Complex-Valued Neural Networks: Theories and Applications

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Complex-Valued Autoencoders (2011, background): “Keywords: autoencoders, unsupervised learning, complex numbers, critical points, linear networks, Principal Component Analysis, deep architectures, differential geometry Preprint submitted to Neural Networks April 28, 2013”
Global Stability of Complex-Valued Recurrent Neural Networks With Time-Delays (2012, neutral): “j = 1, 2, ⋅ ⋅ ⋅ , n, there exists a positive constant ξj, such that for any u, v ∈ C, we have ∣fj(u)− fj(v)∣ ≤ ξj ∣u− v∣ (3)”
Encoding word order in complex embeddings (2019, neutral): “Complex-valued NNs are not new (Georgiou & Koutsougeras, 1992; Kim & Adalı, 2003; Hirose, 2003).”
Unitary Evolution Recurrent Neural Networks (2015, background): “L G ] 2 5 M ay 2 have been considered for neural networks in the past, but with limited success and adoption (Hirose, 2003; Zimmermann et al., 2011).”
Deep Complex Networks (2017, background): “…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 al., 2007,…”