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We train a global matching transformer to find cycle consistent tracks through video via contrastive random walks, using the transformer's attention-based global matching to define the transition matrices for a random walk on a space-time graph. The ability to perform \"all pairs\" comparisons between points allows the model to obtain high spatial precision and to obtain a strong contrastive learning signal, while avoiding many of the complexities of recent approaches (such as coarse-to-fine matching). To do this, we propose a number of design decisions that allow global matching architectures to be trained through self-supervision using cycle consistency. For example, we identify that transformer-based methods are sensitive to shortcut solutions, and propose a data augmentation scheme to address them. 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