https://github.com/xuyang527/NASH.}
The significant computational cost of multiplications hinders the deployment of deep neural networks (DNNs) on edge devices. While multiplication-free models offer enhanced hardware efficiency, they typically sacrifice accuracy. As a solution, multiplication-reduced hybrid models have emerged to combine the benefits of both approaches. Particularly, prior works, i.e., NASA and NASA-F, leverage Neural Architecture Search (NAS) to construct such hybrid models, enhancing hardware efficiency while maintaining accuracy. However, they either entail costly retraining or encounter gradient conflicts, limiting both search efficiency and accuracy. Additionally, they overlook the acceleration opportunity introduced by accelerator search, yielding sub-optimal hardware performance. To overcome these limitations, we propose NASH, a Neural architecture and Accelerator Search framework for multiplication-reduced Hybrid models. Specifically, as for NAS, we propose a tailored zero-shot metric to pre-identify promising hybrid models before training, enhancing search efficiency while alleviating gradient conflicts. Regarding accelerator search, we innovatively introduce coarse-to-fine search to streamline the search process. Furthermore, we seamlessly integrate these two levels of searches to unveil NASH, obtaining the optimal model and accelerator pairing. Experiments validate our effectiveness, e.g., when compared with the state-of-the-art multiplication-based system, we can achieve $\uparrow$$2.14\times$ throughput and $\uparrow$$2.01\times$ FPS with $\uparrow$$0.25\%$ accuracy on CIFAR-100, and $\uparrow$$1.40\times$ throughput and $\uparrow$$1.19\times$ FPS with $\uparrow$$0.56\%$ accuracy on Tiny-ImageNet. Codes are available at \url{