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We present the Chromatin Landscape and Structure to Expression Regressor (CLASTER), an epigenetic-based deep neural network that can integrate different data modalities describing the chromatin landscape and its 3D structure. CLASTER effectively translates them into nascent transcription levels measured at a kilobasepair resolution. The model provides a platform to understand the epigenetic drivers and learned rules of nascent transcription, and to predict the impact of in silico epigenetic perturbations. We conclude that the predominant locality of current machine learning approaches emerges as a signature of genomic organization, having broad implications for future modeling approaches.