Safety fine-tuning data concentrates residual-stream variance into a few principal components, and this dimensional collapse drives false refusals

- Liu et al. introduce FlowLens, a stable PCA-based tool for real residual-stream geometry analysis, and apply it to Llama-3.2-1B (and its Llama-3.2-1B-Instruct/SFT/VCL fine-tuned variants trained on the Tulu-3 recipe, with a broader comparison set including Llama-3.1-8B-Instruct and Llama-2-7B-chat), showing that as the proportion of safety-refusal examples in fine-tuning data rises from 0% to 40%, mid-layer residual-stream variance concentrates increasingly onto a few principal components. [liu-etal-2026-flowlens-variance-concentration-false-refusal] - This measured variance concentration (the paper reports growing variance along, and falling cosine alignment of, a top principal direction -- alignment score 1.0 to 0.85 at 40% safety data in Table 2 -- and describes it as reduced representational smoothness) tracks a concrete behavioral cost: the false-refusal rate (declining benign queries) rises from 63% to 84% (Table 2) over the same safety-data-proportion sweep, establishing a direct link between the geometric collapse and the behavioral failure mode. [liu-etal-2026-flowlens-variance-concentration-false-refusal] - Their own proposed regularizer (Variance Concentration Loss, penalizing excessive mid-layer variance concentration) reduces false refusals by over 35 percentage points while preserving MMLU/GSM8K performance -- but the map-relevant finding is the measured variance-concentration/false-refusal coupling in the real fine-tuned baseline models, not the paper's own fix. [liu-etal-2026-flowlens-variance-concentration-false-refusal]