Improving KAN with CDF normalization to quantiles
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Abstract (arXiv)
Data normalization is crucial in machine learning, usually performed by subtracting the mean and dividing by standard deviation, or by rescaling to a fixed range. In copula theory, popular in finance, there is used normalization to approximately quantiles by transforming x to CDF(x) with estimated CDF (cumulative distribution function) to nearly uniform distribution in [0,1], allowing for simpler representations which are less likely to overfit. It seems nearly unknown in machine learning, therefore, we would like to present some its advantages on example of recently popular Kolmogorov-Arnold Networks (KANs), improving predictions from Legendre-KAN by just switching rescaling to CDF normalization. Additionally, in HCR interpretation, weights of such neurons are mixed moments providing local joint distribution models, allow to propagate also probability distributions, and change propagation direction.
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References · 7
- 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
- 2024KAN: Kolmogorov-Arnold Networkscited by 649
- 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
- 2020The Kolmogorov-Arnold representation theorem revisitedcited by 89
- 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 35
- 2018Hierarchical correlation reconstruction with missing data, for example for biology-inspired neuroncited by 6
- 2017Rapid parametric density estimationcited by 3
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