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Robust multi-object tracking (MOT) is a prerequisite fora safe deployment of self-driving cars. Tracking objects, however, remains a highly challenging problem, especially in cluttered autonomous driving scenes in which objects tend to interact with each other in complex ways and frequently get occluded. We propose a novel approach to MOT that uses attention to compute track embeddings that encode the spatiotemporal dependencies between observed objects. This attention measurement encoding allows our model to relax hard data associations, which may lead to unrecoverable errors. Instead, our model aggregates information from all object detections via soft data associations. The resulting latent space representation allows our model to learn to reason about occlusions in a holistic data-driven way and maintain track estimates for objects even when they are occluded. Our experimental results on the Waymo OpenDataset suggest that our approach leverages modern large-scale datasets and performs favorably compared to the state of the art in visual multi-object tracking.