others. In the latter of these, it exhibits properties that have been unknown (or rather, unreported) till now, namely, a PR capability (which even recognizes masked or occluded patterns) in which the network resonates sympathetically for trained patterns while it is quasi-chaotic for untrained patterns. Finally, the system becomes completely periodic. All these results are, to the best of our knowledge, novel.

Ideal Chaotic Pattern Recognition Is Achievable: The Ideal-M-AdNN - Its Design and Properties

“…Apparently, the above value of y 0 is always negative, which contradicts our assumption that y 0 is a positive fixed point. Similarly, we can see that Equation (16) does not have any negative fixed points either. In other words, we conclude that Equation (16) does not have any fixed point.…”

“…The experimental results reported in [6] claimed that the M-AdNN responds periodically for a trained input pattern. However, it turns out that this periodic output occurs for both trained and untrained patterns, as can be seen in [16].…”

“…Aiming to reduce the computational cost, in our previous paper [16], we proposed a mechanism (the Linearized AdNN (L-AdNN)) to reduce the computational load of the AdNN. This was achieved by using a spanning tree of the complete graph, and invoking a gradient search algorithm to compute the edge weights, thus minimizing the computation time to be linear.…”

“…We shall now clarify this. As explained in detail in [16,17], if the AdNN weights the external inputs with the quantities determined by a i = 2 + 6x i , the properties of the system become closer to mimicing a PR phenomenon. Adachi et al claimed that such a NN yields the stored pattern at the output periodically, with a short transient phase and a small periodicity.…”

“…To complete this historical overview, we mention that in [16], we showed that the AdNN goes through a spectrum of characteristics (i.e., AM, quasi-chaotic, and PR) as one of its crucial parameters, α, changes. In particular, it is even capable of recognizing masked or occluded patterns.…”