Function-Vector Heads Are Two Populations: Writers and Cancellers in In-Context Learning

arXiv:2606.07560v1 Announce Type: cross Abstract: Function-vector (FV) heads (Todd et al., 2024) are typically identified by the magnitude of their causal contribution to in-context rule tasks, under the implicit assumption that the top set is a homogeneous functional class. This assumption fails. We replace magnitude-only ranking with a sign-preserving criterion (refined DLA + permutation FDR) and validate each candidate by path patching. The FV head population then splits into two opposing sub-populations: writers push the rule-correct logit up; cancellers push it down. A four-condition canonical verdict holds in $13/15$ cells across three model families and six Pythia scales, and a sign-shuffle rejects homogeneity in $5/6$ main cells. The structure is invisible to magnitude-only ranking: Todd's top-$20$ captures $64\%$ of cancellers but only $4\%$ of writers on the hierarchical task, and $59\%$ of writers but only $8\%$ of cancellers on the modular task. We rule out six artefact accounts on all $27$ canceller (cell, head) pairs: induction overlap, sinks, generic importance, rank-$1$ copy-suppression, V-cascade, and rank-nearest non-FV controls. Zero-ablating cancellers yields $+0.13$ to $+0.29$ nats of logit gain in $6/6$ main cells with a directionally consistent $+2$ to $+7$ pp accuracy effect.

Abstract:Function-vector (FV) heads (Todd et al., 2024) are typically identified by the magnitude of their causal contribution to in-context rule tasks, under the implicit assumption that the top set is a homogeneous functional class. This assumption fails. We replace magnitude-only ranking with a sign-preserving criterion (refined DLA + permutation FDR) and validate each candidate by path patching. The FV head population then splits into two opposing sub-populations: writers push the rule-correct logit up; cancellers push it down. A four-condition canonical verdict holds in $13/15$ cells across three model families and six Pythia scales, and a sign-shuffle rejects homogeneity in $5/6$ main cells. The structure is invisible to magnitude-only ranking: Todd's top-$20$ captures $64\%$ of cancellers but only $4\%$ of writers on the hierarchical task, and $59\%$ of writers but only $8\%$ of cancellers on the modular task. We rule out six artefact accounts on all $27$ canceller (cell, head) pairs: induction overlap, sinks, generic importance, rank-$1$ copy-suppression, V-cascade, and rank-nearest non-FV controls. Zero-ablating cancellers yields $+0.13$ to $+0.29$ nats of logit gain in $6/6$ main cells with a directionally consistent $+2$ to $+7$ pp accuracy effect.

Computation and Language (cs.CL); Machine Learning (cs.LG)

arXiv:2606.07560 [cs.CL]

(or arXiv:2606.07560v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2606.07560 Focus to learn more arXiv-issued DOI via DataCite

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Function-Vector Heads Are Two Populations: Writers and Cancellers in In-Context Learning

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