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Vision Transformer (ViT) has emerged as a competitive alternative to convolutional neural networks for various computer vision applications. Specifically, ViT multi-head attention layers make it possible to embed information globally across the overall image. Nevertheless, computing and storing such attention matrices incurs a quadratic cost dependency on the number of patches, limiting its achievable efficiency and scalability and prohibiting more extensive real-world ViT applications on resource-constrained devices. Sparse attention has been shown to be a promising direction for improving hardware acceleration efficiency for NLP models. However, a systematic counterpart approach is still missing for accelerating ViT models. To close the above gap, we propose a first-of-its-kind algorithm-hardware codesigned framework, dubbed ViTALiTy, for boosting the inference efficiency of ViTs. Unlike sparsity-based Transformer accelerators for NLP, ViTALiTy unifies both low-rank and sparse components of the attention in ViTs. At the algorithm level, we approximate the dot-product softmax operation via first-order Taylor attention with row-mean centering as the low-rank component to linearize the cost of attention blocks and further boost the accuracy by incorporating a sparsity-based regularization. At the hardware level, we develop a dedicated accelerator to better leverage the resulting workload and pipeline from ViTALiTy's linear Taylor attention which requires the execution of only the low-rank component, to further boost the hardware efficiency. Extensive experiments and ablation studies validate that ViTALiTy offers boosted end-to-end efficiency (e.g., $3\times$ faster and $3\times$ energy-efficient) under comparable accuracy, with respect to the state-of-the-art solution.