Kolmogorov-Arnold Networks achieve dimension-free convergence rate

Researchers have established convergence guarantees for Kolmogorov-Arnold Networks (KANs) that utilize B-splines for their univariate components. The study demonstrates that the least-squares estimator within the KAN spline sieve can achieve a convergence rate of $O((\log n / n)^{2r/(2r+1)})$, which is considered minimax optimal up to a logarithmic factor. This rate is independent of the ambient dimension, reflecting the KAN architecture's structure rather than an escape from standard minimax rates. Additionally, the paper introduces a knot-selection rule for adaptive rate attainment and notes that univariate components are not identifiable solely through centering. AI

IMPACT Establishes theoretical underpinnings for KANs, potentially influencing future neural network design and analysis.

RANK_REASON Academic paper detailing theoretical convergence guarantees for a specific neural network architecture. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• Kolmogorov-Arnold Networks
• Wei Liu

• paper
• model release

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