Spectral Smoothing and Spiking Perturbations Reconfigure Capability Profiles and Selective Task Performance in Large Language Models
Singular-value spectra encode important structure in transformer feed-forward projections, yet their causal role in downstream behavior remains underexplored. We study post-hoc spectral smoothing and spiking interventions on the up_proj and down_proj matrices. Positive perturbation stretches deviations from the geometric mean, making large singular values larger and small ones smaller (spiking), and vice versa. The intervention preserves singular vectors and the geometric mean of the singular values. Across five open Llama and Qwen instruction models, we evaluate the perturbed systems on capability-labeled subtasks, standard and chain-of-thought reasoning benchmarks, judge-scored truthfulness, hallucination, and safety tasks, and TRAIT personality probes. To interpret score shifts, we fit responses in a three-dimensional capability basis consisting of factual knowledge, language understanding, and deductive reasoning. The induced changes suggest structured rather than purely random sensitivity: large positive perturbations more reliably suppress language and deductive responses, moderate negative perturbations can sometimes improve factual or task-local performance on the evaluated grids, and sensitivity varies strongly by model family, benchmark module, and underlying layerwise spectral inequality. These results position spectral perturbation as a lightweight intervention for probing how capabilities are organized and traded off in large language models.