基于切比雪夫多项式的Kolmogorov-Arnold网络：一种用于非线性函数逼近的高效架构
Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation
AI总结：
本文提出Chebyshev KAN，利用切比雪夫多项式参数化边上可学习函数，在数字分类、函数逼近和分形生成任务中相比MLP展现出更高的参数效率与可解释性。
摘要：
复杂非线性函数的精确逼近是众多科学与工程领域中的一项根本性挑战。传统的神经网络架构，如多层感知机（MLPs），往往难以高效捕捉高维函数中存在的复杂模式和异常特征。本文提出了切比雪夫Kolmogorov-Arnold网络（Chebyshev KAN），这是一种受Kolmogorov-Arnold表示定理启发的新型神经网络架构，融合了切比雪夫多项式强大的逼近能力。通过在网络边上使用由切比雪夫多项式参数化的可学习函数，Chebyshev KAN在函数逼近任务中增强了灵活性、效率和可解释性。我们通过数字分类、合成函数逼近和分形函数生成等实验证明了Chebyshev KAN的有效性，突显了其在参数效率和可解释性方面相对于传统MLP的优越性。我们包括消融研究在内的综合评估证实了Chebyshev KAN在解决非线性函数逼近中长期存在的挑战方面的潜力，为各种科学和工程应用中的进一步发展铺平了道路。
英文摘要：
Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently capture intricate patterns and irregularities present in high-dimensional functions. This paper presents the Chebyshev Kolmogorov-Arnold Network (Chebyshev KAN), a new neural network architecture inspired by the Kolmogorov-Arnold representation theorem, incorporating the powerful approximation capabilities of Chebyshev polynomials. By utilizing learnable functions parametrized by Chebyshev polynomials on the network's edges, Chebyshev KANs enhance flexibility, efficiency, and interpretability in function approximation tasks. We demonstrate the efficacy of Chebyshev KANs through experiments on digit classification, synthetic function approximation, and fractal function generation, highlighting their superiority over traditional MLPs in terms of parameter efficiency and interpretability. Our comprehensive evaluation, including ablation studies, confirms the potential of Chebyshev KANs to address longstanding challenges in nonlinear function approximation, paving the way for further advancements in various scientific and engineering applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
