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State-of-the-art works compress SViT models through unstructured pruning, which needs specialized hardware accelerators for their specific sparsity patterns to maximize efficiency gains. Moreover, their manual approach requires a huge design time to find an appropriate pruning setting for each network, thus making this approach not scalable. To address this limitation, we propose PrimeSVT, a novel framework that performs automated memory-aware structured pruning on pre-trained SViT models, thereby maximizing their efficiency gains during inference amenable to widely-used computing architectures. 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