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We explore the hypothesis that learning modular structures which reflect the dynamics of the environment can lead to better generalization and robustness to changes that only affect a few of the underlying causes. We propose Recurrent Independent Mechanisms (RIMs), a new recurrent architecture in which multiple groups of recurrent cells operate with nearly independent transition dynamics, communicate only sparingly through the bottleneck of attention, and compete with each other so they are updated only at time steps where they are most relevant. We show that this leads to specialization amongst the RIMs, which in turn allows for remarkably improved generalization on tasks where some factors of variation differ systematically between training and evaluation.