Supplementary material for TopoSRL: Topology Preserving Self-Supervised Simplicial Representation Learning

Theorem 1. Minimizing the expected loss L The two views come from a probability distribution conditioned on original data distribution X, and X is as distributed as X. Suppose we have T -dimensional features. A similar result can be established for the second term in Equation (S4), which will reduce the variance of representations of simplices and their neighborhoods within the same augmented simplicial complex. In Table S1, we provide details about the datasets used in the experiments in the paper, namely, contact-high-school, contact-primary-school, senate-bills, and email-Enron. A simplex in contact-high-school and contact-primary-school represent a group of people who were in close proximity, and the classes are the classrooms that the students are in. In senate-bills, a simplex is the set of co-sponsors of bills that are put forth in the Senate, and the classes are the political party the sponsors belong to.