Introspection, the ability of a system to access and reason about its internal signals, is crucial for language model (LM) self-consistency and scalable interpretability. Prior work argues that LMs possess introspective capabilities, and that training (SFT) could enhance such behavior. However, most setups leave open the possibility of "causal bypass," in which the self-report relies on signals that are correlated with the self-report's subject, while being causally unrelated to it. Although high-level concepts are difficult to intervene on, lower-level signals (such as a single neuron activation) allow precise interventions. Understanding such signals can serve as a minimal prerequisite before understanding more complex introspection.
In this study, we train hundreds of introspectors across three low-level signal types and eight LMs. We find that straightforward SFT training leads to causal bypass, and propose interventional training, an alternative where we train the model to report on counterfactually perturbed values. This method enables more accurate introspection of endogenous $\textit{and}$ injected signals, particularly in out-of-distribution (OOD) data. The mechanism generalizes across token positions and scales with more data. Our results demonstrate that while causally grounded introspection is possible, it is not guaranteed -- emphasizing the need to train on mechanisms, rather than behaviors alone.