Searches for low-surface-brightness galaxies (LSBGs) in galaxy surveys are\nplagued by the presence of a large number of artifacts (e.g., objects blended\nin the diffuse light from stars and galaxies, Galactic cirrus, star-forming\nregions in the arms of spiral galaxies, etc.) that have to be rejected through\ntime consuming visual inspection. In future surveys, which are expected to\ncollect hundreds of petabytes of data and detect billions of objects, such an\napproach will not be feasible. We investigate the use of convolutional neural\nnetworks (CNNs) for the problem of separating LSBGs from artifacts in survey\nimages. We take advantage of the fact that, for the first time, we have\navailable a large number of labeled LSBGs and artifacts from the Dark Energy\nSurvey, that we use to train, validate, and test a CNN model. That model, which\nwe call DeepShadows, achieves a test accuracy of $92.0 \\%$, a significant\nimprovement relative to feature-based machine learning models. We also study\nthe ability to use transfer learning to adapt this model to classify objects\nfrom the deeper Hyper-Suprime-Cam survey, and we show that after the model is\nretrained on a very small sample from the new survey, it can reach an accuracy\nof $87.6\\%$. These results demonstrate that CNNs offer a very promising path in\nthe quest to study the low-surface-brightness universe.\n