One advertised dial, five interacting knobs
CAA is described as a single dial, a vector and a multiplier, but that simplicity hides several choices that quietly interact with each other. This connective theme pulls five of them apart: where in the network the vector gets added, how strong a push it delivers, and how its magnitude gets standardized before either of those decisions is even made.
The edges show how the choice of injection site entangles with the network's own growing activation norms, how the multiplier's sign and size trade off against text quality at the high end, and how normalization keeps that tradeoff comparable across behaviors without touching the network's own layer-to-layer scale. The last two edges look forward, at two refinements the authors propose for loosening exactly the constraints the first three expose.
CAA advertises one interface, a vector and a multiplier, but five edges show the engineering that interface hides. The injection site comes first: choosing the residual stream over attention activations or individual heads means the stream's exponentially growing norm entangles CAA's own layer-optimality results, since a fixed multiplier is a smaller relative perturbation at a late, high-norm layer than at an early one. The dose comes next: the multiplier sets sign and magnitude on top of that vector, one sycophancy example showing positive and negative settings pushing the same axis to opposite outputs, and a ceiling the authors hit directly -- large multipliers degrade text quality, which is why the reported range is restricted rather than exhaustive. Normalization sits between the two, standardizing vector magnitudes across behaviors so a multiplier means the same thing from one behavior's line to another's on the same plot, while deliberately leaving each layer's own norm alone. The last two edges are the paper's proposed next knobs, aimed at exactly the failure modes the first three expose: targeted token steering would relax the quality ceiling by concentrating perturbation where it matters instead of applying it uniformly to every post-prompt token, and steering outside the residual stream would trade the stream's easy-to-apply, hard-to-localize summing structure for a site that can distinguish which computation is being altered.