  Barlow Twins and VICReg are self-supervised representation learning models
that use regularizers to decorrelate features. Although these models are as
effective as conventional representation learning models, their training can be
computationally demanding if the dimension d of the projected embeddings is
high. As the regularizers are defined in terms of individual elements of a
cross-correlation or covariance matrix, computing the loss for n samples takes
O(n d^2) time. In this paper, we propose a relaxed decorrelating regularizer
that can be computed in O(n d log d) time by Fast Fourier Transform. We also
propose an inexpensive technique to mitigate undesirable local minima that
develop with the relaxation. The proposed regularizer exhibits accuracy
comparable to that of existing regularizers in downstream tasks, whereas their
training requires less memory and is faster for large d. The source code is
available.
