Linear representation hypothesis — licenses the vector arithmetic of → Steering vector

The linear representation hypothesis is what makes it coherent to expect that adding a single vector to activations should shift a whole behavior rather than producing noise. Park et al.'s (2023) formalization holds that high-level concepts are encoded as linear directions in an LLM's activation space (contrastive-activation-addition, §"2 Related work", p. 3); if that is true, then a behavior like sycophancy or refusal has, in principle, a direction, and moving a model's activations along that direction — exactly what a steering vector does when added with a multiplier — should move the model's output distribution toward or away from the behavior. CAA does not derive this hypothesis; it inherits it as background motivation and then supplies empirical support back: behavioral clustering in PCA projections of activations emerges suddenly around a third of the way through the model's layers (contrastive-activation-addition, §"3.2 Visualizing activations for contrastive dataset analysis", p. 4), and steering vectors act as token-level feature detectors under a cosine-similarity measure (contrastive-activation-addition, §"8.1 Similarity between steering vectors and per-token activations", p. 7), both consistent with a single linear direction carrying the behavior.