Improving search efficiency serves as one of the crucial objectives of Neural Architecture Search (NAS). However, many current approaches ignore the universality of the search strategy and fail to reduce the computational redundancy during the search process, especially in one-shot NAS architectures. Besides, current NAS methods show invalid reparameterization in non-linear search space, leading to poor efficiency in common search spaces like DARTS. In this paper, we propose TopoNAS, a model-agnostic approach for gradient-based one-shot NAS that significantly reduces searching time and memory usage by topological simplification of searchable paths. Firstly, we model the non-linearity in search spaces to reveal the parameterization difficulties. To improve the search efficiency, we present a topological simplification method and iteratively apply module-sharing strategies to simplify the topological structure of searchable paths. In addition, a kernel normalization technique is also proposed to preserve the search accuracy. Experimental results on the NASBench201 benchmark with various search spaces demonstrate the effectiveness of our method. It proves the proposed TopoNAS enhances the performance of various architectures in terms of search efficiency while maintaining a high level of accuracy. The project page is available at https://xdedss.github.io/topo_simplification.

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