Title: Locally Free Weight Sharing for Network Width Search. Abstract: Searching for network width is an effective way to slim deep neural networks with hardware budgets. With this aim, a one-shot supernet is usually leveraged as a performance evaluator to rank the performance \wrt~different width. Nevertheless, current methods mainly follow a manually fixed weight sharing pattern, which is limited to distinguish the performance gap of different width. In this paper, to better evaluate each width, we propose a locally free weight sharing strategy (CafeNet) accordingly. In CafeNet, weights are more freely shared, and each width is jointly indicated by its base channels and free channels, where free channels are supposed to locate freely in a local zone to better represent each width. Besides, we propose to further reduce the search space by leveraging our introduced FLOPs-sensitive bins. As a result, our CafeNet can be trained stochastically and get optimized within a min-min strategy. Extensive experiments on ImageNet, CIFAR-10, CelebA and MS COCO dataset have verified our superiority comparing to other state-of-the-art baselines. For example, our method can further boost the benchmark NAS network EfficientNet-B0 by 0.41\% via searching its width more delicately.