A shared rank-one 'evolutionary' direction rectifies noisy steering vectors

measured in 1 paper

Jiang et al. stack cross-layer differences of contrastive positive/negative activation gaps and show via PCA that the first principal component dominates the spectrum across all datasets [jiang-etal-2026-global-evolutionary-steering-cross-layer-consistency] They prove via Wedin's sin-theta theorem that the estimated top singular vector converges to a Global Evolutionary Direction at rate O(1/sqrt(N*L)) [jiang-etal-2026-global-evolutionary-steering-cross-layer-consistency] Rectifying each layer's CAA steering vector by reinforcing its projection onto this shared direction improves over CAA and four baselines across three models and five domains (p<0.05) [jiang-etal-2026-global-evolutionary-steering-cross-layer-consistency] On Qwen2.5-7B, AdvBench refusal rises from 0.647 to 0.775 and GSM8K accuracy from 0.570 to 0.734 without per-layer tuning [jiang-etal-2026-global-evolutionary-steering-cross-layer-consistency]

Structure

Linear Direction

Context

a shared rank-one ("Global Evolutionary") direction dominating the PCA spectrum of cross-layer contrastive tangent vectors, a Wedin sin-Theta / Davis-Kahan perturbation-theory convergence guarantee for the extracted direction, rectifying noisy per-layer steering vectors by reinforcing their projection onto this shared direction

Confirmed in models

Qwen2.5-7B · Qwen, Llama-3.1-8B-Instruct · Llama, Gemma-2-9B-it · Gemma

Method

Difference-in-means direction, Spectral Consensus (Global Evolutionary) Steering

Papers

Global Evolutionary Steering: Refining Activation Steering Control via Cross-Layer Consistency — Jiang, Xinyan, Yu, Wenjing, Wang, Di, Hu, Lijie2026 · arXiv:2603.12298