[17] Ilias Diakonikolas, Surbhi Goel, Sushrut Karmalkar, Adam R Klivans, and Mahdi Soltanolkotabi. Approximation schemes for ReLU regression. In Proceedings of the 33rd Annual Conference on Learning Theory, pages 1452-1485, 2020.
[18] Ilias Diakonikolas, Daniel Kane, Lisheng Ren, and Yuxin Sun. SQ lower bounds for learning single neurons with Massart noise. Advances in Neural Information Processing Systems 35, pages 24006-24018, 2022.
[19] Gilad Yehudai and Ohad Shamir. Learning a single neuron with gradient methods. In Proceedings of the 33rd Conference on Learning Theory, pages 3756-3786, 2020.
[20] Henry Leung and Simon Haykin. The complex backpropagation algorithm. IEEE Transactions on Signal Processing, 39(9):2101-2104, 1991.
[21] Nevio Benvenuto and Francesco Piazza. On the complex backpropagation algorithm. IEEE Transactions on Signal Processing, 40(4):967-969, 1992.
[22] George M Georgiou and Cris Koutsougeras. Complex domain backpropagation. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 39(5):330-334, 1992.
[23] Paolo Arena, Luigi Fortuna, R Re, and Maria Gabriella Xibilia. Multilayer perceptrons to approximate complex valued functions. International Journal of Neural Systems, 6(4):435-446, 1995.
[24] Md Faijul Amin, Ramasamy Savitha, Muhammad Ilias Amin, and Kazuyuki Murase. Complex-valued functional link network design by orthogonal least squares method for function approximation problems. In Proceedings of 2011 International Joint Conference on Neural Networks, pages 1489-1496, 2011.
[25] Akira Hirose and Shotaro Yoshida. Generalization characteristics of complex-valued feedforward neural networks in relation to signal coherence. IEEE Transactions on Neural Networks and Learning Systems, 23(4):541-551, 2012.
[26] Tohru Nitta. Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Networks, 16(8):1101-1105, 2003.
[27] Shao-Qun Zhang and Zhi-Hua Zhou. Flexible transmitter network. Neural Computation, 33(11):2951-2970, 2021.
[28] Warren S McCulloch and Walter Pitts. A logical calculus of the ideas immanent in nervous activity. The Bulletin of Mathematical Biophysics, 5(4):115-133, 1943.
[29] Junming Zhang and Yan Wu. A new method for automatic sleep stage classification. IEEE Transactions on Biomedical Circuits and Systems, 11(5):1097-1110, 2017.
[30] Jingkun Gao, Bin Deng, Yuliang Qin, Hongqiang Wang, and Xiang Li. Enhanced radar imaging using a complex-valued convolutional neural network. IEEE Geoscience and Remote Sensing Letters, 16(1):35-39, 2018.
[31] Chiheb Trabelsi, Olexa Bilaniuk, Ying Zhang, Dmitriy Serdyuk, Sandeep Subramanian, Joao Felipe Santos, Soroush Mehri, Negar Rostamzadeh, Yoshua Bengio, and Christopher J Pal. Deep complex networks. In Proceedings of the 6th International Conference on Learning Representations, 2018.
[32] Adam Tauman Kalai and Ravi Sastry. The isotron algorithm: High-dimensional isotonic regression. In Proceedings of the 22nd Conference on Learning Theory, 2009.
[33] Sham M Kakade, Varun Kanade, Ohad Shamir, and Adam Kalai. Efficient learning of generalized linear and single index models with isotonic regression. In Advances in Neural Information Processing Systems 24, pages 927-935, 2011.
[34] Surbhi Goel, Varun Kanade, Adam Klivans, and Justin Thaler. Reliably learning the ReLU in polynomial time. In Proceedings of the 30th Conference on Learning Theory, pages 1004-1042, 2017.