Topology-Weighted Effective Rank: A Zero-Cost Proxy for Training Dynamics Stability in Neural Architecture Search

Recent training-free Neural Architecture Search (NAS) meth-ods have introduced zero-cost proxies (ZCPs) to automate architecturedesign without expensive training or expert intervention. However, exist-ing ZCPs either completely ignore training dynamics or rely on static orinitialization-time characterizations of optimization that fail to capturefine-grained correlations with performance. Moreover, they overlook theheterogeneous importance of different model components, which limitstheir ability to generalize across datasets and search spaces. To mitigatethese limitations, we propose an Effective Rank Score called ER-Scoreas a novel ZCP to quantify stability in the training dynamics ofover-parameterized networks. Experiments show that ER-Score con-sistently outperforms existing ZCPs across multi-scale tasks and diversearchitectures, including convolutional neural networks (CNNs) and Vi-sion Transformers (ViTs). We further introduce topology-weighted strate-gies for CNNs that incorporate topological information via operation-wise feature map aggregation, resulting in a topology-weighted vari-ant termed TER-Score. Extensive experiments demonstrate that TER-Score achieves state-of-the-art ranking consistency and the best pop-ulation convergence when integrated with evolutionary search on theNAS-Bench-301 benchmark. Finally, our method achieves the lowesttest errors of 2.41% and 23.55% on the DARTS search space for theCIFAR-10 and ImageNet-1k datasets, respectively. Code is released athttps://github.com/Thiswycf/TER-Score.