Demystifying Variance in Circuit Discovery of LLMs

Circuit discovery is a key technique in mechanistic interpretability to pinpoint the model components that are crucial for performing a given task. Although the current state-of-the-art method (EAP-IG) performs well on (un)faithfulness, it suffers from substantial variability. This includes resampling variance, where the circuit changes when we probe with a new batch of data from the same distribution; rephrasing variance, where the discovered circuit shifts when the prompts are rephrased; and sample-wise variance, where a circuit with low population unfaithfulness exhibits large fluctuations in unfaithfulness across individual samples. This paper pinpoints the roots of these variances and reduces them when doing so is desirable. We demonstrate that CEAP, our new circuit discovery method that improves upon EAP-IG with a theoretical guarantee, can substantially lessen resampling variance. We further show that rephrasing variance arises because prompts with different templates tend to activate different circuits in the model. This leads us to argue that it is impossible to find a comprehensive circuit that explains and controls the model’s behavior on a task, which can appear in countless templates, suggesting that LLMs may be inherently hard to steer. We show that sparsity, which claims to form more compact and interpretable circuits, fails to solve this problem. Regarding sample-wise variance, we argue that it is largely benign: extremely poor unfaithfulness scores often stem from how unfaithfulness is defined, rather than from defects in the measured circuits. We show that the magnitude of unfaithfulness is affected by selective contribution scaling, a neural mechanism that accounts for the extremely poor scores sometimes observed.