Methods, systems, and apparatus, including computer programs encoded on computer storage media, for characterizing a gaze position of a user in a query image. One of the methods includes obtaining a query image of a user captured by a camera of a mobile device; obtaining device characteristics data specifying (ii) characteristics of the mobile device, (ii) characteristics of the camera of the mobile device, or (iii) both; and processing a neural network input comprising (i) one or more images derived from the query image and (ii) the device characteristics data using a gaze prediction neural network, wherein the gaze prediction neural network is configured to, at run time and after the gaze prediction neural network has been trained, process the neural network input to generate a neural network output that characterizes a gaze position of the user in the query image.