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.

翻译：本研究对 Kolmogorov-Arnold 网络（KAN）与多层感知机（MLP）进行了全面的比较分析，重点探讨了它们在解决非线性函数逼近、时间序列预测和多变量分类等关键计算挑战方面的有效性。KAN 植根于 Kolmogorov 表示定理，采用基于自适应样条的激活函数和基于网格的结构，相比传统神经网络框架提供了一种变革性的方法。本研究利用涵盖数学函数估计（二次和三次）到实际应用（如预测每日温度和葡萄酒分类）的多种数据集，通过均方误差（MSE）等精度指标以及浮点运算（FLOPs）评估的计算开销，对模型性能进行了全面评估。结果表明，KAN 在所有基准测试中均稳定超越 MLP，以显著降低的计算成本实现了更高的预测精度。这一结果突显了 KAN 在计算效率与精度之间保持平衡的能力，使其在资源受限和实时操作环境中尤其具有优势。通过阐明 KAN 与 MLP 在架构和功能上的差异，本文为针对特定任务选择最合适的神经架构提供了一个系统框架。此外，本研究强调了 KAN 在推动智能系统发展方面的变革性潜力，影响了其在需要可解释性与计算效率并重的场景中的应用。