The principles underlying the spatial organisation of the genome are key to understanding cell type specific gene transcription. Genome-wide chromosome conformation capture methods such as Hi-C and Micro-C produce vast quantities of data which can be noisy and difficult to interrogate. As a result the analysis has so far been limited to pre-defined features curated by manual inspection. Here, we present a newly identified feature from quiescent T-cell chromatin conformation maps, called the chromatin jet. We demonstrate that this feature is mediated by the action of the cohesin protein complex and limited by the CTCF boundary element, in line with the loop extrusion model. We utilise chromatin jets to dissect the properties of cohesin-mediated loop extrusion, demonstrating that cohesin may continue to extrude loops unidirectionally upon an encounter with CTCF. Motivated by the discovery of this new feature, we formulate a deep learning approach based on contrastive learning which we term Twins. Using a Siamese convolutional neural network, we are able to distinguish technical noise from biological variation and outperform naive image similarity metrics across a range of biological systems. Downstream we apply our Twins network to perform simple feature extraction from Hi-C maps after perturbation of cohesin and CTCF. Using this approach we find that Twins networks are able to learn biologically meaningful information which is robust to various common sources of noise. Following the success of the Twins protocol, we apply a Siamese network to a mouse T-cell differentiation system. In this context, Twins identifies enhancer activity as a major driver of 3D genome organisation. Taken together these findings advance our understanding of chromatin conformation and its role in gene regulation. Further, they provide a foundation on which new methods for the analysis of chromatin conformation capture data can be constructed.