Global convergence of neural networks with discontinuous neuron activations

446 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Finite-time synchronization of complex networks with nonidentical discontinuous nodes (2013, background): “Definition 4 [41] A function x : [0, T ) → R, T ∈ (0,+∞], is a solution (in the sense of Filippov) of the discontinuous system (5) on [0, T ) if: (i) x(t) is absolutely continuous on [0, T ); (ii) There exists a measurable function γ (t) = (γ1(t), γ2(t), .”
Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain (2005, background): “Recent work [16] has demonstrated the interest in studying global stability of the equilibrium point for neural networks with discontinuous neuron activations.”
Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations (2006, methodology): “Suppose that −T ∈ LDS and, as in [1] consider for (12) the (candidate) Lyapunov function”
Some Fixed-Circle Theorems on Metric Spaces (2017, background): “Such applications have been become important in some recent studies (see [4,8,11] for more details).”
A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks (2014, background): “6) Discontinuous activation functions [68], [71], [72], [116], [173], [175], [183], [184], [216], [263]: Let g i (·) be a continuous nondecreasing function, and in every compact set of real space R, each g i (·) has only finite discontinuity points.”