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Representation learning provides an opportunity to uncover the link between 3D genome organization and gene regulatory networks, thereby connecting the physical and the biochemical space of a cell. Our method, Image2Reg, uses chromatin images obtained in large-scale genetic and chemical perturbation screens. Through convolutional neural networks, Image2Reg generates gene embedding that represents the effect of gene perturbation on chromatin organization. In addition, combining protein-protein interaction data with cell-type-specific transcriptomic data through a graph convolutional network, we obtain a gene embedding that represents the regulatory effect of genes. Finally, Image2Reg learns a map between the resulting physical and biochemical representation of cells, allowing us to predict the perturbed gene modules based on chromatin images. Our results confirm the deep link between chromatin organization and gene regulation and demonstrate that it can be harnessed to identify drug targets and genes upstream of perturbed phenotypes from a simple and inexpensive chromatin staining.