Persona Intensity Produces a Dose-Response Shift in KV-Cache Spectral Shape: Methodological Lessons from a Multi-Stage Analysis

We investigate whether persona-level system prompt instructions produce detectable geometric signatures in transformer KV-cache representations. Using a five-level persona intensity manipulation (neutral baseline through full entity voice) across three model architectures (Qwen2.5-7B-Instruct, Llama-3.1-8B-Instruct, Mistral-7B-Instruct-v0.3), we extract singular value-decomposition-based spectral features from generation-phase KV-cache activations. Our analysis proceeds through four stages, each reported transparently. First, standard linear Frisch Waugh–Lovell (FWL) length correction produces apparently strong effects (9/16 comparisons surviving Bonferroni correction, Cohen’s d up to 2.83). Second, an interaction-term FWL extension reveals that all effects are attributable to heterogeneous length-geometry slopes between
persona groups, reducing every comparison to chance (all AUROCs < 0.55). Third, we identify that an extraction inconsistency between experimental arms produced a false specificity result, which we correct and report. Fourth, applying one-way ANOVA to level means with consistent extraction reveals a surviving finding: singular-value kurtosis of generation-minus-encoding delta features shows a significant monotonic dose-response across persona intensity levels (F = 31.8, p <0.000001, Spearman ρ = 0.672, Cohen’s d = 1.41 for L0 vs L2). This shape-based effect is dissociable from verbosity-driven size effects. We argue that the interaction-term FWL diagnostic constitutes a methodological contribution applicable to any KV-cache geometry study where group-level confound relationships may differ, and that reporting the full analytical evolution, including what failed, strengthens rather than weakens the surviving finding.