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Across 17 models and 4 language pairs, a matched-spectrum randomization test finds that Whitened Causal Alignment is indistinguishable from spectral regularization alone ($p = 0.95$). However, this failure reveals a broader phenomenon: anti-concentration is observed in residual-stream difference-of-means vectors across five architecture families ($p < 10^{-33}$) and supported by SAE features (e.g., $p = 4.5 \\times 10^{-19}$) and linear probes on Gemma and Llama. We discover a \\emph{dual geometry}: activation-space concept directions anti-concentrate in the spectral tail, while static unembedding-row contrasts \\emph{concentrate} in high-variance directions ($p < 10^{-4}$). Split-injection causal interventions support the functional basis on Gemma and Llama (Cohen's $d$ up to $1.","title":"Concepts Whisper While Syntax Shouts: Spectral Anti-Concentration and the Dual Geometry of Transformer Representations","url":"https://arxiv.org/abs/2605.01609","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.01609v1 Announce Type: cross \nAbstract: We test whether the causal inner product of \\citet{park2024linear} -- defined by the unembedding covariance $\\Sigma$ -- enables cross-lingual concept transport. Across 17 models and 4 language pairs, a matched-spectrum randomization test finds that Whitened Causal Alignment is indistinguishable from spectral regularization alone ($p = 0.95$). However, this failure reveals a broader phenomenon: anti-concentration is observed in residual-stream difference-of-means vectors across five architecture families ($p < 10^{-33}$) and supported by SAE features (e.g., $p = 4.5 \\times 10^{-19}$) and linear probes on Gemma and Llama. 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