Steerable but Not Decodable: Function Vectors Operate Beyond the Logit Lens

Activation steering presupposes that task-relevant behaviors correspond to linear directions in activation space — directions that should both steer the model when added to its residual stream and be readable along the unembedding when probed. Function vectors (FVs), extracted as mean differences across in-context demonstrations, are the canonical test case; the natural prediction is that steering and decoding succeed or fail together. Across 12 tasks, 6 models from 3 families, and 4,032 directed cross-template pairs, we find the opposite. FV steering routinely succeeds where the logit lens cannot decode the correct answer at any intermediate layer, while the predicted converse — decodable without steerable — is nearly empty (3 of 72 task×model instances). The gap is not representational dialect. A diagonal tuned lens closes 1 of 14 steerable-not-decodable cases; a 2-layer MLP probe with a Hewitt & Liang control closes 5 of 10 via nonlinearly encoded structure but leaves 5 invisible to every decoder we tried. Even at > 0.90 steering accuracy, projecting the FV through the unembedding yields incoherent token distributions: FVs encode computational instructions, not answer directions. A model-family asymmetry sharpens the picture. Mistral FVs rewrite intermediate representations, while Llama and Gemma FVs steer the final output without leaving a logit-lens-visible trace, corroborated by three independent signals (post-steering deltas, activation-patching recovery, FV norm–transfer correlations). A previously reported negative cosine–transfer correlation dissolves at scale, adding at most ΔR² = 0.011 beyond task identity. These results decompose the linear representation hypothesis into linear decodability and linear steerability and show they come apart in the opposite direction from naive intuition, with direct implications for safety monitoring: vocabulary-projection tools are blind to FV-style interventions on the most widely deployed model families.