Title: Triple-Search: Differentiable Joint-Search of Networks, Precision, and Accelerators. Abstract: The record-breaking performance and prohibitive complexity of deep neural networks (DNNs) have ignited a substantial need for customized DNN accelerators which have the potential to boost DNN acceleration efficiency by orders-of-magnitude. While it has been recognized that maximizing DNNs' acceleration efficiency requires a joint design/search for three different yet highly coupled aspects, including the networks, adopted precision, and their accelerators, the challenges associated with such a joint search have not yet been fully discussed and addressed. First, to jointly search for a network and its precision via differentiable search, there exists a dilemma of whether to explode the memory consumption or achieve sub-optimal designs. Second, a generic and differentiable joint search of the networks and their accelerators is non-trivial due to (1) the discrete nature of the accelerator space and (2) the difficulty of obtaining operation-wise hardware cost penalties because some accelerator parameters are determined by the whole network. To this end, we propose a Triple-Search (TRIPS) framework to address the aforementioned challenges towards jointly searching for the network structure, precision, and accelerator in a differentiable manner, to efficiently and effectively explore the huge joint search space. Our TRIPS addresses the first challenge above via a heterogeneous sampling strategy to achieve unbiased search with constant memory consumption, and tackles the latter one using a novel co-search pipeline that integrates a generic differentiable accelerator search engine. Extensive experiments and ablation studies validate that both TRIPS generated networks and accelerators consistently outperform state-of-the-art (SOTA) designs (including co-search/exploration techniques, hardware-aware NAS methods, and DNN accelerators), in terms of search time, task accuracy, and accelerator efficiency. All codes will be released upon acceptance.