Sam Jeong

Sam Jeong, Hae Yong Kim

Machine learning has revolutionized biomedical signal analysis, particularly in electrocardiogram (ECG) classification. While convolutional neural networks (CNNs) excel at automatic feature extraction, the optimal integration of time- and frequency-domain information remains unresolved. This study introduces the Convolutional Fourier Analysis Network (CFAN), a novel architecture that unifies time-frequency analysis by embedding Fourier principles directly into CNN layers. We evaluate CFAN against four benchmarks - spectrogram-based 2D CNN (SPECT); 1D CNN (CNN1D); Fourier-based 1D CNN (FFT1D); and CNN1D with integrated Fourier Analysis Network (CNN1D-FAN) - across three ECG tasks: arrhythmia classification (MIT-BIH), identity recognition (ECG-ID), and apnea detection (Apnea-ECG). CFAN achieved state-of-the-art performance, surpassing all competing methods with accuracies of 98.95% (MIT-BIH), 96.83% (ECG-ID), and 95.01% (Apnea-ECG). Notably, on ECG-ID and Apnea-ECG, CFAN demonstrated statistically significant improvements over the second-best method (CNN1D-FAN, $p \leq 0.02$), further validating its superior performance. Key innovations include CONV-FAN blocks that combine sine, cosine and GELU activations in convolutional layers to capture periodic features and joint time-frequency learning without spectrogram conversion. Our results highlight CFAN's potential for broader biomedical and signal classification applications.

Sam Jeong, Hae Yong Kim

Fourier Analysis Network (FAN) was recently proposed as a simple way to improve neural network performance by replacing part of Rectified Linear Unit (ReLU) activations with sine and cosine functions. Although several studies have reported small but consistent gains across tasks, the underlying mechanism behind these improvements has remained unclear. In this work, we show that only the sine activation contributes positively to performance, whereas the cosine activation tends to be detrimental. Our analysis reveals that the improvement is not a consequence of the sine function's periodic nature; instead, it stems from the function's local behavior near x = 0, where its non-zero derivative mitigates the vanishing-gradient problem. We further show that FAN primarily alleviates the dying-ReLU problem, in which a neuron consistently receives negative inputs, produces zero gradients, and stops learning. Although modern ReLU-like activations, such as Leaky ReLU, GELU, and Swish, reduce ReLU's zero-gradient region, they still contain input domains where gradients remain significantly diminished, contributing to slower optimization and hindering rapid convergence. FAN addresses this limitation by introducing a more stable gradient pathway. This analysis shifts the understanding of FAN's benefits from a spectral interpretation to a concrete analysis of training dynamics, leading to the development of the Dual-Activation Layer (DAL), a more efficient convergence accelerator. We evaluate DAL on three tasks: classification of noisy sinusoidal signals versus pure noise, MNIST digit classification, and Electrocardiogram (ECG)-based biometric recognition. In all cases, DAL models converge faster and achieve equal or higher validation accuracy compared to models with conventional activations.