Abstract: Neural Architecture Search (NAS) is a promising paradigm in automatic architecture engineering. Zero-shot NAS can evaluate the network without training via some specific metrics called zero-cost proxies. Though effective, the existing zero-cost proxies either invoke at least one backpropagation or depend highly on the data and labels. To alleviate the above issues, in this paper, we first reveal how the Pearson correlation matrix of the feature maps impacts the convergence rate and the generalization capacity of an over-parameterized neural network. Enlightened by the theoretical analysis, we propose a novel zero-cost proxy called $\mathsf{MeCo}$, which requires only one random data for a single forward pass. We further propose an optimization approach $\mathsf{MeCo_{opt}}$ to improve the performance of our method. We design comprehensive experiments and extensively evaluate $\mathsf{MeCo}$ on multiple popular benchmarks. $\mathsf{MeCo}$ achieves the highest correlation with the ground truth (e.g., 0.89 on NATS-Bench-TSS with CIFAR-10) among all the state-of-the-art proxies, which is also fully independent of the data and labels. Moreover, we integrate $\mathsf{MeCo}$ with the existing generation method to comprise a complete NAS. The experimental results illustrate that $\mathsf{MeCo}$-based NAS can select the architecture with the highest accuracy and a low search cost. For instance, the best network searched by $\mathsf{MeCo}$-based NAS achieves 97.31% on CIFAR-10, which is 0.04% higher than the baselines under the same settings. Our code is available at https://github.com/HamsterMimi/MeCo