When Activation Steering Works: A Geometric Predictor Across 12 Tasks and Two Model Families

Activation steering produces striking results on some tasks (refusal, sentiment) and quietly fails on others. When does it work? We run a unified, controlled protocol across 12 tasks and characterize each task's contrastive direction along two axes: a geometric axis (split-half cosine stability and per-pair angular variance) and an empirical axis (Δ vs. baseline and Δ vs. a random-direction control). The data refutes the naive hypothesis that low per-pair variance signals a steerable axis: near-zero variance instead correlates with the contrast collapsing onto a cosmetic framing word the model does not condition on. The empirically derived rule — split-half cosine ≥ 0.7 AND per-pair variance ≥ 0.3 implies steering succeeds — reaches 9/12 (75%) task-level accuracy on Llama-3.2-3B-Instruct; three exceptions reveal a third axis (contrast asymmetry). The augmented three-axis rule generalizes out-of-sample: pooled leave-one-task-out across 48 (model, task) pairs from four models (Llama-3.2-{1B,3B}, Qwen2.5-{3B,7B}) gives 79.2% accuracy. Geometric features agree across families to within ±0.05 on all 12 tasks — the (cosine, variance) signature is a property of the contrast, not the model — and the conventional behavioral-vs-content task taxonomy is not predictive of steering.