Summary of Comprehensive Survey Of Complex-valued Neural Networks: Insights Into Backpropagation and Activation Functions, by M. M. Hammad
Comprehensive Survey of Complex-Valued Neural Networks: Insights into Backpropagation and Activation Functions
by M. M. Hammad
First submitted to arxiv on: 27 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A recent surge in interest has seen artificial neural networks (ANNs) employing deep learning models being applied widely across fields like computer vision, signal processing, and wireless communications. However, despite the prevalent use of real-number implementations in current ANN frameworks, there is a growing desire to develop ANNs that utilize complex numbers. This paper presents a comprehensive survey of recent advancements in complex-valued neural networks (CVNNs), focusing on their activation functions (AFs) and learning algorithms. The extension of the backpropagation algorithm to the complex domain enables the training of neural networks with complex-valued inputs, weights, AFs, and outputs. This review delves into three complex backpropagation algorithms: the complex derivative approach, the partial derivatives approach, and algorithms incorporating the Cauchy-Riemann equations. A significant challenge in CVNN design is the identification of suitable nonlinear Complex Valued Activation Functions (CVAFs), due to the conflict between boundedness and differentiability over the entire complex plane as stated by Liouville theorem. The survey examines both fully complex AFs, which strive for boundedness and differentiability, and split AFs, which offer a practical compromise despite not preserving analyticity. This comprehensive overview of CVNNs provides an in-depth analysis of various CVAFs essential for constructing effective CVNNs. Moreover, this review contributes to ongoing research and development by introducing new set of CVAFs (fully complex, split, and complex amplitude-phase AFs). The paper’s findings have significant implications for the development of more efficient and effective deep learning models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Complex neural networks are being developed that use complex numbers instead of real numbers. This helps in fields like computer vision and signal processing where complex numbers are important. Researchers have been working on finding new ways to train these networks using a method called backpropagation. They’ve found three different ways to do this: the complex derivative approach, the partial derivatives approach, and algorithms that use the Cauchy-Riemann equations. One challenge is finding activation functions that work well with complex numbers. This paper looks at different types of activation functions and how they can be used to make complex neural networks more effective. |
Keywords
» Artificial intelligence » Backpropagation » Deep learning » Signal processing
