Concepts Whisper: Spectral Anti-Concentration and the Dual Geometry of Transformer Representations

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arXiv:2605.01609v2 Announce Type: replace-cross Abstract: We find that transformer concept representations systematically anti-concentrate in the spectral tail of the unembedding covariance, encoding word-level concepts in low-variance directions across a 17-model core suite and an expanded set of 22 semantic concept categories, with convergent replications from three independent extraction methods. Residual-stream difference-of-means vectors anti-concentrate in all 17 models (model-level one-sample t-test, p = 3.8e-9), and remain more tail-aligned than norm-matched random directions in 13 of 17; convergent support comes from sparse autoencoder (SAE) features (p = 4.5e-19 across concepts within a model) and linear probes on Llama and Qwen. We identify a dual geometry: activation-space concept directions anti-concentrate while static unembedding-row contrasts concentrate in high-variance directions (p < 10^-4). This investigation arose from testing whether the causal inner product of Park et al. (2024) aids cross-lingual concept transport; a matched-spectrum randomization across 17 models and four language pairs finds no evidence that Whitened Causal Alignment improves over spectral regularization alone (p = 0.95). Split-injection interventions, restricted to steering strengths at which both arms remain interpretable, show the predicted interference asymmetry in four of five models (paired Cohen's d_z up to 1.19) with no significant reversal inside that regime, and POS-tag probing across eight models shows syntax preferentially encoded in the high-variance subspace in six …

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