Token merging has emerged as a new paradigm that can accelerate the inference of Vision Transformers (ViTs) without any retraining or fine-tuning. To push the frontier of training-free acceleration in ViTs, we improve token merging by adding the perspectives of 1) activation outliers and 2) hierarchical representations. Through a careful analysis of the attention behavior in ViTs, we characterize a delayed onset of the convergent attention phenomenon, which makes token merging undesirable in the bottom blocks of ViTs. Moreover, we augment token merging with a hierarchical processing scheme to capture multi-scale redundancy between visual tokens. Combining these two insights, we build a unified inference framework called DSM: Delayed Spatial Merging. We extensively evaluate DSM on various ViT model scales (Tiny to Huge) and tasks (ImageNet-1k and transfer learning), achieving up to 1.8$\times$ FLOP reduction and 1.6$\times$ throughput speedup at a negligible loss while being two orders of magnitude faster than existing methods.

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