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[2512.14873] How Does Fourier Analysis Network Work? A Mechanism Analysis and a New Dual-Activation Layer Proposal
Summary
This article analyzes the Fourier Analysis Network (FAN) and introduces a new Dual-Activation Layer (DAL) that enhances neural network performance by addressing gradient issues in traditional activation functions.
Why It Matters
Understanding the mechanisms behind FAN and the proposed DAL is crucial for improving neural network training efficiency. This research provides insights into overcoming common activation function limitations, which can lead to faster convergence and better performance in machine learning tasks.
Key Takeaways
- FAN improves neural network performance by replacing ReLU activations with sine and cosine functions.
- Only the sine activation contributes positively to performance, while cosine can be detrimental.
- FAN helps alleviate the vanishing-gradient problem and the dying-ReLU issue.
- The Dual-Activation Layer (DAL) accelerates convergence and improves validation accuracy across various tasks.
- This research shifts the focus from spectral interpretations to concrete training dynamics.
Computer Science > Machine Learning arXiv:2512.14873 (cs) [Submitted on 16 Dec 2025 (v1), last revised 20 Feb 2026 (this version, v2)] Title:How Does Fourier Analysis Network Work? A Mechanism Analysis and a New Dual-Activation Layer Proposal Authors:Sam Jeong, Hae Yong Kim View a PDF of the paper titled How Does Fourier Analysis Network Work? A Mechanism Analysis and a New Dual-Activation Layer Proposal, by Sam Jeong and 1 other authors View PDF HTML (experimental) Abstract: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 r...