IC-744The decoded vocabulary of a function vector often reflects the task's output space, but reconstructing a vector that matches this vocabulary distribution does not recover the FV's full causal effect.
Eric Todd, Millicent Li, Arnab Sen Sharma, Aaron Mueller, Byron C Wallace, David Bau
The authors decode each function vector to a token probability distribution and find that for most tasks the top tokens lie within the task's output vocabulary (e.g., plural nouns for singular-plural, past-tense verbs for present-past). They then optimize a new vector to match the top-100 or full-50k-token distribution of the original FV and test it as an intervention. The reconstructions perform substantially worse than the original FV: for antonym, 48.2% drops to 4.8% (top-100) or 39.6% (full vocabulary), indicating the FV carries essential information beyond its decoded word distribution.
Evidence
interventional
Key metric
Antonym: v_t 48.2 ± 2.0% vs v̂_t_100 4.8 ± 2.0% (KL 0.0033) vs v̂_t_all 39.6 ± 2.6% (KL 0.0137); Capitalize: 70.5 ± 2.4% vs 5.7 ± 2.2% vs 51.5 ± 11.6%; Country-capital: 83.2 ± 2.7% vs 58.1 ± 18.5% vs 29.0 ± 15.1%
Caveat
The reconstruction matches the decoded distribution (near-zero KL divergence) but still underperforms, suggesting the missing information is in the geometry of the vector rather than in the vocabulary it projects onto.