Eye movements are intricate and dynamic events that contain a wealth of information about the subject and the stimuli. We propose an abstract representation of eye movements that preserve the important nuances in gaze behavior while being stimuli-agnostic. We consider eye movements as raw position and velocity signals and train a deep temporal convolutional autoencoder to learn micro-scale and macro-scale representations corresponding to the fast and slow features of eye movements. These joint representations are evaluated by fitting a linear classifier on various tasks and outperform other works in biometrics and stimuli classification. Further experiments highlight the validity and generalizability of this method, bringing eye tracking research closer to real-world applications.