One-Step Steering is Not Sequential Control

Sparse autoencoder (SAE) features give steering methods activation directions, but a direction specifies only one step: once the first intervention moves the hidden state, the second must be evaluated at a state where it was never specified. We call the rule that resolves this the execution law and study it for encoder–decoder controllers. We derive an exact identity showing that re-encoding after each step adds an interaction defect driven by the encoder–decoder round trip, and prove that good reconstruction does not bound this defect. Across eight public GPT-2 SAE widths, wider dictionaries reconstruct better while their round-trip error grows monotonically. On 493 held-out feature pairs in GPT-2 and Gemma-2-2B, the identity predicts which application order produces less interaction (Spearman 0.98–0.99), although accuracy falls when a controlled feature changes support. Choosing the predicted order cuts the interaction residual by 24–38%, yet direct error to the joint target changes by about 1% or less, because interaction accounts for only 4–7% of endpoint error and can cancel singleton errors. Reconstruction, interaction fidelity, and target delivery are therefore separate evaluation axes, and sequential steering must specify its execution law and measure outcomes directly.