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

Function vectors (FVs) -- mean-difference directions extracted from in-context learning demonstrations -- can steer large language model behavior when added to the residual stream. We hypothesized that FV steering failures reflect an absence of task-relevant information: the logit lens would fail alongside steering. We were wrong. In the most comprehensive cross-template FV transfer study to date - 4,032 pairs across 12 tasks, 6 models from 3 families (Llama-3.1-8B, Gemma-2-9B, Mistral-7B-v0.3; base and instruction-tuned), 8 templates per task - we find the opposite dissociation: FV steering succeeds even when the logit lens cannot decode the correct answer at any layer. This steerability-without-decodability pattern is universal: steering exceeds logit lens accuracy for every task on every model, with gaps as large as -0.91. Only 3 of 72 task-model instances show the predicted decodable-without-steerable pattern, all in Mistral. FV vocabulary projection reveals that FVs achieving over 0.90 steering accuracy still project to incoherent token distributions, indicating FVs encode computational instructions rather than answer directions. FVs intervene optimally at early layers (L2-L8); the logit lens detects correct answers only at late layers (L28-L32). The previously reported negative cosine-transfer correlation (r=-0.572) dissolves at scale: pooled r ranges from -0.199 to +0.126, and cosine adds less than 0.011 in R-squared beyond task identity. Post-steering analysis reveals a model-family divergence: Mistral FVs rewrite intermediate representations; Llama/Gemma FVs produce near-zero changes despite successful steering. Activation patching confirms causal localization: easy tasks achieve perfect recovery at targeted layers; hard tasks show zero recovery everywhere.