Steering vector normalization choices — makes cross behavior comparable for → Steering multiplier

Steering multipliers are only meaningful for comparing behaviors because of an upstream normalization choice: the authors "normalize steering vector magnitudes across all behaviors to standardize across behaviors before applying steering multipliers" (contrastive-activation-addition, §"Vector normalization choices", p. 10). Without that step, a multiplier of 1 could denote a large perturbation for one behavior's vector and a tiny one for another's, and the layer sweeps in Figure 3 — which overlay all seven behaviors on the same multiplier scale — would not be comparable across lines. But the normalization is deliberately partial: it standardizes across behaviors at a fixed layer while leaving each layer's raw norm alone, since the residual stream's norm grows over the forward pass and the authors want multipliers to act on the vector's natural norm at whatever layer it was extracted from. That asymmetry is why the paper's hyperparameter search proceeds in two separate stages rather than one joint sweep: first find the best layer holding the multiplier constant, then sweep multipliers only at that resultant layer (contrastive-activation-addition, §"Vector normalization choices", p. 10).