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To cope with the ever-increasing computational demand of the DNN execution, recent neural architecture search (NAS) algorithms consider hardware cost metrics into account, such as GPU latency. To further pursue a fast, efficient execution, DNN-specialized hardware accelerators are being designed for multiple purposes, which far-exceeds the efficiency of the GPUs. However, those hardware-related metrics have been proven to exhibit non-linear relationships with the network architectures. Therefore it became a chicken-and-egg problem to optimize the network against the accelerator, or to optimize the accelerator against the network. In such circumstances, this work presents DANCE, a differentiable approach towards the co-exploration of the hardware accelerator and network architecture design. At the heart of DANCE is a differentiable evaluator network. By modeling the hardware evaluation software with a neural network, the relation between the accelerator architecture and the hardware metrics becomes differentiable, allowing the search to be performed with backpropagation. Compared to the naive existing approaches, our method performs co-exploration in a significantly shorter time, while achieving superior accuracy and hardware cost metrics.