  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.
