Demystifying Variance in Circuit Discovery of LLMs
2026-06-15 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors study how to find the important parts of large language models (LLMs) that help perform specific tasks, a process called circuit discovery. They show that their new method, CEAP, reduces inconsistency caused by using different data samples compared to the previous method EAP-IG. However, they find that changing the prompt wording activates different circuits, making it hard to find one complete explanation for the model's behavior. They also explain that some variability in results is due to how the evaluation is done rather than real problems with the circuits.
Circuit discoveryMechanistic interpretabilityLarge language models (LLMs)Unfaithfulness metricResampling varianceRephrasing varianceSample-wise varianceCEAP methodSparsitySelective contribution scaling
Authors
Frank Zhengqing Wu, Francesco Tonin, Volkan Cevher
Abstract
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 the metric of (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 studies the roots of these variances. 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 may be challenging to find a comprehensive circuit that explains and controls the model's behavior on a task, which can be expressed in countless templates, suggesting that LLMs may be inherently hard to steer. We show that sparsity, which has been claimed to form more compact and interpretable task 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.