Such embeddings induce the so-called maximum mean discrepancy (MMD; [Smola et al., 2007, Gretton et al., 2012]), which quantifies the discrepancy Many estimators for HSIC exist. The classical ones rely on U-statistics or V -statistics [Gretton et al., 2005, Quadrianto et al., 2009, Pfister et al., 2018] and are known to converge at a rate of Lower bounds for the related MMD are known [Tolstikhin et al., 2016], but the existing analysis considers radial kernels and relies on independent Gaussian distributions.

Currently, two mainstream GNN-based methods have been developed for constructing force fields: group theory-based methods and direction-based methods.

However, previous NF-based methods forcibly transform the distribution of all features into a single distribution (e.g., unit normal distribution), even when the features can have locally distinct semantic information and thus follow different