Optimizing Spectral Activation Functions for Spectral Convolutional Neural Networks: Balancing Efficiency and Fidelity

Spectral Convolutional Neural Networks (SpCNNs) represent a critical domain in signal processing and machine learning, where the integration of activation functions (AFs) presents significant computational and theoretical challenges. This study systematically evaluates six spectral-domain AFs, employing a comprehensive methodology that assesses their performance across multiple critical metrics including signal quality, computational efficiency, and spectral domain characteristics. Using the MNIST dataset and a high-performance computational infrastructure, we conducted a rigorous analysis of AFs including ACReLU, SReLU, Split-tanh, Split-LReLU, PhaseReLU, and ModReLU. Our findings reveal substantial variations in signal processing capabilities, with novel AFs demonstrating marked improvements in signal quality metrics. Notably, Split-tanh and Split-LReLU exhibited significant noise reduction, achieving Signal-to-Noise Ratio (SNR) and Peak Signal-to-Noise Ratio (PSNR) values approaching 0 dB and 9.47 dB, respectively, compared to traditional AFs. The research provides critical insights into the trade-offs between computational efficiency and signal transformation capabilities, highlighting the potential of advanced spectral-domain AFs in improving neural network performance across complex signal processing tasks.