Improving KAN with CDF normalization to quantiles Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2507.13393

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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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2507.13393
PDF: https://arxiv.org/pdf/2507.13393
OA Status: green
OpenAlex ID: https://openalex.org/W4416832916

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OpenAlex ID: https://openalex.org/W4416832916

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DOI: https://doi.org/10.48550/arxiv.2507.13393

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Title: Improving KAN with CDF normalization to quantiles

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-07-16

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Authors: Jakub Strawa, Jarek Duda

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Landing page: https://arxiv.org/abs/2507.13393

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PDF URL: https://arxiv.org/pdf/2507.13393

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OA status: green

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Cited by: 0

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