The development of Neural Architecture Search (NAS) is hindered by high costs associated with evaluating network architectures. Recently, several zero-cost proxies have been proposed as a promising method to reduce the evaluation cost of network architectures in NAS. They can quickly estimate the final performance of the network in a few seconds during the initial phase. However, existing zero-cost proxies either ignore the network structure's impact on performance or are limited to specific tasks. To address these issues, we propose a novel zero-cost proxy called Skeleton Path Kernel Trace (SPKT) that leverages the whole network architecture's skeleton path structure information. We then integrate it into an effective Bayesian optimization for NAS framework called PATNAS, and demonstrate its efficacy on different datasets. The results show that our proposed SPKT zero-cost proxy can achieve a high correlation with the final performance of the network across multiple tasks. Furthermore, it can significantly accelerate the search process for finding the best-performing network architectures.

Instead of searching the entire network directly, current NAS approaches increasingly search for multiple relatively small cells to reduce search costs. A major challenge is to jointly measure the similarity of cell micro-architectures and the difference in macro-architectures between different cell-based networks. Recently, optimal transport (OT) has been successfully applied to NAS as it can capture the operational and structural similarity across various networks. However, existing OT-based NAS methods either ignore the cell similarity or focus solely on searching for a single cell architecture. To address these issues, we propose a hierarchical optimal transport metric called HOTNN for measuring the similarity of different networks. In HOTNN, the cell-level similarity computes the OT distance between cells in various networks by considering the similarity of each node and the differences in the information flow costs between node pairs within each cell in terms of operational and structural information. The network-level similarity calculates OT distance between networks by considering both the cell-level similarity and the variation in the global position of each cell within their respective networks. We then explore HOTNN in a Bayesian optimization framework called HOTNAS, and demonstrate its efficacy in diverse tasks. Extensive experiments demonstrate that H OT-NAS can discover network architectures with better performance in multiple modular cell-based search spaces.