HOTNAS: Hierarchical Optimal Transport for Neural Architecture Search

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. Unfortunately, existing OT for NAS methods either ignore the similarity between cells 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 HOTNAS can discover network architectures with better performance in multiple modular cell-based search spaces.