Özdemir N, Iskender BB, Özgür NY (2011) Complex valued neural network with Möbius activation function. Comm Nonlinear Sci Numer Simulat 16:4698–4703Özdemir, N., İskender, B.B., Özgür, N.Y.:
However, the complex-valued backpropagation algorithm with this regular complex-valued activation function never converged in our experiments. We considered that the cause was nonboundedness of the complex function [Eq.(3)] and decided to adopt bounded functions. Actually, Eq.(3) has the periodic...
Recently, decent advances have been made with optics, such as complex-valued matrix multiplication operations using delicate photonic integrated circuits42 or diffractive optics22,43, and complex-valued activation functions involving 2D materials44. However, existing work primarily focuses on the ...
and the computation employs complex-valued arithmetic. The neuron is built by weighting each input with a complex number, as shown in Fig.3a. The weighted inputs are summed up and processed by an activation function. The output of the neuron is expressed as ...
* Theoretical aspects of CVNNs such as complex-valued activation functions, gradient, and stability * Learning/Self-organization algorithms and processing dynamics in CVNNs * Chaos in the complex domain, coherence, and causality * Complex-valued associative memories and attractor networks ...
* Theoretical aspects of CVNNs such as complex-valued activation functions, gradient, and stability * Learning/Self-organization algorithms and processing dynamics in CVNNs * Chaos in the complex domain, coherence, and causality * Complex-valued associative memories and attractor networks ...
We have reported a novel deep learning reconstruction that works with multi-coil and complex-valued 4D (3D + cardiac phases) data. The proposed architecture reflects an unrolled optimization algorithm with complex-valued convolutions and activation functions and intermittent data consistency blocks ...
This paper investigates the existence, uniqueness, and global asymptotic stability of equilibrium point for a complex-valued Cohen–Grossberg delayed bidirectional associative memory neural networks. The two types of complex-valued behaved functions, amplification functions and activation functions, are ...
3.2. Equivariant Non-Linearity Non-linear activation functions are necessary to construct deep hierarchical representations. [18, 19, 37, 38] have inves- tigated several complex-valued non-linearities. CReLU, the most prominent example, computes ReLU independently on the real and imaginar...
CVNNs can be categorized into two types according to the selection of activation functions: split CVNNs (Nitta, 1997) and fully CVNNs (Kim and Adalı, 2003). Split CVNNs employ a pair of real-valued activation functions to handle the real and imaginary parts (or amplitude and phase) of...