Interpretability can be defined as the ability to understand a neural network and explain its behavior. In practice, Multi-Layer Perceptrons (MLPs) are considered opaque due to their size and complexity. To overcome this, a more interpretable alternative was proposed recently, i.e. Kolmogorov–Arnold Networks (KANs). In this work, we discuss the difference between Kolmogorov–Arnold representation Theorem (KAT) and Universal Approximation Theorem (UAT), i.e. the underlying theorems of KAN and MLP. Moreover, we highlight that KAN violates the size constraint in KAT; thus, it is not more interpretable than MLP. Furthermore, we present practical scenarios and argue that KANs are less interpretable than MLPs when dealing with high-dimensional data like images and text. Additionally, we perform several experiments and show that KANs contain larger number of trainable parameters compared to MLPs, causing a significant additional computational cost without noticeable performance improvement.

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Is KAN More Interpretable than MLP? A Comparative Study on Image and Text Data

  • Modafar Al-Shouha,
  • Gábor Szűcs

摘要

Interpretability can be defined as the ability to understand a neural network and explain its behavior. In practice, Multi-Layer Perceptrons (MLPs) are considered opaque due to their size and complexity. To overcome this, a more interpretable alternative was proposed recently, i.e. Kolmogorov–Arnold Networks (KANs). In this work, we discuss the difference between Kolmogorov–Arnold representation Theorem (KAT) and Universal Approximation Theorem (UAT), i.e. the underlying theorems of KAN and MLP. Moreover, we highlight that KAN violates the size constraint in KAT; thus, it is not more interpretable than MLP. Furthermore, we present practical scenarios and argue that KANs are less interpretable than MLPs when dealing with high-dimensional data like images and text. Additionally, we perform several experiments and show that KANs contain larger number of trainable parameters compared to MLPs, causing a significant additional computational cost without noticeable performance improvement.