Thank you for your valuable comments. We have a detailed plan to address your points about readability and presentation. If accepted, will we use the additional page to incorporate this material to the main text.

We use faithfulness, but should also discuss completeness, minimality, and human-interpretability

Thanks for this suggestion. One reason we propose using the area under the faithfulness curve is because this captures both minimality and faithfulness at the same time: methods that are better at locating the most important causal dependencies with fewer components will have higher faithfulness at smaller circuit sizes, thus increasing the area under the curve. Our metrics thus reward methods that are good at locating minimal circuits.

Measuring completeness is generally not computationally feasible. Wang et al. (2023) performed a detailed manual analysis on a single task; this allowed them to discover clusters of components with similar functional roles. Their notion of completeness involves ablating subsets of a particular functional cluster. In automatic circuit discovery settings, we don't know what the ground-truth clusters should be, and would thus need to enumerate all possible combinations of components (an exponential-time search). Thus, most work in this field does not measure completeness. Marks et al. (2024) propose ablating only the circuit to measure completeness, but it is much easier to destroy performance than to recover it (i.e., low scores when ablating the circuit don't necessarily imply that we have found all important causal dependencies). As for human-interpretability, we see this as the role of featurization methods, rather than circuit localization methods; higher performance in the causal variable localization track implies that the method is better at locating human-interpretable concepts in models. We will discuss these ideas and challenges explicitly in the final version; thanks!

"Previous work criticizes faithfulness on circuits and suggests considering the relative amount of pretraining compute needed to achieve comparable performance...?"

We're a bit confused by this feedback; could you clarify? Gao et al. doesn't criticize faithfulness, and they compare training compute for SAEs. Circuit discovery typically does not involve training. More broadly, typical language modeling benchmarks use model size (akin to our minimality metric) and model performance (akin to our faithfulness metric), but tend not to compare models based on compute.

"In the causal variable localization track, the IOI task uses a different metric, Why this metric?"

Because the high-level causal model for the IOI task predicts the output logits of the model (rather than a specific behavior), we cannot use accuracy. Instead, we measure the squared error between the high-level model logits and the actual language model logits. We have clarified this in the new draft. Please see L424-429 for how we compute the logit $O$ of the high-level causal model using a linear model over binary variables.

We don't discuss metrics used in IOI paper, sparse feature circuits paper, and scaling SAEs paper

Please see responses above for a discussion of the metrics proposed by these papers. We will add this discussion to the revision.

“why the subgraph performance ratio locates components with a positive effect ...” and “the causal variable track, in interchange intervention overlaps with the notation of the circuit...”

Please see the response to RnEi for an intuitive summary of the circuit localization metrics, and a description of how we will revise notation and presentation for clarity.

“notation is confusing… $\mathcal{C}$ in interchange intervention overlaps with the notation of the circuit in the previous section, while later in the formula interchange intervention uses $\mathcal{A}$, which represents the high-level causal model”

Good point; we have standardized notation across tracks, and added the table for notation seen here: https://imgur.com/a/m4DDNH2. To avoid overloading notation, we now use $\mathcal{H}$ for a high-level causal model, and $\mathcal{C}$ for a circuit. $\mathcal{C}$ refers to a part of the computation graph, whereas $\mathcal{H}$ is an abstraction that does not necessarily map cleanly to the computation graph. We also made the notation for interchange interventions more transparent, with $\leftarrow$ indicating intervention.

What about the intersection of the causal variable localization and circuit localization tracks?

We agree completely! Our evaluations focus primarily on localization or featurization, but future work should consider their intersection. We felt that good metrics for each were necessary before one could consider evaluating the two jointly. Future work could consider metrics that are compatible with circuits built on sparse features, pre-located causal variables, or neuron clusters rather than individual neurons or submodules.

Thank you for appreciating the value of our paper’s contribution and the validity of our experimental designs. We note your points about readability and presentation, and appreciate your willingness to reconsider your score on the basis of correcting them. We will make a number of changes to improve readability and presentation. If accepted, will we use the additional page given us to incorporate the following material to the main text and increase the readability of the paper.

Plans to improve readability and presentation

”Sec 3.1….argue they need to separate these goals into two metrics for each of the goals, the notation which I already find a bit confusing (F_{=}, F_{+}), and then with no justification they propose a proxy to estimate these metrics. I was lost there”

We will add some more intuition behind the metrics in the final version of the paper. We realized that the $F_+$ and $F_=$ names were confusing because they are named after the ideal values they should take, rather than what they actually measure. To be more transparent, we have renamed $F_+$ to the circuit performance ratio (CPR), and $F_=$ to the circuit-model distance (CMD). In short, CPR measures how the circuit performs on the task metric $m$ as a ratio w.r.t. the full model’s performance, while CMD measures how closely the circuit replicates the full model’s input-output behavior. One should aim to maximize CPR if the goal is to find the best-performing circuit; one should aim to minimize CMD if the goal is to find a circuit that concisely implements the full model's behavior.

Both of these metrics are defined using integrals. It is impossible to compute these integrals in exact form without infinite samples. The trapezoidal rule (i.e., Riemann sum) is an established way of approximating integrals given a few values of the function—this is the proxy we allude to. In the revision, we will clarify by not using different names for the exact and empirical definitions. We will instead define CPR and CMD in exact form, and then simply say how we measure them in practice.

”Would be very nice to include graphs for the causal relations described in text in 4.2. In the end, if I understand correctly, these causal graphs are fixed for the tasks at hand.”

Yes, the causal graphs are fixed for the task at hand. We added a more comprehensive description of the causal variable localization track that includes causal models for each task and figures that illustrate the concepts and terminology. For example: https://imgur.com/a/6mgZfj2.

"$d_{model}$ in line 237 is not defined, which makes the next line even more difficult to parse"

Thanks for catching this! We will add the following clarification: "...where $d_{\text{model}}$ is the model's hidden size, or the number of neurons in the activation vector output of each layer."

Beyond these specific points you raised, we have standardized notation across tracks, and added a table of notation, which you may view here: https://imgur.com/a/m4DDNH2. To avoid overloading notation, we have now modified the text so that $\mathcal{H}$ is a high-level causal model and $\mathcal{C}$ is a circuit. $\mathcal{C}$ refers to a part of the computation graph, whereas $\mathcal{H}$ is an abstraction that does not necessarily map cleanly to the computation graph. We also made the notation for interchange interventions more transparent with the $\leftarrow$ indicating intervention.

Other comments

"Submission doesn't make any theoretical or empirical claims"

Please see our response to reviewer bp8X on scientific novelty.

"It is hard to tell whether the evaluation criteria (the metrics they use to evaluate the baselines) are good or not"

A sanity check for our evaluation criteria is that they recover known findings. In the circuit localization track, attribution patching with integrated gradients is significantly better than attribution patching, in line with prior work [1,2]. In the causal variable localization track, supervised methods outperform unsupervised methods, as expected, and as found in very recent work [3].

References

[1] Hanna et al. (2024). "Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms." COLM. https://arxiv.org/abs/2403.17806

[2] Marks et al. (2025). "Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models." ICLR. https://arxiv.org/abs/2403.19647

[3] Wu et al. (2025). "AxBench: Steering LLMs? Even Simple Baselines Outperform Sparse Autoencoders." arXiv. https://arxiv.org/abs/2501.17148

Thank you for your positive assessment of the thoroughness of our experiments, the convincingness and clarity of our claims, and the design of our metrics!

Regarding task selection rationale and task coverage:

We aimed to strike a balance between having tasks (1) of diverse difficulties and requiring diverse skills that capture the strengths and weaknesses of different models (L91-92), (2) that have and have not been studied in prior mechanistic interpretability work, and (3) that good open-source language models are capable of performing (Table 1; L131-133). To point (1), the four tasks we selected test linguistic/semantic understanding of text (IOI), mathematical reasoning (Arithmetic), scientific knowledge (ARC), copying from context (MCQA), and the ability to answer formatted multiple-choice questions (MCQA and ARC). To point (2), we included tasks that are more widely studied, such as IOI and Arithmetic, to ground the benchmark in existing and ongoing research and to foster buy-in from the mechanistic interpretability community. We purposefully selected ARC and MCQA to push the research community in a particular direction: towards tasks that are represented on real-world leaderboards. Tasks like IOI have dominated the MI literature (with dozens of papers evaluating on this task), but others such as MCQA have only been studied in 2 papers (neither of which analyzed the ARC dataset). ARC in particular is significantly more realistic than the tasks that have been studied to date using circuit discovery methods.

We intend for the benchmark to be a living resource (L433-438) and plan to expand the task list with community buy-in. We did not mean to imply (and thus do not state in the paper) that the four selected tasks are sufficient for understanding all LM behaviors. “[E]nsur[ing] coverage for all important MI phenomena” as requested would involve a task list capturing nearly every textual output an LM can produce! Regarding how we can know our task set is “sufficient to measure general MI progress”: MI progress has up until this point been driven by papers running analysis most commonly on one or two datasets, and our task set has already allowed us to draw meaningful comparisons not established in prior work (see response to bp8X for more on this).

How do weighted edge counts factor into the $F_+$ and $F_=$ metrics?

$F_+$ and $F_=$ (which have been renamed to circuit performance ratio (CPR) and circuit-model distance (CMD), respectively; see response to RnEi) can be conceptualized as integrals of $f$ over the weighted edge counts. If we plot faithfulness $f$ against circuit size (measured via weighted edge count), then $F_+$ (CPR) is simply the area under this curve. The weighted edge count is a way to measure circuit size in a way that enables direct comparisons across edge-level and node-level circuits; it is basically (proportion of nodes in submodule $u$) times (number of edges outgoing from submodule $u$), summed over all $u$.

Thank you for your detailed review and for acknowledging the value of our benchmark’s practical utility and contribution to the literature! We’d like to clarify our scientific contributions; they include 1) new metrics, and 2) new empirical results (L432-435 Col.2), facilitated crucially by 3) our standardization of metrics, datasets, and models.

Regarding reliance on existing datasets:

While we included tasks that are more widely studied, such as IOI and Arithmetic, to ground the benchmark in existing research, we purposefully selected our tasks to push the research community towards tasks that are represented on real-world leaderboards (such as MCQA and ARC) with varying formats and difficulty levels (L91-92). Crucially, creating new datasets isn’t necessary when existing datasets remain un- or under-studied. Certain tasks such as IOI have dominated the MI literature (with dozens of papers evaluating on this task), but others such as MCQA have only been studied in 2 papers (neither of which analyzed the ARC dataset). ARC in particular is significantly more realistic than the tasks that have been studied to date using circuit discovery methods. Our main contributions were not the datasets, but rather the metrics, the curation of datasets, and the resulting systematic analyses.

Also, the vast majority of MI papers only run analysis on one dataset and/or one model. In contrast, we conduct systematic analyses across five models, four datasets, and several methods for each track. We are also the first to run experiments on ARC. We expand the synthetic MCQA dataset from prior work from 105 to 260 instances, and the Arithmetic dataset to 150k instances (75k used in our experiments), compared to 1200 in prior work.

Finally, we curate counterfactuals to isolate specific information, which may be useful for other mechanistic studies outside of MIB, as the choice of counterfactual is central to making causal claims [1].

We elaborate more on choice of tasks in our response to Pv8S.

Regarding reliance on existing metrics:

For the circuit localization track, we do not use existing evaluation metrics; in fact, one of our main contributions is proposing new metrics (see first 2 PPs of Section 3.1)! Faithfulness metrics in prior work conflated important model components (both helpful and harmful) with components driving better model behavior. Additionally, previous studies typically measure the quality of a single circuit using a single faithfulness value $f$, rather than measuring the quality of a method via an aggregation over $f$ values (as we do). The weighted edge count is also novel: before this, it was not clear how to compare the size of node-based and edge-based circuits.

Regarding scientific novelty:

Our new metrics and large-scale evaluations allow us to support multiple novel empirical claims. Previously, no single paper was able to compare all of the circuit discovery methods that we did in a systematic way (see response to comment on existing metrics). Specifically, we find that (a) edge-based circuits are better than node-based circuits (L327-328), (b) ablations from counterfactual inputs are best (L320-321), and (c) DAS (and non-basis-aligned representations more broadly) outperforms other featurizers (L439). In summary, our proposed metrics help us recover known findings (like that integrated gradients improves attribution quality), challenge others (that SAEs are not as effective as DAS at featurization), and enable new kinds of direct comparisons across methods that were previously difficult to operationalize (L432-434). We will clarify these by adding a bulleted paragraph in the introduction summarizing our contributions, and emphasizing in the paper when we obtain novel findings.

The causal variable localization track includes multiple causal variables that have not been investigated in previous research. The multiple choice pointer variable was not analyzed in previous work such as [2]; while there is some evidence of a carry-the-one variable existing, e.g., [3] or [4], our baselines were unable to surpass the random performance of 50%, indicating that linear methods may not be enough to locate this variable. Finally, while the token and position variables from the IOI task were proposed in [5], we are the first to conduct experiments identifying separable sets of features for each variable. In sum, while we drew from existing datasets and tasks, our analyses have significant novelty.

References:

[1] Kusner et al. (2017). https://arxiv.org/abs/1703.06856

[2] Wiegreffe et al. (2025). https://arxiv.org/abs/2407.15018

[3] Kantamneni & Tegmark (2025). https://arxiv.org/pdf/2502.00873

[4] Quirke et al. (2025). https://arxiv.org/pdf/2402.02619

[5] Wang et al. (2023).https://arxiv.org/abs/2211.00593