KAN比MLP更高效准确,适合资源受限场景
Kolmogorov Arnold Networks and Multi-Layer Perceptrons: A Paradigm Shift in Neural Modelling
- 用可学习的样条函数替代传统激活函数,结构更灵活
- 在多项式拟合、温度预测等任务中精度更高,计算量减少30%以上
- 适合需要解释性和实时性的智能系统应用
本研究对柯尔莫哥洛夫-阿诺德网络(KAN)与多层感知机(MLP)进行系统比较,评估其在非线性函数逼近、时间序列预测和多变量分类等任务中的表现。基于柯尔莫哥洛夫表示定理,KAN采用自适应样条激活函数和网格化结构,相较传统神经网络具有范式革新意义。实验覆盖数学函数估计(二次与三次)、日气温预测及葡萄酒分类等数据集,以均方误差(MSE)和浮点运算量(FLOPs)为评估指标。结果表明,所有基准测试中KAN均优于MLP,实现更高预测精度且计算成本显著降低。该性能平衡使其在资源受限与实时场景中尤为适用。论文还揭示了两类模型的架构与功能差异,提供了针对特定任务选择合适模型的系统框架,并强调了KAN在提升智能系统可解释性与计算效率方面的变革潜力。
原文摘要 · Abstract (English)
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.
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