Hopfield neural network: The hyperbolic tangent and the piecewise-linear activation functions

Sputtering-deposited amorphous SrVOx-based memristor for use in neuromorphic computing

“…In the ideal case, the accuracy was saturated at 89.7% within 100,000 iterations, while the accuracy of our simulated device was saturated at 86.8%. The reason why the accuracy of the ideal case was not saturated at 100% could be that, in our simulation, a sigmoid function was adopted, which produces a non-binary response, or a Hopfield network energy that is localized at certain minimum energy states 61,62 . The synaptic weight maps of 100 × 100 synapses for 0, 20,000, and 100,000 asynchronous iterations when NL = 0.12 for potentiation and NL = 0.34 for depression are presented in Fig.…”

Spiral periodic structures in a parameter plane of an ecological model

“…1. As we said before in Section 1, spiral organization of periodic structures have been observed in parameter planes of different systems [1,[29][30][31]43,49,50], modeled by different sets of nonlinear differential equations, that may involve polynomial functions and exponential functions among other mathematical functions. This may be an indicator of the importance of this type of organization of periodic structures, which is present in various fields of the knowledge.…”

“…One such type of organization consists of a set of shrimp-shaped periodic structures forming a spiral that coils up around a focal point while period-adding bifurcations take place. To our knowledge these spiral bifurcations have been observed in parameter planes of electronic circuits [1,29,49], a Rössler model [50], a chemical oscillator [1], a Hopfield neural network [30], modified optical injection semiconductor lasers [31], and a tumor growth mathematical model [43]. The spiral periodic structures were experimentally detected in electronic circuits [51], and the global mechanism responsible for its origin and organization was reported simultaneously by Vitolo et al [14] and Barrio et al [15].…”

Discrete Hopfield Neural Network in Restricted Maximum k-Satisfiability Logic Programming

“…Hence k = 2 and k = 3 will be abbreviated as and HNN-MAX3SAT, respectively. Equations (5) - (6) are vital to establish the degree of convergence of the neurons in HNN (Ioneschu et al 2010;Mathias & Rech 2012). Thus, the energy value is vital to separate local minimum and global minimum solution.…”