For the Fourier Analysis FANs
FANs are better than MLP/KAN/Transformers in predicting periodicity
Paper: FAN: Fourier Analysis Networks (14 Pages)
Researchers from Peking University and ByteDance are interested in a novel neural network architecture called FAN (Fourier Analysis Network).
Hmm..What’s the background?
Existing neural networks, despite their strengths, face challenges when it comes to modeling and reasoning about periodicity in data. This means they may struggle to accurately represent and predict patterns that repeat over time or other dimensions. Periodicity is a fundamental aspect of many natural and engineered systems, making it crucial for networks to understand this concept.
Ok, So what is proposed in the research paper?
FAN's design incorporates Fourier Series directly into its structure. FAN embeds the concept of representing functions as sums of sines and cosines, a powerful mathematical tool for analyzing periodic patterns.
FAN significantly outperforms existing architectures in fitting both basic and complex periodic functions, especially in scenarios where the test data falls outside the training data distribution
FAN demonstrates superior performance on tasks like symbolic formula representation, time series forecasting, and language modeling, even surpassing specialized architectures
Notably, FAN achieves this while often using fewer parameters and FLOPs (floating-point operations) compared to standard MLP layers, making it a potentially more efficient alternative.
What’s next?
The authors identify two main directions for future research:
Scaling Up: Exploring the performance of FAN at larger scales
Broader Applications: Investigating the use of FAN in a wider range of tasks beyond those explicitly focused on periodicity
So essentially,
FANs are better than MLP/KAN/Transformers in predicting periodicity
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