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Natural human interactions for Mixed Reality Applications are overwhelmingly multimodal: humans communicate intent and instructions via a combination of visual, aural and gestural cues. However, supporting low-latency and accurate comprehension of such multimodal instructions (MMI), on resource-constrained wearable devices, remains an open challenge, especially as the state-of-the-art comprehension techniques for each individual modality increasingly utilize complex Deep Neural Network models. We demonstrate the possibility of overcoming the core limitation of latency--vs.--accuracy tradeoff by exploiting cross-modal dependencies -- i.e., by compensating for the inferior performance of one model with an increased accuracy of more complex model of a different modality. We present a sensor fusion architecture that performs MMI comprehension in a quasi-synchronous fashion, by fusing visual, speech and gestural input. The architecture is reconfigurable and supports dynamic modification of the complexity of the data processing pipeline for each individual modality in response to contextual changes. Using a representative "classroom" context and a set of four common interaction primitives, we then demonstrate how the choices between low and high complexity models for each individual modality are coupled. In particular, we show that (a) a judicious combination of low and high complexity models across modalities can offer a dramatic 3-fold decrease in comprehension latency together with an increase 10-15% in accuracy, and (b) the right collective choice of models is context dependent, with the performance of some model combinations being significantly more sensitive to changes in scene context or choice of interaction.