Improving KAN with CDF normalization to quantiles

TL;DR

This paper introduces the use of CDF normalization to quantiles in machine learning, demonstrating improvements in Kolmogorov-Arnold Networks (KANs) by adopting this technique for better predictions and interpretability.

Contribution

It presents the novel application of CDF normalization to machine learning models, specifically enhancing KAN performance and interpretability.

Findings

CDF normalization improves KAN prediction accuracy

Switching to CDF normalization simplifies model representations

Enhanced interpretability of neuron weights as local joint distribution models

Abstract

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.