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While this reduces the overhead of online full-vector rotations, the effect of block structure on outlier suppression remains poorly understood. To fill this gap, we present the first systematic, non-asymptotic analysis of outlier suppression for block Hadamard rotations. Our analysis reveals that outlier suppression is fundamentally limited by the geometry of the input vector. In particular, in the deterministic worst case, post-rotation outliers are minimized when the pre-rotation $\\ell_1$ norm mass is evenly distributed across blocks. Guided by these insights, we introduce PeRQ (Permute, Rotate, then Quantize), a PTQ framework that redistributes activation mass via permutations prior to rotation. We propose a greedy mass diffusion algorithm to calibrate permutations by equalizing the expected blockwise $\\ell_1$","title":"Pushing the Limits of Block Rotations in Post-Training Quantization","url":"https://arxiv.org/abs/2601.22347","vendor":"arxiv_cs_ai"},"summary":"arXiv:2601.22347v2 Announce Type: replace-cross \nAbstract: Recent post-training quantization (PTQ) methods have adopted block rotations to diffuse outliers prior to rounding. While this reduces the overhead of online full-vector rotations, the effect of block structure on outlier suppression remains poorly understood. To fill this gap, we present the first systematic, non-asymptotic analysis of outlier suppression for block Hadamard rotations. Our analysis reveals that outlier suppression is fundamentally limited by the geometry of the input vector. In particular, in the deterministic worst case, post-rotation outliers are minimized when the pre-rotation $\\ell_1$ norm mass is evenly distributed across blocks. Guided by these insights, we introduce PeRQ (Permute, Rotate, then Quantize), a PTQ framework that redistributes activation mass via permutations prior to rotation. 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