When a Conceptor Complement Becomes Gain: Operator Geometry and Behavioral Attribution in Language Models

Activation steering promises modular control of language model behavior: a behavior such as politeness corresponds to a direction in a model's activations, and adding that direction while it generates should switch the behavior on and leave everything else alone. It does not. We ask what decides which other behaviors move, and by how much, and find that it is the model rather than the behavior being steered. A steer relaxes the model toward a small set of behaviors it already favors, chiefly refusal, sycophancy, and poeticism, and that set is much the same whatever is steered. Three results across 24 behaviors and ten instruction-tuned models support this, every effect read off the generated text by a language-model judge rather than off a probe. That readout matters: all 24 behaviors are linearly decodable, but only 20 change what the model writes. First, a direction carrying no behavioral content, matched to a real steer only in the size of the vector it adds, moves the same behaviors in the same order as real steers do, while producing none of the behaviors that need a specific direction. Second, most interference runs one way, so it cannot be an overlap between two directions: steering profanity makes the model toxic, while steering toxicity leaves profanity untouched. Third, with a behavior held out entirely, geometry measured on the others explains almost none of the interference it takes part in. The account holds on all ten models, the pull toward defaults strongest below 10B parameters and weakening in each family's largest. Reading a steer as a perturbation whose endpoint the model fixes implies that disentangling behavior directions cannot by itself make steering modular.

We present an automated, contrastive evaluation pipeline for auditing the behavioral impact of interventions on large language models. Given a base model $M_1$ and an intervention model $M_2$, our method compares their free-form, multi-token generations across aligned prompt contexts and produces human-readable, statistically validated natural-language hypotheses describing how the models differ, along with recurring themes that summarize patterns across validated hypotheses. We evaluate the approach in synthetic setting by injecting known behavioral changes and showing that the pipeline reliably recovers them. We then apply it to three real-world interventions, reasoning distillation, knowledge editing and unlearning, demonstrating that the method surfaces both intended and unexpected behavioral shifts, distinguishes large from subtle interventions, and does not hallucinate differences when effects are absent or misaligned with the prompt bank. Overall, the pipeline provides a statistically grounded and interpretable tool for post-hoc auditing of intervention-induced changes in model behavior.

Large language models reuse the same attention heads across tasks, but identifying these shared heads does not explain what they do differently in each task. A natural source of inspiration is task-dependent interactions among shared brain regions, which motivate a network view of language-model computation. Here, we compare fixed model components across tasks using identical graph facts, statements specifying which directed connections are present. We measure how interventions affect attention heads and the activation state in later layers (influence), as well as the answer (importance). Task changes redistribute the influence in five open-weight models spanning four families and 1.5-14 billion parameters. In Gemma-2-9B and Qwen3-14B, an activation edit changes an early internal activation vector and switches which fact the model reads while the written instruction stays fixed. The same heads then respond to different graph facts and influence later components differently. For each prompt, we construct two linear response maps, one before the edit and one after it. Each map predicts a later head's response from a measured change in an earlier head. For a separate factual intervention, the map for the corresponding 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 the shared components respond to and how their outputs affect later computation. A network account may help explain how models use shared parameters to perform different computations. Measurements of task-dependent influence could also guide interventions intended to alter one behavior while preserving others.