View a PDF of the paper titled FAN: Fourier Analysis Networks, by Yihong Dong and 9 other authors
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Abstract: Despite the remarkable successes of general-purpose neural networks, such as MLPs and Transformers, we find that they exhibit notable shortcomings in modeling and reasoning about periodic phenomena, achieving only marginal performance within the training domain and failing to generalize effectively to out-of-domain (OOD) scenarios. Periodicity is ubiquitous throughout nature and science. Therefore, neural networks should be equipped with the essential ability to model and handle periodicity. In this work, we propose FAN, a novel general-purpose neural network that effectively addresses periodicity modeling challenges while offering broad applicability similar to MLP with fewer parameters and FLOPs. Periodicity is naturally integrated into FAN’s structure and computational processes by introducing the Fourier Principle. Unlike existing Fourier-based networks, which possess particular periodicity modeling abilities but face challenges in scaling to deeper networks and are typically designed for specific tasks, our approach overcomes this challenge to enable scaling to large-scale models and maintains general-purpose modeling capability. Through extensive experiments, we demonstrate the superiority of FAN in periodicity modeling tasks and the effectiveness and generalizability of FAN across a range of real-world tasks. Moreover, we reveal that compared to existing Fourier-based networks, FAN accommodates both periodicity modeling and general-purpose modeling well.
Understanding the Need for Fourier Analysis in Neural Networks
In recent years, neural networks have revolutionized numerous fields, showcasing unprecedented performance in various applications. However, there has been a critical discovery regarding their limitations, especially when dealing with periodic phenomena. These recurrent patterns are prevalent in numerous domains, such as signal processing, climatology, and any field involving cyclic behavior.
- Understanding the Need for Fourier Analysis in Neural Networks
- Introducing FAN: A Solution to Overcoming Periodicity Challenges
- The Fourier Principle: A Game-Changer for Neural Networks
- Proven Effectiveness Through Extensive Experiments
- A Broader Implication for Real-World Applications
- Submission and Revision History
Despite the effectiveness of models like Multi-Layer Perceptrons (MLPs) and Transformers, they are increasingly recognized for their struggles to accurately model periodic data. This inadequacy inhibits their ability to generalize beyond the training data, making it necessary to introduce new frameworks that incorporate a better understanding of periodicity.
Introducing FAN: A Solution to Overcoming Periodicity Challenges
In response to this pressing need, a team of researchers led by Yihong Dong introduced FAN, or Fourier Analysis Networks. This innovative approach integrates the Fourier Principle into the architecture of neural networks, allowing them to model periodic data more effectively.
FAN is classified as a general-purpose neural network, similar in versatility to MLPs, while requiring fewer parameters and performing fewer floating-point operations per second (FLOPs). This results in enhanced efficiency without compromising the network’s performance. The fundamental objective of FAN is to provide robust periodicity modeling, enabling the framework to adequately capture and process periodic patterns across various tasks.
The Fourier Principle: A Game-Changer for Neural Networks
At the heart of FAN’s architecture is the Fourier Principle, which serves as a foundational concept for efficiently representing and processing periodic signals. Implementing this principle allows FAN to embed periodicity inherently within its computational processes.
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Unlike traditional Fourier-based neural networks that are constructed specifically for periodic tasks, FAN overcomes significant obstacles related to depth and scalability. This adaptability renders FAN a powerful tool not only for tasks centered around periodic phenomena but also for broader applications across various disciplines. The research showcases FAN’s capacity to tackle complex modeling challenges where previous architectures have faltered.
Proven Effectiveness Through Extensive Experiments
To validate FAN’s capabilities, a series of comprehensive experiments were conducted, demonstrating its superiority over existing models, particularly in periodicity-related tasks. Results illustrate that FAN doesn’t merely excel within its training domain but also generalizes effectively to unfamiliar OOD scenarios. This is a crucial improvement over less versatile models, establishing FAN as a reliable choice for practical applications in real-world environments.
The performance metrics highlight that FAN achieves significant benchmarks with less computational overhead, establishing itself as a frontrunner in the quest for advanced neural networks capable of seamlessly handling periodic phenomena.
A Broader Implication for Real-World Applications
The design and effectiveness of FAN have vast implications for a myriad of industries where periodicity plays a vital role. From financial modeling to environmental science, the ability to accurately capture and generalize periodic data without extensive resource consumption accelerates innovation.
Moreover, as FAN successfully marries periodic modeling with general-purpose capabilities, it stands to revolutionize approaches in education, where cyclical learning methodologies can be better understood and implemented through intelligent systems, or in healthcare, where patient data often displays cyclic trends.
Submission and Revision History
Yihong Dong’s paper detailing FAN has undergone several revisions, which demonstrates the authors’ commitment to refining their findings and methodologies. The submission history includes:
- [v1] Thu, 3 Oct 2024
- [v2] Sat, 9 Nov 2024
- [v3] Fri, 31 Jan 2025
- [v4] Wed, 2 Apr 2025
- [v5] Tue, 30 Sep 2025
Each version reflects a step toward an increasingly robust framework, suggesting ongoing improvements and a deeper understanding of FAN’s potential applications.
In summary, FAN represents a decisive advancement in neural network architecture, particularly for applications involving periodic phenomena. Its ability to generalize effectively across different domains positions it as a transformative tool for future research and industry applications. The era of more sophisticated and capable neural networks is upon us, making it imperative to stay informed about breakthroughs like FAN.
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