Improving KAN with CDF normalization to quantiles
This work addresses data normalization for machine learning practitioners, offering an incremental improvement by adapting a known technique from finance to enhance KAN performance.
The paper tackles the problem of data normalization in machine learning by introducing CDF normalization to quantiles, a method from copula theory, and applies it to Kolmogorov-Arnold Networks (KANs), resulting in improved predictions over Legendre-KAN with just a rescaling switch.
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.