KAN versus MLP on Irregular or Noisy Functions
This work addresses the problem of selecting neural network architectures for irregular or noisy functions, providing insights for researchers, but it is incremental as it compares existing methods without introducing new ones.
The paper compared Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptron (MLP) networks on irregular or noisy functions, finding that KAN does not always perform best, with MLP outperforming or matching it for some function types, and performance improved with larger training samples.
In this paper, we compare the performance of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptron (MLP) networks on irregular or noisy functions. We control the number of parameters and the size of the training samples to ensure a fair comparison. For clarity, we categorize the functions into six types: regular functions, continuous functions with local non-differentiable points, functions with jump discontinuities, functions with singularities, functions with coherent oscillations, and noisy functions. Our experimental results indicate that KAN does not always perform best. For some types of functions, MLP outperforms or performs comparably to KAN. Furthermore, increasing the size of training samples can improve performance to some extent. When noise is added to functions, the irregular features are often obscured by the noise, making it challenging for both MLP and KAN to extract these features effectively. We hope these experiments provide valuable insights for future neural network research and encourage further investigations to overcome these challenges.