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Minimum redundancy among different elements of an embedding in a latent spaceis a fundamental requirement or major preference in representation learning tocapture intrinsic informational structures. Current self-supervised learningmethods minimize a pair-wise covariance matrix to reduce the feature redundancyand produce promising results. However, such representation features ofmultiple variables may contain the redundancy among more than two featurevariables that cannot be minimized via the pairwise regularization. Here wepropose the High-Order Mixed-Moment-based Embedding (HOME) strategy to reducethe redundancy between any sets of feature variables, which is to our bestknowledge the first attempt to utilize high-order statistics/information inthis context. Multivariate mutual information is minimum if and only ifmultiple variables are mutually independent, which suggests the necessaryconditions of factorized mixed moments among multiple variables. Based on thesestatistical and information theoretic principles, our general HOME framework ispresented for self-supervised representation learning. Our initial experimentsshow that a simple version in the form of a three-order HOME scheme alreadysignificantly outperforms the current two-order baseline method (i.e., BarlowTwins) in terms of the linear evaluation on representation features.

HOME: High-Order Mixed-Moment-based Embedding for Representation Learning