Vision Transformers (ViT) have recently demonstrated success across a myriad of computer vision tasks. However, their elevated computational demands pose significant challenges for real-world deployment. While low-rank approximation stands out as a renowned method to reduce computational loads, efficiently automating the target rank selection in ViT remains a challenge. Drawing from the notable similarity and alignment between the processes of rank selection and One-Shot NAS, we introduce FLORA, an end-to-end automatic framework based on NAS. To overcome the design challenge of supernet posed by vast search space, FLORA employs a low-rank aware candidate filtering strategy. This method adeptly identifies and eliminates underperforming candidates, effectively alleviating potential undertraining and interference among subnetworks. To further enhance the quality of low-rank supernets, we design a low-rank specific training paradigm. First, we propose weight inheritance to construct supernet and enable gradient sharing among low-rank modules. Secondly, we adopt low-rank aware sampling to strategically allocate training resources, taking into account inherited information from pre-trained models. Empirical results underscore FLORA's efficacy. With our method, a more fine-grained rank configuration can be generated automatically and yield up to 33% extra FLOPs reduction compared to a simple uniform configuration. More specific, FLORA-DeiT-B/FLORA-Swin-B can save up to 55%/42% FLOPs almost without performance degradtion. Importantly, FLORA boasts both versatility and orthogonality, offering an extra 21%-26% FLOPs reduction when integrated with leading compression techniques or compact hybrid structures. Our code is publicly available at https://github.com/shadowpa0327/FLORA.

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