Recently, zero-shot (or training-free) Neural Architecture Search (NAS) approaches have been proposed to liberate NAS from the expensive training process. The key idea behind zero-shot NAS approaches is to design proxies that can predict the accuracy of some given networks without training the network parameters. The proxies proposed so far are usually inspired by recent progress in theoretical understanding of deep learning and have shown great potential on several datasets and NAS benchmarks. This paper aims to comprehensively review and compare the state-of-the-art (SOTA) zero-shot NAS approaches, with an emphasis on their hardware awareness. To this end, we first review the mainstream zero-shot proxies and discuss their theoretical underpinnings. We then compare these zero-shot proxies through large-scale experiments and demonstrate their effectiveness in both hardware-aware and hardware-oblivious NAS scenarios. Finally, we point out several promising ideas to design better proxies. Our source code and the list of related papers are available on https://github.com/SLDGroup/survey-zero-shot-nas.

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