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Brain-computer interfaces have so far focused largely on enabling the control of a single effector, for example a single computer cursor or robotic arm. Restoring multi-effector motion could unlock greater functionality for people with paralysis (e.g., bimanual movement). However, it may prove challenging to decode the simultaneous motion of multiple effectors, as we recently found that a compositional neural code links movements across all limbs and that neural tuning changes nonlinearly during dual-effector motion. Here, we demonstrate the feasibility of high-quality bimanual control of two cursors via neural network (NN) decoders. Through simulations, we show that NNs leverage a neural 'laterality' dimension to distinguish between left and right-hand movements as neural tuning to both hands become increasingly correlated. In training recurrent neural networks (RNNs) for two-cursor control, we developed a method that alters the temporal structure of the training data by dilating/compressing it in time and re-ordering it, which we show helps RNNs successfully generalize to the online setting. With this method, we demonstrate that a person with paralysis can control two computer cursors simultaneously. Our results suggest that neural network decoders may be advantageous for multi-effector decoding, provided they are designed to transfer to the online setting. [ABSTRACT FROM AUTHOR]