Despite the availability of chromatin conformation capture experiments, discerning the relationship between the 1D genome and 3D conformation remains a challenge, which limits our understanding of their affect on gene expression and disease. We propose Hi-C-LSTM, a method that produces low-dimensional latent representations that summarize intra-chromosomal Hi-C contacts via a recurrent long short-term memory (LSTM) neural network model. We find that these representations contain all the information needed to recreate the original Hi-C matrix with high accuracy, outperforming existing methods. These representations enable the identification of a variety of conformation-defining genomic elements, including nuclear compartments and conformation-related transcription factors. They furthermore enable in-silico perturbation experiments that measure the influence of cis-regulatory elements on conformation.