Kolmogorov Arnold Networks and Multi-Layer Perceptrons: A Paradigm Shift in Neural Modelling

TL;DR

The paper investigates Kolmogorov-Arnold Networks (KAN) as an efficient alternative to Multi-Layer Perceptrons (MLP) for nonlinear function approximation, time-series forecasting, and multivariate classification. By grounding KAN in the Kolmogorov-Arnold representation theorem and implementing spline-based activations on edges with grid-based extensions, the approach emphasizes both accuracy and computational efficiency, particularly in resource-limited settings. Empirical results across square and cube function estimation, daily temperature forecasting, and the Wine dataset show that KAN achieves higher predictive accuracy while substantially reducing FLOPs, following a scaling tendency of $N^{-4}$ for test loss and enabling continual learning and interpretability. The findings suggest a paradigm shift toward edge-friendly, interpretable architectures that balance performance and efficiency, providing a framework for selecting neural models tailored to task complexity and hardware constraints; future work includes pruning, quantization, and FPGA acceleration to further boost deployment feasibility.

Abstract

The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function approximation, time-series prediction, and multivariate classification. Rooted in Kolmogorov's representation theorem, KANs utilize adaptive spline-based activation functions and grid-based structures, providing a transformative approach compared to traditional neural network frameworks. Utilizing a variety of datasets spanning mathematical function estimation (quadratic and cubic) to practical uses like predicting daily temperatures and categorizing wines, the proposed research thoroughly assesses model performance via accuracy measures like Mean Squared Error (MSE) and computational expense assessed through Floating Point Operations (FLOPs). The results indicate that KANs reliably exceed MLPs in every benchmark, attaining higher predictive accuracy with significantly reduced computational costs. Such an outcome highlights their ability to maintain a balance between computational efficiency and accuracy, rendering them especially beneficial in resource-limited and real-time operational environments. By elucidating the architectural and functional distinctions between KANs and MLPs, the paper provides a systematic framework for selecting the most suitable neural architectures for specific tasks. Furthermore, the proposed study highlights the transformative capabilities of KANs in progressing intelligent systems, influencing their use in situations that require both interpretability and computational efficiency.

Figures (8)

• Figure 1: Comparison of MLP's and KAN's liu2024kankolmogorovarnoldnetworks.
• Figure 2: Left: Symbols representing the flow of activations in the network. Right: activation function is defined as expressed in the form of a B-spline, enabling the transition from coarse to fine grids liu2024kankolmogorovarnoldnetworks.
• Figure 3: Demonstration of Continual Learning: A KAN model's ability to acquire new tasks while preserving previously learned information liu2024kankolmogorovarnoldnetworks.
• Figure 4: Illustration of Interpretability: A KAN model providing comprehensible insights into decision-making processes liu2024kankolmogorovarnoldnetworks.
• Figure 5: Illustration of Grid extension: Increasing the efficiency of the model, (Bodner et al. gridextension).