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We propose a learning algorithm to design a light-weight neural multiplexer that given the input and computational resource requirements, calls the model that will consume the minimum compute resources for a successful inference. Mobile devices can use the proposed algorithm to offload the hard inputs to the cloud while inferring the easy ones locally. Besides, in the large scale cloud-based intelligent applications, instead of replicating the most-accurate model, a range of small and large models can be multiplexed from depending on the input's complexity which will save the cloud's computational resources. The input complexity or hardness is determined by the number of models that can predict the correct label. For example, if no model can predict the label correctly, then the input is considered as the hardest. The proposed algorithm allows the mobile device to detect the inputs that can be processed locally and the ones that require a larger model and should be sent a cloud server. Therefore, the mobile user benefits from not only the local processing but also from an accurate model hosted on a cloud server. Our experimental results show that the proposed algorithm improves mobile's model accuracy by 8.52% which is because of those inputs that are properly selected and offloaded to the cloud server. In addition, it saves the cloud providers' compute resources by a factor of 2.85x as small models are chosen for easier inputs.