Explanation Multiplicity: Circuit-Level Interpretability Evidence Does Not Survive Defensible Analytic Variation

Mechanistic interpretability (MI) aims to explain a model's behaviour through analyzing its internal computations; circuit-based explanations aim to isolate these computations with compact subnetworks validated by ablating the rest of the model. We show that circuits validated this way may fail to recover the underlying mechanism of the model's behaviour by closely reproducing its successful decisions while failing to account for most of its errors. Such explanations should account for the model's particular errors as well as its successes. We evaluate this requirement by measuring exact answer agreement separately on model successes and failures, across circuit sizes and ablation settings, on IOI, Docstring, and six model-task settings from the Mechanistic Interpretability Benchmark. We discover that many tested circuits closely replicate correct behaviour while missing most of the model's errors. On indirect object identification (IOI) for GPT-2 small, under mean ablation, the manual circuit and tested automated circuits, including one trained against the model's full output distribution, agree with the model on 97.3-99.5% of prompts it answers correctly but only 11.4-41.7% of errors. An IOI case study shows that lost errors are recoverable by restoring omitted attention-heads which raise error reproduction from 14.2% to 75.1% on a separate held-out set with 0.41 percentage point decrease on correct agreement, exceeding matched random extensions and scalar-biased control. Intervention traces show how omitted computations produce specific wrong answers for a reproducible subset of errors. In all, these findings show circuits can preserve task success without adequately explaining model's failures, and support exact error reproduction as a necessary, but not sufficient, test of circuit-based explanations of model behaviour.

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.

Understanding how neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying circuits--minimal subnetworks responsible for specific behaviors. However, existing circuit discovery methods are brittle: circuits depend strongly on the chosen concept dataset and often fail to transfer out-of-distribution, raising doubts whether they capture the concept or merely dataset-specific artifacts. We introduce Certified Circuits, which provide provable stability guarantees for circuit discovery. Our framework wraps any black-box discovery algorithm with randomized data subsampling to certify that inclusion decisions over circuit components--neurons or edges of the model graph, depending on the base algorithm--are invariant to bounded edit-distance perturbations of the concept dataset. Unstable components are abstained from, yielding circuits that are more compact and more accurate. We validate across three architectures (ResNet, ViT, GPT-2) on vision (ImageNet and four OOD datasets) and language (IOI, IOI-Hard, Greater-Than) tasks. Certified circuits achieve up to 56% higher accuracy and up to 80% fewer components, and remain reliable where baselines degrade. Certified Circuits puts circuit discovery on formal ground by producing mechanistic explanations that are provably stable and better aligned with the target concept. Code: https://github.com/AlaaAnani/certified-circuits.