Large language models reuse the same attention heads across tasks, yet merely identifying shared heads does not reveal their task‑specific functions. Inspired by task‑dependent interactions among brain regions, the authors treat a language model as a network and compare fixed components across tasks using identical graph facts—statements that specify which directed connections exist. They measure how interventions affect attention heads and later‑layer activations (influence) and how they affect the final answer (importance). Across five open‑weight models (four families, 1.5‑14 B parameters) task changes redistribute influence. In Gemma‑2‑9B and Qwen3‑14B, editing an early internal activation vector switches the fact the model reads while the written instruction stays unchanged. The same heads then respond to different graph facts and influence downstream components differently. For each prompt the authors build two linear response maps, before and after the edit, to predict a later head’s response from a measured change in an earlier head. For a separate factual intervention, the map corresponding to that condition reduces mean‑squared prediction error by 53.6% in Gemma and 5.0% in Qwen compared with the average of the two maps. These findings show that task context changes both which graph facts shared components respond to and how their outputs affect later computation. A network account may help explain how models use shared parameters for different computations, and task‑dependent influence measurements could guide interventions that alter one behavior while preserving others.
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