Complex domain backpropagation

By George M. Georgiou, C. Koutsougeras. 1992

How researchers see this paper

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

1. Yoshua Bengio
2. Bo Li
3. C. Pal
4. Deliang Wang
5. Sandeep Subramanian
6. Kyunghyun Cho
7. Kristen Grauman
8. Zhe Gan

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].”
• Encoding word order in complex embeddings (2019, unknown): “Complex-valued NNs are not new (Georgiou & Koutsougeras, 1992; Kim & Adalı, 2003; Hirose, 2003).”
• Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability (2001, methodology): “Generalising the discussion for real activation functions, properties that a function σ(z) = u(x, y)+jv(x, y) should satisfy so that it represents a suitable activation function in the complex plane are (Georgiou and Koutsougeras 1992) • u and v are nonlinear in x and y; • σ(z) is bounded ⇒ u and v ”
• Generalization Characteristics of Complex-Valued Feedforward Neural Networks in Relation to Signal Coherence (2012, background): “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, methodology): “In their 1992 paper [9], Georgiou and Koutsougeras presented an activation that attenuates the magnitude of the signal while preserving the phase.”
• Deep Complex Networks (2017, background): “As pointed out in Reichert and Serre [2013], the use of complex-valued neural networks [Georgiou and Koutsougeras, 1992, Zemel et al., 1995, Kim and Adalı, 2003, Hirose, 2003, Nitta, 2004] has been investigated long before the earliest deep learning breakthroughs [Hinton et al., 2006, Bengio et…”