From Refusal Cones to Truth Cones
A common working assumption in interpretability is the Linear Representation Hypothesis: a high-level concept is a single direction in a model’s residual stream, and pushing along that direction changes the behaviour. Truth is a classic example. Take the mean activation on true statements minus the mean on false ones, and you get a direction that separates the two and can sometimes flip the model’s verdict.
The refusal result
Wollschläger et al. (2025) looked at refusal and found that one direction is not the whole story. Instead of computing a direction from activation means, they optimized it by gradient descent against what refusal should do: removing it should stop the model from refusing, and adding it should make the model refuse. Pushing this further, they found concept cones: small multi-dimensional regions in which every direction mediates refusal. The single direction looks like the one-dimensional case of something bigger.
Porting it to truth
The question I am working on is whether truth has the same structure. If it does, a single truth probe would only capture a projection of the concept, which matters for anyone who wants to monitor or steer a model’s honesty through its internals.
The port is not direct, and a few challenges stand out:
- Truth is not a behaviour. Refusal shows up in the output on its own. For truth I need a setup where the model commits to a verdict, for example a few-shot prompt that ends in “This statement is:” and forces a choice between “True” and “False”.
- Where to intervene. Truth is assembled over several layers and token positions, so the intervention has to target the place where the judgment is actually formed, not where it is read out.
- What counts as success. Removing a candidate truth direction should flip true statements to “False” while leaving unrelated prompts untouched. Measuring that side effect is as important as the flip itself.
- Copies of the probe. A cone could simply be several noisy versions of the mean-difference probe. Checking how its directions relate to the probe is the only way to know it captures something new.
- Generalization. A cone fit on cities might not transfer to animals or chemical elements. If truth is one concept, it should.
I have a first draft that tries this across several model families; it is here, and I will write about the results once they are more settled.