Multi-layer perceptrons (MLPs) are integral to modern deep learning models for their versatility in replicating nonlinear functions across various tasks. However, interpretation and scalability challenges and reliance on fixed activation functions have raised concerns about their adaptability and scalability. Researchers have explored alternative architectures to overcome these issues, such as Kolmogov-Arnold Networks (KANs).
KANs have undergone substantial enhancements, such as replacing B-spline functions with more flexible mathematical representations, including Chebyshev polynomials, wavelet functions, and orthogonal polynomials, to increase their adaptability and performance. Developing hybrid approaches that incorporate KANs with other established network architectures can improve performance in applications including image classification, medical image processing, graph-related tasks and 3D reconstruction.
Researchers from the National University of Singapore conducted a detailed comparison between KANs and MLPs to understand their capabilities and limitations fully. The study performed a balanced assessment of the architectures by controlling parameters and FLOPs for both network types across various domains, including symbolic formula representation, machine learning, computer vision, natural language processing, and audio processing. The study also evaluated the impact of activation functions on network performance.
The research found that MLPs typically outperformed KANs in machine learning tasks across multiple datasets. Despite varied configurations for both architectures, MLPs demonstrated superior performance in six out of eight datasets, suggesting that they maintain an overall advantage in machine learning applications. In computer vision tasks, MLPs also consistently outperformed KANs across multiple datasets. They displayed a significant advantage in processing visual data, regardless of the configurations tested.
In audio and text classification tasks, MLPs generally performed better than KANs. Varied configurations were tested for both architectures, with MLPs consistently excelling in audio tasks and specific text datasets. However, KANs demonstrated an advantage when controlling for parameters in certain datasets, but not when controlling for FLOPs due to their high computational requirements. Still, despite occasional exceptions, MLPs generally remain more effective for processing audio and textual data compared to KANs.
In contrast, for symbolic formula representation tasks, KANs usually outperformed MLPs. They excelled in seven out of eight datasets when parameter counts were equal. However, when controlling for FLOPs, KANs’ performance was similar to that of MLPs due to their higher computational complexity, revealing their superior capability in representing symbolic formulas.
Overall, this study offers valuable insights for future research on neural network architectures. MLPs, despite their issues, seem to outperform KANs in various tasks, except for symbolic formula representation. These findings may guide the future development of neural network architectures to attain improved performance.
