Title: PareCO: Pareto-aware Channel Optimization for Slimmable Neural Networks. Abstract: Slimmable neural networks provide a flexible trade-off front between prediction error and computational cost (such as the number of floating-point operations or FLOPs) with the same storage cost as a single model. They have been proposed recently for resource-constrained settings such as mobile devices. However, current slimmable neural networks use a single width-multiplier for all the layers to arrive at sub-networks with different performance profiles, which neglects that different layers affect the network's prediction accuracy differently and have different FLOP requirements. Hence,  developing a principled approach for deciding width-multipliers across different layers could potentially improve the performance of slimmable networks. To allow for heterogeneous width-multipliers across different layers, we formulate the problem of optimizing slimmable networks from a multi-objective optimization lens, which leads to a novel algorithm for optimizing both the shared weights and the width-multipliers for the sub-networks. We perform extensive empirical analysis with 15 network and dataset combinations and two types of cost objectives, i.e., FLOPs and memory footprint, to demonstrate the effectiveness of the proposed method compared to existing alternatives. Quantitatively, improvements up to 1.7% and 8% in top-1 accuracy on the ImageNet dataset can be attained for MobileNetV2 considering FLOPs and memory footprint, respectively. Our results highlight the potential of optimizing the channel counts for different layers jointly with the weights for slimmable networks.