Three-dimensional nuclear DNA architecture comprises well-studied intra-chromosomal (cis) folding and less characterized inter-chromosomal (trans) interfaces. Current predictive models of 3D genome folding can effectively infer pairwise cis-chromatin interactions from the primary DNA sequence but generally ignore trans contacts. There is an unmet need for robust models of trans-genome organization that provide insights into their underlying principles and functional relevance. We present TwinC, an interpretable convolutional neural network model that reliably predicts trans contacts measurable through genome-wide chromatin conformation capture (Hi-C). TwinC uses a paired sequence design from replicate Hi-C experiments to learn single base pair relevance in trans interactions across two stretches of DNA. The method achieves high predictive accuracy (AUROC=0.80) on a cross-chromosomal test set from Hi-C experiments in heart tissue. Mechanistically, the neural network learns the importance of compartments, chromatin accessibility, clustered transcription factor binding and G-quadruplexes in forming trans contacts. In summary, TwinC models and interprets trans genome architecture, shedding light on this poorly understood aspect of gene regulation.