Design of monotonic binary-valued cellular neural networks

Template design methods for binary stable cellular neural networks

“…The following major results have been obtained: (1) we have provided two Theorems (1 and 2), that yield some su cient conditions, for which the mapping is well-posed and can be rigorously deÿned through a simple algorithm; (2) we have enunciated two Theorems (3 and 4) and two Corollaries (5 and 6) that yield some very simple rules for identifying the template class, which satisÿes Theorems 1 and 2; (3) we have veriÿed that such a class is rather large and includes, as particular cases, the monotonic templates [25][26][27][28] and several kinds of non-monotonic templates.…”

“…For these networks we study and deÿne the analysis and the design problem. We yield the following major results: (1) we provide two theorems (1 and 2), that give some su cient conditions, in order that the non-linear mapping, implemented by the binary CNNs, be rigorously determined through a simple algorithm based on the sign of the initial derivatives; (2) the templates satisfying these conditions are identiÿed through some rules, easy to check, reported in two theorems (3 and 4) and two corollaries (5 and 6); (3) it is veriÿed that the class of templates deÿned through the above theorems is rather large and includes, as particular cases, the monotonic templates References [25][26][27][28], and several types of non-monotonic templates; and (4) a rigorous design procedure, based on the direct template derivation is proposed. Finally, we brie y discuss the application of the results to the CNN modiÿed model, described in Reference [31], that is more suitable for VLSI implementation.…”

“…the derivative at t = 0) of the cell states. The major drawback of this method is that, apart from uncoupled networks, some kind of unidirectional templates Reference [23], and the monotonic templates References [25][26][27][28], we do not know the class of templates for which the knowledge of the initial derivative allows to rigorously predict the asymptotic dynamics of the network: this step is essential for ensuring that the local rules are correctly implemented by the CNN. However, despite some disadvantages, the techniques based on the direct template derivation appear to be more suitable for CNN design, because they allow to understand the network spatio-temporal dynamics and to develop methods for robust design References [29,30].…”

An exact and direct analytical method for the design of optimally robust CNN templates

“…The strict greater than inequality may also be a greater than or equal to inequality for, at most, of these inequalities. 3 Note that a value of zero in is only possible in case of zero initialization or zero boundary values.…”

“…Hence, the relative robustness is strictly monotonically increasing with increasing but it is upperbounded by . 3 If none of the inequalities were strict, a template for which _ x 0 would be allowed. No operation would be performed, since the initial state would be the equilibrium.…”