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This article focuses on the utilization of limited data available to predict spatial adjacencies (“contact maps”) as a proxy for 3D structure of RNA. The model, BARNACLE, combines the utilization of unlabeled data through self-supervised pre-training and efficient use of the sparse labeled data through an XGBoost classifier. BARNACLE shows a considerable improvement over both the established classical baseline and a deep neural network. The findings of this work can be applied to tasks with similar data constraints, such as accessible surface area prediction.