# Demystifying Variance in Circuit Discovery of LLMs

arXiv: https://arxiv.org/abs/2606.16920 · HTML: https://mlsanity.com/paper/2606.16920/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 23 of 23)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model](https://mlsanity.com/paper/2305.00586/) (2023)
- [Open Problems in Mechanistic Interpretability](https://mlsanity.com/paper/2501.16496/) (2025)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [How Important Is a Neuron?](https://mlsanity.com/paper/1805.12233/) (2018)
- [Knowledge Circuits in Pretrained Transformers](https://mlsanity.com/paper/2405.17969/) (2024)
- [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (2025)
- [Refining Targeted Syntactic Evaluation of Language Models](https://mlsanity.com/paper/2104.09635/) (2021)
- [EAP-GP: Mitigating Saturation Effect in Gradient-based Automated Circuit Identification](https://mlsanity.com/paper/2502.06852/) (2025)
- [Computationally Efficient Measures of Internal Neuron Importance](https://mlsanity.com/paper/1807.09946/) (2018)
- [Towards Understanding Fine-Tuning Mechanisms of LLMs via Circuit Analysis](https://mlsanity.com/paper/2502.11812/) (2025)
- [Mechanistic Interpretability as Statistical Estimation: A Variance Analysis](https://mlsanity.com/paper/2510.00845/) (2025)
- [When does gradient descent with logistic loss find interpolating two-layer networks?](https://mlsanity.com/paper/2012.02409/) (2020)
- [Discovering Influential Neuron Path in Vision Transformers](https://mlsanity.com/paper/2503.09046/) (2025)
- [What Drives Representation Steering? A Mechanistic Case Study on Steering Refusal](https://mlsanity.com/paper/2604.08524/) (2026)
- [Latent Noise Segmentation: How Neural Noise Leads to the Emergence of Segmentation and Grouping](https://mlsanity.com/paper/2309.16515/) (2023)
- [Computing as compression: the SP theory of intelligence](https://mlsanity.com/paper/1303.2013/) (2013)

## Built on by (most cited first, 2 of 2)

- [Context-Grounding Gains Are Mediated by Pre-existing Machinery: Auditing GRPO, SFT, and DPO](https://mlsanity.com/paper/2609.00925/) (2026)
- [From Trait Vectors to Circuits: Tracing Refusal and Sycophancy Through Language Models](https://mlsanity.com/paper/2609.22224/) (2026)

## Abstract (arXiv)

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.