Abstract:We audit alignment-induced shifts in residual-stream activations of three open-weight instruction-tuned LLMs (Llama-3.1-8B-Instruct, Gemma-2-9B-it, Qwen-2.5-7B-Instruct) using the effective rank of the alignment modification matrix on safety-relevant inputs, rho_eps := rank_eps(M_Ds)/d, which formalizes the single-refusal-direction observation of Arditi et al. (2024) as a continuous quantity. The paper has three contributions. (1) Confound-controlled measurement: a four-variant decomposition (M_naive, M_template, M_aligned, M_DiD) separates chat-template formatting, alignment-stage shift, and the refusal-mediating direction, and recovers the Arditi refusal direction on M_DiD at |cos| in {0.77, 0.86, 0.50} (Llama/Gemma/Qwen); chat-template-controlled rho_eps is {0.0029, 0.0048, 0.0044}, and the centered SVD residual is 4-7x larger. (2) Constructive calibration on a 3-layer MLP across rho_eps in {0.008, 0.17, 0.33, 0.40} exhibits a sweet-spot vs. brittle distinction: mild rank-maximization (lambda=5) buys ablation robustness, while strong regularization at the same nominal rho_eps (lambda=50) does not. rho_eps is a diagnostic for fragility, not a target whose mechanical inflation buys robustness. (3) Limits of rank-based diagnostics: (a) not safety-specific (LRH baseline is 2-3x the safety value); (b) SVD principal ordering does not match causal ordering (Llama u_2 inert despite ranking second; cumulative ablation non-monotone at k=5); (c) the spectral-gap hypothesis required to upgrade the O(rho_eps * d) achievability bound to a matching Mirsky-route lower bound fails empirically (1/90 Llama layer-reference pairs, 0/36 MLP combinations) and structurally (kappa_lb <= 2/(eps * r)). The matching lower bound remains an open problem.
| Comments: | 18 pages, 1 figure, 21 tables. Code, data, and an immutable Zenodo archive are available at this https URL (DOI: https://doi.org/10.5281/zenodo.20341445) |
| Subjects: | Machine Learning (cs.LG); Computation and Language (cs.CL); Machine Learning (stat.ML) |
| MSC classes: | 68T07, 68T50, 15A18 |
| ACM classes: | I.2.7; I.2.6 |
| Cite as: | arXiv:2605.24583 [cs.LG] |
| (or arXiv:2605.24583v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24583 arXiv-issued DOI via DataCite (pending registration) |
From: Yuki Nakamura [view email]
[v1]
Sat, 23 May 2026 13:47:17 UTC (59 KB)
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