On the complex backpropagation algorithm

By Nevio Benvenuto, Francesco Piazza. 1992

How researchers see this paper

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

Citations in the corpus

Time-Frequency Masking in the Complex Domain for Speech Dereverberation and Denoising (2017, positive): “Complex domain backpropagation is used [10], [24].”
Deep Learning Approach for Intelligent Intrusion Detection System (2019, methodology): “The DNN is trained using the backpropogation mechanism [60].”
Generalization Characteristics of Complex-Valued Feedforward Neural Networks in Relation to Signal Coherence (2012, background): “Digital Object Identifier 10.1109/TNNLS.2012.2183613 actually obtained by paying attention to the real and imaginary parts [16]–[18] or amplitude and phase [19], [20].”
Better than real: Complex-valued neural nets for MRI fingerprinting (2017, background): “Past research has explored a range of potential solutions, for example, limiting the range of the activation input to avoid unbounded regions [6], or applying non-linearities to real and imaginary components separately [7, 8].”
Holographic reduced representations (1995, background): “There has been some research on creating adapting neural network architectures to wok with units with complex valued activations (e.g., [ 2 ]).”
Lending direction to neural networks (1995, background): “Just as for the Hop eld binary-state network, it can be shown that the free energy FMF always decreases during the dynamical evolution described in Equation 13. The equilibrium solutions are free energy minima. The Appendix contains a convergence proof for FMF , in the style of Hop eld (1984). 5 Lea”
Complex-Valued Neural Networks (2006, unknown): “The second source of nonholomorphism arises because boundedness and analiticity cannot be achieved at the same time in the complex domain, and it is the boundedness that is often preferred over analyticity for the activation functions [3, 23].”
Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability (2001, unknown): “Another proposed complex sigmoid is (Benvenuto and Piazza 1992) σ(z) = 2c1 1 + e−c2z − c1, (4.”
Dynamic behavioral modeling of 3G power amplifiers using real-valued time-delay neural networks (2004, methodology): “Experiments conducted for the training and validation of the neural network used a real-time two-channel time-domain sampling system. and components of the equivalent complex baseband input signal of the PA are used as two independent inputs of the RVTDNN.”