fvs-constructed-from-middle-layer-attention-heads

IN premise — summaries/2026/08/24/todd-2023-function-vectors-s0-abstract-chunk-1.md

Created 2026-08-25T02:58:39+00:00

Function Vectors (FVs) are constructed by summing the mean task-conditioned activations of a small fixed set of attention heads identified via causal mediation analysis, with strongest causal effects concentrated in early-to-middle layers (approximately L/3).

Summary

This says that to capture what a network is doing for a given task, you only need to look at a handful of attention heads sitting in roughly the first third of the network's depth, average out their task-specific behavior, and sum those averages together. It matters because it gives a concrete, small extraction recipe and pins down that the causal "work" for a function happens early and middle, not in the final layers, so downstream tooling can focus its analysis there.