Kolmogorov-Arnold Networks：对声明、性能与实用性的批判性评估
Kolmogorov-Arnold Networks: A Critical Assessment of Claims, Performance, and Practical Viability
AI总结：
本文批判性评估了KANs的性能，发现其仅在符号回归任务中优于MLPs，且计算开销大、理论声明缺乏基础，为未来研究提供了基于证据的指导。
摘要：
Kolmogorov-Arnold Networks (KANs) 作为传统多层感知机（MLP）的替代方案受到了广泛关注，支持者声称其通过可学习的单变量激活函数实现了卓越的可解释性和性能。然而，近期的系统评估揭示了理论声明与实证证据之间的重大差异。本批判性评估采用控制参数和计算成本的公平比较方法，考察了 KANs 在多个领域的实际性能。分析表明，KANs 仅在符号回归任务中优于 MLPs，而在机器学习、计算机视觉和自然语言处理基准测试中始终表现不佳。其所声称的优势主要源于 B-spline 激活函数而非架构创新，且计算开销（慢 1.36-100 倍）严重限制了实际部署。此外，关于打破“维度灾难”的理论声明缺乏严格的数学基础。我们系统性地识别了 KANs 相比传统方法具有价值的条件，确立了未来研究的评估标准，并提出了基于优先级的路线图以解决根本局限。本研究为研究人员和从业者合理采用 KANs 提供了基于证据的指导，同时指出了实现更广泛适用性必须解决的关键研究空白。
英文摘要：
Kolmogorov-Arnold Networks (KANs) have gained significant attention as an alternative to traditional multilayer perceptrons, with proponents claiming superior interpretability and performance through learnable univariate activation functions. However, recent systematic evaluations reveal substantial discrepancies between theoretical claims and empirical evidence. This critical assessment examines KANs' actual performance across diverse domains using fair comparison methodologies that control for parameters and computational costs. Our analysis demonstrates that KANs outperform MLPs only in symbolic regression tasks, while consistently underperforming in machine learning, computer vision, and natural language processing benchmarks. The claimed advantages largely stem from B-spline activation functions rather than architectural innovations, and computational overhead (1.36-100x slower) severely limits practical deployment. Furthermore, theoretical claims about breaking the "curse of dimensionality" lack rigorous mathematical foundation. We systematically identify the conditions under which KANs provide value versus traditional approaches, establish evaluation standards for future research, and propose a priority-based roadmap for addressing fundamental limitations. This work provides researchers and practitioners with evidence-based guidance for the rational adoption of KANs while highlighting critical research gaps that must be addressed for broader applicability.
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