# Perfect Detection, Failed Control: The Geometry of Knowing vs. Steering in Language Models

arXiv: https://arxiv.org/abs/2606.24952 · HTML: https://mlsanity.com/paper/2606.24952/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Probing deception, bias and beliefs, one of 13 directions in Mechanistic interpretability.
- Builds on 0 of its 3 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Placed in

- Mechanistic interpretability / [Probing deception, bias and beliefs](https://mlsanity.com/mechinterp/probing-deception-bias-and-beliefs/)

## Built on by (most cited first, 5 of 5)

- [Asymmetries in Spontaneous and Instructed Deception](https://mlsanity.com/paper/2609.00180/) (2026)
- [Locating and Steering Refusal Beyond Attention](https://mlsanity.com/paper/2609.04721/) (2026)
- [Steering Interference Reflects the Model's Defaults, Not the Behavior Directions](https://mlsanity.com/paper/2609.06951/) (2026)
- [Capacity, Responsiveness and Alignment: What Makes a Latent Structure Actionable](https://mlsanity.com/paper/2610.06897/) (2026)
- [Does the Model Use the Feature? Separating Steering from Mechanism in LLMs](https://mlsanity.com/paper/2610.07270/) (2026)

## Abstract (arXiv)

A central aspiration of mechanistic interpretability is controllability: if we know where a behavior is represented in a model's activations, we should be able to modify it. This rests on a hidden premise -- that the direction which detects a behavior and the direction which controls it are the same, or close. We test this geometrically: what is the angle between the direction that best detects a behavior and the one that best causes it? If detection implies control the cosine is near 1; otherwise it quantifies a detection-intervention gap. On Gemma 2-2B-it, output format (clean JSON vs markdown fencing) collapses both roles onto one axis. Hallucination does not: the model detects fake entities with perfect linear separability (AUC = 1.000 from layer 5), yet that direction sits at cos = 0.12 (about 83 degrees) from the direction producing a refusal -- a small, reproducible alignment, far from the cos = 1 that "detection is control" would require. A detector built from activations, with no chosen tokens, likewise fails to align (cos = -0.06). The gap generalizes: across four models from three families and two scales (1B-9B), cos stays in [0.12, 0.20], identical before and after instruction tuning (0.1197 vs 0.1200), placing its origin in pretraining. A 15-degree rotation toward the refusal direction partially bridges it -- 73% and 60% refusal on two held-out fake-entity categories at 1.8% false positives. We then ask whether this cosine predicts steerability, and it does not: detection is a high-dimensional class, not a single direction, and what separates the steerable case is functional, not readable from a static angle. The cosine is a weight-computable signature of the dissociation between knowing and steering, not a predictor of it.