Demystifying Variance in Circuit Discovery of LLMs

2026-06-15

AI Summary

This work investigates the instability and interpretability challenges in large language model (LLM) circuit discovery, which are primarily driven by three sources of variance: resampling, prompt rephrasing, and sample-level fluctuations. The study systematically analyzes these variance origins and introduces CEAP, a theoretically grounded algorithm that substantially reduces resampling variance. It further demonstrates that diverse prompt templates activate distinct functional circuits, revealing that LLMs may rely on multiple non-unique circuits for the same task. The paper clarifies that sparsity alone cannot eliminate variance and shows that sample-level variance often stems from the definition of evaluation metrics rather than genuine circuit failure, with extreme unfaithfulness scores rooted in benign neural mechanisms.

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.

Problem

• circuit discovery
• variance
• mechanistic interpretability
• large language models
• unfaithfulness

Innovation

• circuit discovery
• variance analysis
• CEAP
• mechanistic interpretability
• unfaithfulness