Multi-layer steering with layer-incremental vectors — strengthens → Preventative steering

Single-layer preventative steering does not always fully block trait acquisition, particularly on datasets intentionally designed to elicit the trait (persona-vectors, §"5.2 Preventative steering limits behavioral shifts during finetuning", p. 8). The fix is not simply applying the same persona vector at every layer, since directly injecting overlapping directional information at each layer would double-count signal that has already propagated forward through the residual stream from earlier injections. Instead, multi-layer steering uses a layer-incremental vector, v_incremental_l = v_l - v_(l-1), so each layer's injection reflects only that layer's marginal contribution (§"J.3 Steering across all layers", p. 46). Applied throughout training, this pushes trait acquisition down to near-baseline levels even on the hardest datasets, with no MMLU cost relative to ordinary finetuning - meaning single-layer preventative steering's limitation was incomplete suppression, not capability damage, and multi-layer steering fixes precisely that gap rather than trading one problem for another. Notably the same upgrade solves a different problem on the inference-time side of the sign flip: for post-hoc steering, all-layer application achieves suppression similar to single-layer but with better preserved MMLU accuracy (§J.3, p. 46-47). The layer-incremental construction is thus a single technical fix - avoiding redundant double-counted signal across layers - that happens to strengthen preventative steering along the suppression axis and post-hoc steering along the capability-preservation axis, depending on which direction the vector is being pushed.