EAP-GP: Mitigating Saturation Effect in Gradient-based Automated Circuit Identification
Authors: Lin Zhang
Wenshuo Dong
Zhuoran Zhang
Shu Yang
Lijie Hu
Ninghao Liu
Pan Zhou
Di Wang
Venue: NeurIPS 2025 poster ()
Keywords: interpretability
explainable AI
model interpretability
Primary area: social_and_economic_aspects_of_machine_learning

Abstract: Understanding the internal mechanisms of transformer-based language models remains challenging. Mechanistic interpretability based on circuit discovery aims to reverse engineer neural networks by analyzing their internal processes at the level of computational subgraphs. In this paper, we revisit existing gradient-based circuit identification methods and find that their performance is either affected by the zero-gradient problem or saturation effects, where edge attribution scores become insensitive to input changes, resulting in noisy and unreliable attribution evaluations for circuit components. To address the saturation effect, we propose Edge Attribution Patching with GradPath (EAP-GP), EAP-GP introduces an integration path, starting from the input and adaptively following the direction of the difference between the gradients of corrupted and clean inputs to avoid the saturated region. This approach enhances attribution reliability and improves the faithfulness of circuit identification. We evaluate EAP-GP on 6 datasets using GPT-2 Small, GPT-2 Medium, and GPT-2 XL. Experimental results demonstrate that EAP-GP outperforms existing methods in circuit faithfulness, achieving improvements up to 17.7\%. Comparisons with manually annotated ground-truth circuits demonstrate that EAP-GP achieves precision and recall comparable to or better than previous approaches, highlighting its effectiveness in identifying accurate circuits.

EAP-GP: Mitigating Saturation Effect in
Bradient-based Automated Circuit Identification
Lin Zhang 122, Wenshuo Dong Zhuoran Zhang Shu Yang",, 2, Lijie Hu
Ninghao Liu?, Pan Zhou Di Wang!..
King Abdullah University of Science and Technology (KAUST) Provable Responsible Al and Data Analytics (PRADA) Lab
Harbin Institute of Technology, Shenzhen
4 University of Copenhagen
Peking University
MBZUAI
Hong Kong Polytechnic University
Huazhong University of Science and Technology
Abstract
Understanding the internal mechanisms of transformer- language models remains challenging. Mechanistic interpretability based on circuit discovery aims to reverse engineer neural networks by analyzing their internal processes at the level of computational subgraphs.
this paper, we revisit existing gradient-based circuit identification methods and find that their performance is either affected by the zero-gradient problem or saturation effects, where edge attribution scores become insensitive to input changes, resulting in noisy and unreliable attribution evaluations for circuit components. To address the saturation effect, we propose Edge Attribution Patching with GradPath (EAP-GP). EAP-GP introduces an inte- gration path, starting from the input and adaptively following the direction of the difference between the gradients of corrupted and clean inputs avoid the saturated region. This approach enhances attribution reliability and improves the faithfulness of circuit identification. We evaluate EAP-GP six datasets using GPT-2 Small, GPT-2 Medium, and GPT-2 XL. Experimental results demonstrate that EAP-GP outperforms existing methods in circuit faithfulness, achieving improvements up 17.7%. Comparisons with manually annotated ground-truth circuits demonstrate that EAP-GP achieves precision and recall comparable or better than previous approaches, highlighting its effectiveness in identifying accurate circuits.
Introduction
(Vaswani et al. 2017) have achieved remarkable with different applications Yao et al. (2025a); (2025b), but their internal mechanisms remain unclear. Mechanistic interpretability OOah 2022; Nandaj 2023) aims to precisely describe neural network computations, potentially in the form of pseudocode (also called reverse engineering). to
In recent years, transformer-baser language models
success (Devlin et al. 2019 Achiam et al. 2023)
Wang et al. (2025b); Li et al. (2025); ; Yang et al.
better understand model behavior (Geva et al. 2020) Geiger et al. 2021 Meng et al. [2022] [Su et al.
2025: Yao al. 2025b; Zhang et al. 2024 Jiang al. 2025 | al. 2025a Dong al. 2025
Zhang et al. 2025a). Much research in mechanistic interpretability conceptualizes neural networks as
computational graphs (Conmy al. 2023 Geiger al. 2021), where circuits minimal subgraphs
Di Wang is supported in part by the funding BAS/I/1689-01-01 and funding from KAUST Center of Excellence for Generative AI, under award number 5940. Corresponding author: wan @ Lauuseedu.sa
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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200 Matrod EUP-G
comppttd
Gradient
1.00
Saturated Region
0.73
0.90
ongginal
EAP
1.0
Edge Activation
Figure 1: Visualization of path constructions and gradient behavior in EAP-GP and its variants. The left panel shows the gradient magnitude with respect to edge activation along different integration paths. The right panel compares the straight-line path used in EAP-IG (blue) with the dynamically adjusted GradPath in EAP-GP (green), which follows the steepest gradient directions. Circles (o) and triangles (A) represent original and corrupted inputs, respectively, and ellipses visualize the gradient field. The red-shaded region denotes the saturated gradient zone, which the EAP-IG path inevitably passes through, while EAP-GP dynamically avoids it.
representing critical components for specific tasks and serving fundamental building blocks of the model. Thus, identifying such circuits is crucial to understanding the inner workings of language
models (LMs) (Olah et al. 2020 Wang et al. 2023 Zhang et 2025b Yang et al.] 2025a).
Prior research on circuit identification in LMs follows a straightforward methodology (Conmy et al. 2023 Hanna et al. 2024b): employing causal interventions to identify components that contribute to specific behaviors, then formulating and testing hypotheses about the functions implemented by each component in the circuit. This approach has led to the development of frameworks that provide causal explanations for model outputs, such as predicting indirect objects (Conmy et al., (023). brain-inspired modular training (Nainani, 2024), completing year-spans (Hanna al. 2024a)) and
more (Lieberum et al. 2023 Tigges et al. 2023 Prakash et al. 2024 Merullo et al. 2024).
Recent work on circuit identification often aims to identify important components (e.g., attention heads, residual streams, or MLPs) and important edges, i.e.. critical connections between compo- nents. Causal intervention-base circuit identification methods require forward pass to test an edge's importance by observing whether the relevant model behavior changes (Conmy et al.) 2023). However, as LMs contain extremely large number of edges, testing all edges requires significant computational resources, and as the model size increases, this challenge becomes even more severe. To address this issue, researchers have developed faster gradient-based automated circuit identifica- tion methods (O'Neill and Bui 2024 Marks et al. 2024). Edge Attribution Patching (EAP) (Syed) et al. 2023) attributes each edge's s importance using two forward and one backward pass instead. However, it can be affected by the zero- zero-gradie grrddind problem, which may lead to incomplete attributions. EAP-IG (Hanna al. 2024b) incorporates Integrated Gradients (IG) into EAP mitigate this, which produces more reliable attribution evaluations by computing the average gradients of corrupted inputs (activations) along straight-line path from the original inputs the baseline inputs (counterfactual input), resulting in more reliable importance (attribution) evaluation.
While EAP-IG can significantly improve the faithfulness of the discovered circuit, in this paper, carefully revisit the approach and identify a critical issue called the saturation effect. This effect occurs when the corrupted input enters saturation regions, where the gradient becomes nearly zero (see Section for details). As a result, the loss function becomes insensitive to further input variations, reducing the attribution's 's responsiveness to input variations. This leads to inaccurate and unfaithful edge attributions, ultimately reducing the faithfulness of circuit identification.
To address this issue, we propose Edge Attribution Patching with GradPath (EAP-GP). a novel method for mitigating saturation effects that can identify edges in circuits more accurately. Unlike previous methods, which are model-agnostic, EAP-GP constructs an integral path between the clean input and

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the baseline input in an adaptive and model-dependent way. Specifically, for the current corrupted input, EAP-GP gradually adjusts its next movement based on its difference in gradient the baseline input rather than moving directly along pre-fixed direction as in FAP-IG. Thus, intuitively, each step of EAP-GP follows the steepest direction to rapidly decrease the model's s prediction, effectively avoiding saturation regions and guiding a more efficient and faithful attribution evaluation.
We evaluate EAP-GP across six tasks and demonstrate that, at the same sparsity, it achieves im- provements up to 17.7% across individual datasets in terms of circuit faithfulness, outperforming previous suddent-bbssed cireuit identification methods. To further assess its performance, we extend our experiments to larger models, including GPT-2 Medium and GPT-2 XL, and find that EAP- GP maintains excellent performance. Finally, we compare the eircuits identified by EAP-GP with manually annotated ground-truth circuits from prior research (Syed et al. (202)). The results show that EAP-GP achieves precision and recall comparable to or better than existing methods, further validating its reliability for circuit identification.
2 Related Work
Neural networks can be conceptualized as computational graphs, where circuits are defined as subgraphs that represent the critical components necessary for specific tasks and serve as fundamental computational units and building blocks of the network (Bereska and Gavves 2024). The task of circuit identification leverages task-relevant parameters (Bereska and Gavves 2024) and feature connections (He et al. (2024) within the network to capture core computational processes and attribute outputs to specific components (Miller et al. 2024), thereby avoiding the need to analyze the entire model comprehensively. Existing research has demonstrated that decomposing neural networks into circuits for interpretabilityy is highly effective in small-scale models for specific tasks, such as indirect object identification (Wang et al. 2023), greater-than computations (Hanna et al. 2024b), and multiple-choice question answering (Lieberum et al.. 2023). However, due to the complexity of manual causal interventions, extending such comprehensive circuit analysis to more complex behaviors in large language models remains challenging.
Automated Circuit Discovery (ACDC) (Conmy al., 2023) proposed an automated workflow for circuit discovery, but its recursive Activation Patching mechanism leads to slow forward passes, making it inefficient. [Sydd et al. (2023) introduced Edge EAP, which estimates multiple edges using only two forward passes and one backward pass. Building upon this, |Hanna et al. (2024b) introduced EAP-IG, enhancing the fidelity of the identified circuits. Our method is variant of gradient- based Automated Circuit Identification. As we will show in Section 4 EAP-IG is limited by gradient saturation. Our proposed EAP-GP aims to address this issue. In concurrent work, [Hanna et al. (2024a) argued that faithfulness metrics are more suitable for evaluating circuits than measuring overlap with manually annotated circuits. Recent work has explored other notions of a circuit. Inspired by the fact that Sparse Autoencoders (SAEs) can find numan-interpreee activations, (Cunningham et al. 2023). Marks et al. (2024) identified circuits based on these features. Additionally, Wu et al. (2024) aligned computation in Alpaca (Taori et al. 2023 with proposed symbolic algorithm (Geiger et al. 2024).
features in LM
3 Preliminaries
To better illustrate our motivation and method, in this section we will revisit previous methods for circuit discovery.
Integrated Gradients Method. Integrated Gradients (IG) (Sundararajan et al. (017)) is gradient- based attribution method in explainable AI that aims to quantily how each input feature contributes to deep neural network's 's output. Generally, the idea is to evaluate how the model performance will be changed if we change the target feature of the input to the baseline input (or counterfactual input). It does so by estimating the accumulated gradients along path from the baseline input to the target input. The performance of IG largely depends on two key hyperparameters: the path and the baseline. Specifically, consider an input E IR",, a path for integrating gradients is formally defined as 7(a) for a E [0, 1). This path a sequence of points in R²" that transitions from the baseline x' to the target input x, i.c., 70) = x' and 7(1) x.
3

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Given a path y and model f R + R. the integrated gradient for the i-th feature is computed by integrating the model's gradient with respect to that feature along the path. Formally, following Sundararajan et al. (2017) we have
@)(((())) Path
0rs(a) da, ( 07((a)
ao
where #f(n(a)) is the gradient of the model's output with respect to the i-th feature at 7(0), and (x((a)
(x((a) the rate of change of that feature along the path. To simplify the computation, in practice, da
the simplest path is a straight line from x' to x, given by
(a) = x' + xa(x-x)
a [0.
(2)
The choice of baseline x' is an active research topic. Sturmfels et al. (2020) provide a thorough study of common baselines, including the zero vector (x' 0), the one vector (x" 1), and samples drawn from the training data distribution (x' ~ D-
However, directly computing the integral in Eq ①1 is impractical. To address this computational challenge, a discrete sum approximation with & points along the path commonly used. For a straight-ling path, IG is calculated as:
k Of Σ k j=1
1
(x'
+ ( x')
= (x. - x/}
x
(3)
dr,
where the index corresponds to the j-th sampling point along the path from the baseline x' the input x, and the gradients are computed at each of these points.
Circuit discovery. Given a model G, which can be represented as a computational subgraph, circuit C' C G is a subgraph, where it can be represented as a set of edges in the circuit Olah et al. (2020).
Definition 3.1 (Computational Graph Hanna et al. (2024b) ). A transformer LM G's computational graph is a digraph describing the computations it performs. flows from the LM's inputs to the unembedding that projects its activations into vocabulary space. We define this digraph's 's nodes to be the LM's attention heads and MLPs, though other levels of granularity, c.g., neurons, are possible. Edges specify where a node's s output goes; node v's input is the sum of the outputs of all nodes with an edge to v. A circuit C' is subgraph of G that connects the inputs to the logits.
Definition 3.2 (Circuit Discovery). Given full model G and a subgraph C, for any pair of clean and corrupted input (prompt) and z', denote T as the task distribution, EG as the activations of G with input z, Ec(z, 2') as the activations of the subgraph when 2 is input, with all edges in G not present in C' overwritten by their activations on z'. Moreover, denote L(A) as loss on the logits for activations A (with input 2), which is used to measure the performance of subgraphs. Formally, circuit discovery can be formulated as
arg min ((Fe(z,,)) [(F](==))]
In practice, we always use logit difference or probability difference as the loss L.
Many studies identify circuits using activation patching (Vig et al. 2020) Geiger et al. 2021). which evaluates the change by replacing (clean) edge activation with a corrupted one during the model's forward pass. ACDC (Conmy et al. (023) automatically checks whether for each edge such a change exceeds some threshold. However, causal interventions scale poorly because their iterative cost increases significantly as the model size grows. EAP (Syed et al. 2023) alleviates this issue. It estimates edge importance (attribution) and selects the most important ones by computing the product of activation changes and input gradients. Specifically, given an edge e = (u, v) with clean and corrupted activations F. and a/ we aim to approximate the change in loss (note that since Ec, and v. are clear in the text, we will denote L(s) = L(Fo(z)= Iu + 8) as the loss where we change the activation from F. to 8), i.e.
L(xu) - L(x()) = (xa - x',) (l())
(5)
dz.

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However, EAP may suffer from the zero pero-gradient problem, which may lead to inaccurate attributions. To address this issue, based on the similarities between the goals of feature attribution and circuit discovery, EAP-IG (Hanna et al. (024b) incorporates IG, which averages gradients along straight- line path (a) in (2) from original to corrupted activations. This method provides more stable and reliable attributions. Similar to 33. the IG score for edge (u, is defined as:
aL (2'a + m [ z'm)
(u.v)
(I a'a)
(6)
az.
This gradient is computed along an interpolated path from the original activation zu the corrupted activation xzy, The interpolation factor determines the position along this path, ensuring that the gradient is averaged over multiple steps. This approach helps mitigate the zero-gradient problem, reducing the risk of incomplete attributions.
4 Saturation Effects in Circuit Discovery
In this section, we revisit the above-mentioned gradient- based automatic circuit identification methods, EAP and EAP-IG. Both of them determine edge importance by computing the activation difference multiplied by the loss gradient. This product approximates the metric difference in (5) and is used to evaluate each edge's s contribution.
Specifically, we analyze a circuit edge (u, with its clean activation Iu in the IOI dataset and examine how different input choices influence the gradient of the loss 0L in both EAP and EAP-IG. år., EAP in (5) evaluates an edge's 's importance by computing the product of the metric's derivative at øy. and the change in the edge's 's activation. However, illustrated in Figure[[ poinck this approach can be misleading: a nearly zero derivative at Tu suggests that the edge has minimal influence and will not contribute to the attribution, even if the activation has non-zero gradient at ay and the difference in activations is significant.
We also conduct experiments under the same setting for EAP-IG in 66 with & = 5. As illustrated in Figure I we find that the gradient remains close to zero when falls within the ranges [0, 0.2] and (0.8, IT. where the IG score changes slowly. In contrast, slight variations the score occur only within the range E [0.2, 0.8). While this approach partially mitigates the zero-grade grodggrddeet issue in EAP, the nature of the chosen straight-line path inevitably leads it into regions where the gradient remains nearly zero (0, 0.2] and [0.8, I)). The perturbed activation inputs within these regions cause the loss function to become insensitive to further input variations, reducing the attribution's 's responsiveness to input perturbations. This results in inaccurate and unfaithful edge attribution evaluations and ultimately leads to unfaithful circuit identification. We provide the following definition for this saturation effect for gradient-based EAP methods.
Saturation Effeets and Regions:
For an edge (u, v) in a circuit discovery task, its saturation regions aL remains close to zero,
refer to segments of the integration path where the gradient of the loss, az." reducing the sensitivity of L to activation changes. Saturation effects occur when scores accumulate in these regions, reducing the attribution's 's responsiveness to activation variations. This distortion ultimately compromises the reliability of circuit analysis, leading to unfaithful circuit evaluations.
5 Mitigating Saturation Effect via EAP-GP
In the previous section, we discussed how EAP suffers from the zero-gradient problem and how EAP-IG is affected by saturation effects. Our previous experiments show that the main reason EAP-IG gets stuck in the saturation region is that the integration path is a direct line between the clean and baseline input, which is independent of the full model G. Such a model-agnostic way will unintentionally make the gradient nearly zero for some perturbed activations. Thus, we need to construct integral path that depends the model to avoid the saturation region.
To address these issues, we propose Edge Attribution Patching with GradPath (EAP-GP). Unlike the pre-fixed straight-line paths used in EAP-IG, EAP-GP introduces GradPath, dynamically adjusted path designed to integrate gradients more effectively and reduce saturation effects, as shown in Figure Specifically, given target number of steps k, step EAP-GP iteratively finds the best
5

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Algorithm Edge Attribution Patching with GradPath (EAP-GP) for edge (u,w) v)
Require: Tuz d'y Original/Corrupted activations; k: GradPath steps; C: Circuit; G: Full model;
L()): Loss; n: Top edges to select.
Ensure: Circuit C' and final intervention results.
1: A. GradPath Construction
2: (0) -- Zu
3: for = 1 + k do
4: 9j+1 + V
5:
( + (1) W. 9j+1
6: end for
7: B. Edge Attribution (EAP-GP)
8: for each edge (u, v) in G do
9: score(u, v) < (In - - x x Σド=
8zc
end for
11: C. Circuit Extraction
12: Sort edges by (u, w) select top n into O: prune isolated nodes
13: D. Intervention & Evaluation
14: for each node v do
15: for each edge e == (u, v) do
ie f 17: end for
16:
18: Input to v: E(u,YEE [eee au + (1 iz) x'y]
19:
end for
20: Evaluate the model output under this intervention
21:
return C
movement of the current perturbed input (activation), denoted as 7 ())), starting from the original
input vu (i.e., 7 (0) = x. and ending at the baseline input x' (i.e., 7 (() = x.,) In detail, at the current input 7 (2), we aim to find the best direction toward Ty,, i.c., we aim to solve the following optimization problem locally.
min |G -))
Here, for an activation s, G(ss) = G(Ec(z)
+ s) is the output of the model G with prompt
and activations (2) - Tu + s, where we change the activation from V, to s. Intuitively, such a task can make sure that we can move the current input ( ( to make closer to the baseline input. Thus,
the gradient could not be too small to be nearly zero, making the path avoid the saturation region.
Here, we use one step of gradient descent for and get the next perturbed input (
(++1
as
(I(G()((()) G(r
Ij+1
0,0(+)
(8)
79 - k -
1
W 9j+1.
where W,- |19j+1 |a is normalization factor that dynamically adjusts the step size. Our integrating path will be determined by these corrupted activations in G And we can approximate the integration by using the finite sum to get the EAP-GP score for edge (u, v):
k OL (7)
1 = (5. x.)
K
Ox,
1=1
After attributing each edge in the model, we follow the approach in Hanna al. 2024b) and employ greedy search strategy to iteratively evaluate the top-ranked edges iteratively, selecting the top

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101
Gender-Bias
0..0
48.0%
Sparaaa (%)
0.55
9%
-10
895%
Steps
Steps
Figure 2: Faithfulness circuits obtained using EAP-GP across different edge sparsity levels and step counts for IOI and gender-bias tasks.
101
Greaten-Than
Ganden-Blae
CAP
CAP
CAP
Edge Sparsity (34)
Edge Sparsity (%)
Edge Sparsity (96
Country Capital
Hypernymyy
Vectec
Ver
Melftd
SAP
RAP
SAP
(9.11
Figure 3: Comparison circuit performance across different methods on GPT-2 Small. In all plots, a higher value indicates better performance. EAP-GP identifies circuits that outperform other methods across all six tasks.
edges (a hyperparameter) with the highest scores to form the circuit. Once the circuit is identified, recursively prune nodes and edges with no parents or children, as they are redundant. We evaluate the circuit by applying the following intervention. Let represent node in the model's computational graph, and let E, denote the set of all incoming edges to v. For each edge E E.., let ie be a binary the edge is part of the circuit and 0 otherwise. Without intervention,
indicator, where the input to is:
Σ
Fa
(10)
E.
which represents the sum of the outputs from all parent nodes of v. With intervention, the input is modified as:
i + (1 - ie) s'y-
(11)
all edges are in the circuit (i, = e), this intervention equivalent to running the model on original inputs. Conversely, if no edges are in the circuit (i. 0 for all e), the intervention corresponds running the model on corrupted inputs. The overall pseudocode the EAP-GP algorithm is provided in Algorithm!]
7

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IOI: Node
Greater-Than: Node PR
Precision
0.3
Precision
2.9
0.3
Michoo
Mothos
EAP
EAP
EARO
EAPN EAP-P
EAP-P
Recall
Recall
IOI: Edge
Creater-Thans Edge PR
Methos
Metrod
CAP
CAP
Precision
0.3
CAIN
CAPOP
Precision
2.9
EAP
EAP-GP
0.3
02
Recall
Recall
Figure 4: Precision-recall curves for IOI (left) and Greater- Than (right) node/edge overlap.
Experiments
6.1
Experimental Setup
Datasets. We evaluate model performance using six datasets: Indirect Object Identification (IOI), Subject-Vert Verb Agreement (SVA), Gender-Bias, Capital-Country, Hypernymy, and Greater-Than (Hanna et al., 2024b). IOI tests the model's 'ss ability to identify indirect objects, while SVA assesses subject-verb agreement. Gender-Bias examines gender bias in language models, and evaluates the prediction of country given its capital. Hypernymy focuses identifying hypernyms (superordinate categories), and Greater- Than measures the model's ''s ability to predict numbers that greater than specified value in sentence. Table I provides representative task examples, and Appendix A. details the datasets and the loss functions used for circuit identification.
Baselines. Since EAP-GP is gradient-based method, we primarily compare it with previous gradient-based approaches, such as EAP and EAP-IG. Both are outlined in Section
Evaluation Metrics. A circuit is considered faithful to a model's behavior on a task if all model edges outside the eircuit can be corrupted while still preserving the model's original outputs (Hanna et al. 2024b). Following the setting of Hanna et al.] (002b)), we evaluate circuit faithfulness across all tasks using the Normalized Faithfulness Score (NFS), which measures the similarity between the circuit's ss output and the full model's output:
)0(),))) 8_
score
(12)
84 8_
where 82 and 8_ represent the full model's performance on the original and corrupted inputs, respectively, and 8c(r,z)) represents the circuit's performance. The value of òc(z,z") is measured using the task-specific Logit Difference or Probability Difference, with detailed explanations provided in the appendixA.1] 8_ and &_ for each dataset are provided in Table Additionally, for the IOI and Greater-Thane Than datasets, we compare the precision-recit (PR) performance curve of gradient- based methods with manually identified circuits from prior research (Syed et al. 2023).
Experimental Setup. All experiments are conducted on GPT-2 Small (117M), GPT-2 Medium (345M), and GPT-2 XL (I.5B), which contain 32,491 231,877, and 2,235,02 33,50255 edges, respectively. We set in EAP-GP. Following (Hanna et al. 2024b), we perform EAP-IG with hyperparameters set to A = 5 steps. All experiments conducted NVIDIA A40 GPU.

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6.2
Experimental Results
This section compares the three methods based on our primary faithfulness metrics, with all experi- ments conducted on GPT-2 Small (117M). Additional experiments on GPT-2 Medium (345M) (see Figure and Table 5) and GPT-2 XI. (1.5B) (see Figure 6 and Table 6). along with examples of circuits identified by EAP-GP (see Figure 7 are reported in Appendix A.2
Circuit Faithfulness. We compare the faithfulness of identified circuits for three gradient- based circuit identification methods (EAP, EAP-IG, and EAP-GP) across six tasks under edge sparsity levels ranging from 96.9% to 99.9%, as shown Figure 3 and Table4
In IOI, SVA, and Hypernymy, EAP-GP significantly outperforms the other methods. For example, in the IOI task, when sparsity 97.5%. EAP-GP achieves a score of 80. 1%, far exceeding EAP-IG (62.4%) and EAP (56.9%) (see Table 3 In IOI and SVA, the performance gap is small at low sparsity levels, but as sparsity increases, EAP-GP's advantage becomes more pronounced. However, when edge sparsity ranges from 99.0% to 99. 99.9%, EAP generates completely unfaithful circuits, with a regularized faithfulness score of 0. This is partly due to EAP producing many "parentless heads", which are subsequently pruned. As result, EAP's generated circuits are entirely pruned to an empty structure. In the Hypernymy task, this performance gap remains large across all sparsity levels, indicating that EAP-GP consistently outperforms both EAP and EAP-IG in this task.
For Greater-Than and Gender-Bias, the performance differences among the three methods are smaller, remaining relatively close across all sparsity levels. Although EAP-GP maintains slight advantage, the performance gap minimal. For example, in the Gender-Bias task, EAP-GP (92.68%) only slightly outperforms EAP-IG (90.76%), This is because these tasks primarily rely on direct feature mappings rather than complex reasoning models. The Gender-Bias task focuses on the direct association between professions and pronouns (e.g., banker + he), while the Greater-Thar task involves simple sequential relations in numerical data (e.g., 1352 + 1353). These tasks are characterized by their reliance explicit, localized features rather than requiring multi-step reasoning or complex relational identification, as seen IOI and Hypernymy.
In the Country-Capita task, EAP performs poorly, failing to maintain faithful circuit structures as sparsity increases. EAP-IG performs better but remains slightly weaker than EAP-GP. Overall, EAP-GP demonstrates superior performance, outperforming both EAP and EAP-IG, as it achieves more effective edge attribution evaluation.
Comparison with Manual Circuit. We follow the approach of (Syed et al. 2023) to check whether method EAP-CH GP can identify the ground-truth circuits. Specifically, we compute the precision and recall of the EAP, EAP-IG, and EAP-GP circuits concerning the manually found circuits. Our results in Figure 4 indicate that EAP-GP performs well in retrieving nodes and edges. Specifically, for the 1OI task, edge precision/recall and node precision/recall exhibit similar trends for all three methods. EAP-GP initially performs worse but improves slightly as recall increases when it is greater than 0.8 and 0.25 for node and edge, respectively. However, for IOI, this assessment may be somewhat flawed due to the ambiguous role of MLPs in the manually found IOI circuit, which is mentioned by (Hannal it al. 2024b). In the Greater-Ther task, where the manually identified circuit also includes MLPs, we can easily see that EAP- GP outperforms both EAP and EAP-IG both edge and node retrieval. It identifies circuits with higher precision and recall than EAP and EAP-IG.
Effect on Number of Steps in EAP-GP. Note that the number of steps is the only hyperparameter in EAP-GP. Here we perform an ablation study to see its effect on the performance of IOI and Gender-Bias tasks. We use their respective logit difference and probability difference as metrics to assess the circuit. Specifically, we run EAP-GP for l steps, where l ranges from to 20. Notably, when k = 1, EAP-GP is equivalent to EAP, as illustrated in Figure [] When l: 2, the gradient used for evaluation is the average of the gradients of the clean and corrupted inputs.
We identify circuits at various edge sparsity levels, ranging from 96.9% to 99.9%. Our results (Figure 2) indicate that, across all edge sparsity levels, only a few steps are sufficient to achieve high faithfulness. At k = 4 or 5 steps, EAP-GP already produces faithful circuits for both the IOI and Gender-Bian tasks.
We also observe that, in some cases, reducing sparsity (e.g., 101 from 97.5% to 97.2%) or increasing the number of steps (e.g., >> 5) leads to a decline in the metric. This may be because the greedy and top-n edge selection strategies rely absolute attribution scores to select edges, which may

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inadvertently include components that harm model performance, such as edges encoding noise or adversarial patterns. Furthermore, as the step count k increases. based on our method, the gradient norm will become smaller, resulting in reciprocal growth of the normalized step sizes ; This amplifies high-frequency oscillations in the integration path near the corrupted input x', where gradient directions become unstable. Consequently, noise-domings steps accumulate, diluting the accurate attribution signals and ultimately degrading the metric.
7 Conclusion
In this paper, we revisited gradient-based automatic circuit identification and identified the saturation effects and regions, which cause inaccurate edge attributions and unfaithful circuit identification. To address this, we proposed Edge Attribution Patching with GradPath (EAP-GP), which replaces EAP- IG's fixed straight-ling paths with GradPath. This dynamically adjusted path integrates gradients more effectively and mitigates saturation effects. Extensive experiments showed that EAP-GP enhances edge attribution accuracy and circuit faithfulness, outperforming previous methods.
References
Joshua Achiam, Shya Adler, Sandhini Agarwal, and et al. GPT-4 Technical Report. arXiv preprint arXiv:2303.08774, 2023. URLLhttpp://rxxi..rorr 2at0b.//33300000 08774
L Bereska and E Gavves. arXiv:2404. 14082, 2024.
Mechanistic interpretability for ai safety a review. arXiv preprint
Abhijith Chintam, Rahel Beloch, Willem Zuidema, Michael Hanna, and Oskar van der Wal. Identifying and adapting transformer-componeee responsible for gender bias in an english language model. Yonatan Belinkov, Sophie Hao, Jaap Jumelet, Najoung Kim, Arya Mc- Carthy, and Hosein Mohebbi, editors, Proceedings of the 6th BluckboxNLP Workshop: Ana- lyzing and Interpreting Neural Networks for NLP., pages 379-394, Singapore, December 2023. Association for Computational Linguistics. doi: 10. 10.186331/0002bbeeexxxbp 1.29. URL https://accaatthol.gg /2033. blackboxnlp- 1. 29
Arthur Conmy, Alexa Mavor-Parker Andrew Lynch, et al. Towards automated circuit discovery for mechanistic interpretability. In Advances in Neural Information Processing Systems, volume 36, pages (6318-16352. NeurIPS, 2023.
H. Cunningham, A. Ewart, L. Riggs, et al. Sparse autoencoders find highly interpretable features in language models. arXiv preprint arXivv2309.088000 2023.
Jacob Devlin, Ming-Wes Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguisties: Human Lan- guage Technologies, pages 4171-4186, Minneapolis, USA, 2019. Association for Computational Linguistics.
Wenshuo Dong, Qingsong Yang, Shu Yang. Lijie Hu, Meng Ding, Wanyu Lin, Tianhang Zheng, and Di Wang. Understanding and mitigating cross-lingual privacy leakage via language-specific and universal privacy neurons. arXiv preprint arXiv:2506. 00759, 2025.
A. Geiger, H. Lu, Icard, Smith, and J. Doe. Causal abstractions of neural networks. In Advances in Neural Information Processing Systems, volume 34, pages 9574-9586. NeurIPS, 2021.
Atticus Geiger, Zhengxuan Wu, Christopher Potts, Thomas Icard, and Noah Goodman. Finding alignments between interpretable causal variables and distributed neural representations. In Francesco Locatello and Vanessa Didelez, editors, Proceedings of the Third Conference on Causal Learning and Reasoning, volume 236 of Proceedings of Machine Learning Research, pages 160- 187. PMLR, Apr 2024. holp:ttttt::/proceddngg mlr. prw.sprsssssee. v236//v26//////// geiger24a. html
Mor Geva, Richard Schuster, Jonathan Berant, and Omer Levy. Transformer feed-forward layers are key-value memories. arXiv preprint 1eXXi:20/22.49//3 2020. URI ptatttss://rrxx /ttpxx/.ivv//////////eae//aaaal/ org/ abs/ 2012. 14913
10

---

M. Hanna, O. Liu, and A. Variengien. How does gpt-2 compute greater-than?: Interpreting mathe- matical abilities in a pre-trained language model. Advances in Neural Information Processing Systems, volume 36. NeurIPS, 2024a.
M. Hanna, S. Pezzelle, and Y. Belinkov. Have faith in faithfulness: Going beyond circuit overlap when finding model mechanisms. arXiv preprint arXiv:2403. 2024b. URL https:// arxiv. wwg.ass///////aaoooo/...os..ssa/ 22/3
Zhaozhi He, Xinyuan Ge. Qixun Tang, et al. Dictionary learning improves patch-free circuit discovery in mechanistic interpretability: A case study on othello-gpt. arXiv preprint arXiv:2402. 12201,
2024.
Xinyan Jiang, Lin Zhang, Jiayi Zhang, Qingsong Yang. Guimin Hu, Di Wang, and Lijie Hu. Msrs: Adaptive multi- sulti-su representation steering for attribute alignment in large language models. arXiv preprint arXiv:2508. 10599, 2025.
Tong Li, Shu Yang, Junchao Wu, Jiyao Wei, Lijie Hu, Mengdi Li, Derek Wong, Joshua R. Oltmanns, and Di Wang. Can large language models identify implicit suicidal ideation? an empirical evaluation, 2025. URL https: /ttp://:////vvvvveae wwtp://///b/////////
17899
Lieberum, M. Rahtz, J. Kramár, et al. Does circuit analysis interpretability scale? evidence from multiple choice capabilities in chinchilla. arXiv preprint arXiv:2307.09458, 2023. URL
https://arxiv. wwwg/a/////.....00 09458
S. Marks, C. Rager, E. J. Michaud, et al. Sparse feature circuits: Discovering and editing interpretable causal graphs language models. arXiv preprint arXhv:2403.196// 2024. URL htttps://arxi: org/ abs/ 2403. 19647
K. Meng, D. Bau, A. Andonian, et al. Locating and editing factual associations in gpt. In Advances in Neural Information Processing Systems, volume 35, pages 17359-17372. NeurIPS, 2022.
Merullo, C. Eickhoff, and E. Pavlick. Circuit component reuse across tasks transformer language models. In Proceedings of the Twelfth International Conference on Learning Representations. OpenReview.net, 2024.
John Miller, Bilal Chughtai, and William Saunders. Transformer circuit faithfulness metrics are not robust, arXiv preprint arXiv:2407.08734. 2024.
Nainani. Evaluating brain-inspired modular training in automated circuit discovery for mechanistic interpretability. arXiv preprint 2xXiv:2401003644 2024. URL /tRLl/tttee///xxx..oor/a/bbb///
036666
Neel Nanda. Mechanistic interpretability quickstart guide. Neel Nanda's Blog, January 2023. Accessed: 2023-01-26.
C. Olah, N. Cammarata, L. Schubert, et al. Zoom in: An introduction circuits. Distill, 5(3): c00024.001, 2020.
Chris Olah. Mechanistic interpretabilitty. variables, and the importance of interpretable bases. https
// //www /twp.ttaanst....oot//tt/t.t www.srranrrooooo wrrraasfoomrr-crruutttsesseeoe wwt..ruiit...pub//////eeeeeeee http:////w/mncniiieeoeeeeeee essay 2022.
C. O' O'Neill and Bui. Sparse autoencoders enable scalable and reliable circuit identification in language models. arXiv preprint arXiv:2405.12552, 2024. URL https://arxiv org/aba/ 2405. 12522
N. Prakash, T. R. Shaham, T. Haklay, et al. Fine-tuning enhances existing mechanisms: case study entity tracking. arXiv preprint 248. 2024. /ttpp: 2402.
Pascal Sturmfels, Scott Lundberg, and Su-In Lee. Visualizing the impact of feature attribution baselines. Distill, 5(1):e22, 2020. doi: 10.23995//istill.0002..
Yi Su, Jiayi Zhang, Shu Yang, Xinhai Wang, Lijie Hu, and Di Wang. Understanding how value neurons shape the generation of specified values in 1lms. arXiv preprint arXiv:2505.17712 2025.

---

Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic attribution for deep networks. In Proceedings of the International Conference on Machine Learning, volume 70, pages 3319-3328. PM 2017.
A. Syed, C. Rager, and A. Conmy, Attribution patching outperforms automated circuit discovery. arXiv preprint 2tt::2331.11344.. 2023.
http://aaxxvv....aaba/ abs///as/// /aabs///1.... 10348
Rohan Taori, Ishaan Gulrajani, Tianyi Zhang, Yann Dubois, Xuechen Li, Carlos Guestrin, Percy Liang, and Tatsunori B. Hashimoto. Stanford alpaca: An instruction-follovin Ilama model. 2023.
C. Tigges, O. J. Hollinsworth, A. Geiger, al. Linear representations of sentiment in large language models. arXiv preprint arXiv:2310.155::1 2023. URLpttts://axxx org/ 2210. 15154
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in Neural Information Processing Systems, volume 30, 2017.
Jesse Vig, Sebastian Gehrmann, Yonatan Belinkov, Sharon Qian, Daniel Nevo, Yaron Singer, and Stuart Shieber. Investigating gender bias in language models using causal mediation analysis. In Hugo Larochelle, Marc' Aurelio Ranzato, Raia Hadsell, Maria-Flonin editors, Proceedings of the 33rd Advances in Neural Information Processing Systems (NeurIPS), volume 33, pages 2338 2401. Curran Associates, Inc., 2020. URL URL.stps::/proceddnggg http://c...ppp.../..../////6222/
Balcan, and Aesuan-Tien Lin,
Kevin Ro Wang, Alexandre Variengien, Arthur Conmy, Buck Shlegeris, and Jacob Steinhardt. Interpretability in the wild: A circuit for indirect object identification in gpt-2 small. In International
Conference on Learning Representations, 2023. URL httppss//opprreeieeee wwwpeeewwwwwwwwwefooeoeeeeeeeeee net//frummidi NpsVSS604ul
Keyu Wang, Jin Li, Shu Yang, Zhuoran Zhang, and Di Wang. When truth is overridden: Uncovering the internal origins of sycophancy in large language models. arXiv preprint 27X0072508.02087, 2025a.
Liangyu Wang. Jie Ren, Hang Xu, Junxiao Wang, Huanyi Xie, David E Keyes, and Di Wang. Zo2: Scalable zeroth-order fine-tuning for extremely large language models with limited gpu memory. arXiv preprint arXiv:2503. /2668, 2025b.
Z. Wu, A. Geiger, T. Icard, et al. Interpretability at scale: Identifying causal mechanisms in alpaca. In Advances in Neural Information Processing Systems (NeurIPS), volume 36, 2024.
Shu Yang. Junchao Wu, Xin Chen, Yunze Xiao, Xinyi Yang. Derek F Wong, and Di Wang. Un- derstanding aha moments: from external observations to internal mechanisms. arXiv preprint arXiv:2504.02956. 2025a.
Shu Yang, Shenzhe Zhu, Zeyu WI, Keyu Wang, Junchi Yao, Junchao Wu, Lijie Hu, Mengdi Li, Derek Wong, and Di Wang. Fraud-rl: A multi-round benchmark for assessing the robustness of LLM against augmented fraud and phishing inducements. In Wanxiang Che, Joyce Nabende, Ekaterina Shutova, and Mohammad Taher Pilehvar, editors, Findings of the Association for Computational Linguistics: ACL 2025, pages 4374 4420, Vienna, Austria, July 2025b. Association for Computational Linguistics. ISBN
doi: 10.18653/v1/2025. findiigs-idnndnn acl.226. URL https://aclantholooyy org 2025 findings----ii acc..266
Junchi Yao. Jianhua Xu, Tianyu Xin, Ziyi Wang, Shenzhe Zhu, Shu Yang, and Di Wang. Is your Ilmeb multi-agent a reliable worl-world planner? exploring fraud detection in travel planning. arXiv preprint arXiv:2505.165:: 2025a.
Junchi Yao, Shu Yang, Jianhua Xu, Lijie Hu, Mengdi Li, and Di Wang. Understanding the repeat curse in large language models from a feature perspective. arXiv preprint S50V:2504.142.8, 2025b.
Jiayi Zhang, Shu Yang, Junchao Wu, Derek F. Wong, and Di Wang. Understanding and mitigating political stance cross-topic generalization in large language models, 2025a. URL htt.::ttts///t... //axxiv org/abs. at/////bb///...////// /508 02360
12

---

Lin Zhang, Lijie Hu, and Di Wang. Mechanistic unveiling of transformer circuits: Self-influence as key to model reasoning. arXiv preprint arXiv:2502.09022, 2025b.
Zhuoran Zhang, Yongxiang Li, Zijian Kan, Keyuan Cheng, Lijie Hu, and Di Wang. Locate-then-edii for multi-hop factual recall under knowledge editing. arXiv preprini arXiv:2410006331, 2024.
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A Appendix
A.1 Datasets
2023) involves inputs such as: "When Amy and Laura got snack the house, Laura decided to give it to"; where models are expected to predict "Amy". Predictions are evaluated using logit difference (logit diff), computed as the logit of "Amy" minus the logit of "Laura". Corrupted inputs replace the second occurrence of "Laura" with a third name (e.g., "Nicholas"). " making "Laura" and "Amy" roughly equiprobable. We generate dataset using Wang al. (2023) 's dataset generator.
Indirect Object Identification (ION): The IOI task ( (Wang et al.
The Gender-Bias task is designed to examine gender bias in language models. provides inputs such as "The banker wished that", where biased models tend to complete the sentence with "he". Bias is measured using logit difference (logit diff), computed as the logit of "he" minus the logit of "she", or vice versa if the profession is male-stereotyped. Corrupted inputs replace female- strrotyee professions with "man" and male-stereotyped professions with "woman", such as transforming "The banker wished that" into "The woman wished that", prompting the model to generate the opposite pronoun. This task originates from Vig et al. (2020) and was later analyzed in a cireuit-based context by Chintam et al. (2023).
Bias:
Capital-Country: In the Capital-Country task, models receive inputs such as "Port Vila, the capital of",, and are expected output the corresponding country (Vanuatu). Corrupted instances replace the correct capital with another one, such as changing "Port Vila, the capital of"" to "Niamey, the capital of"" Performance is evaluated using the logit difference, defined the logit of the correct country (Vanuatu) minus the logit of the corrupted country (Niger).
Subject- Verb Agreement (SVA): In the Subject- Verb Agreement (SVA) task, models are given sentences such as "The pilot the assistant" and must generate verb that matches the subject's 'ss number (e.g., "is" or "has" for pilot). In corrupted inputs, the subject's number is modified, such as changing "The pilot the assistant" to "The pilot the assistants", causing the model to produce verbs with the opposite agreement. The model's performance is evaluated using probability difference, defined as the probability assigned to verbs that agree with the subject minus the probability assigned to those that do not.
Hypernymy: In the Hypernymy task, models must predict a word's hypernym (or superordinate category) given inputs such as ", second cousins and other", where the correct answer is "relatives". Comrupted inputs replace the target word with an instance from different category, such as changing "second cousins and other"' to "robins and other". Model performance is evaluated using probability difference, defined as the probability assigned to the correct hypernyms minus the probability assigned to incorrect ones.
Greater-Thant In the Greater-Than task, models receive a sentence containing chronological sequence of years as input and must predict the next year that follows the pattern. Given a clean input, such as "The contract lasted from the year 1352 the year 13", the expected completion is the next valid number in the sequence. Corrupted inputs replace the last number with an incorrect continuation that disrupts the numerical pattern, such as "The contract lasted from the year 1301 to the year 13". Model performance is evaluated using probability difference (prob diff), defined as the probability assigned to the correct next number minus the probability assigned the incorrect one (e.g., "52" in the example above).
Each dataset consists of both positive and negative examples. Positive examples require the model to utilize specific circuits to predict the correct next token, whereas negative examples are semantically similar but intentionally corrupted to ensure that no valid next token exists. This design enables us to distinguish attention heads involved in semantic processing from those responsible for circuit-specific computations. To ensure fair comparisons, the number of positive and negative examples in each dataset is kept consistent with (Hanna et al.) (024b)). In this study, positive examples correspond to the original input, while negative examples represent the corrupted input. Table Lable[prowe provides an example of each task. Overall, For 10I, Gender-Bias, and Capital-Country, we also use Logit Difference defined as:
log P(correct) log P(misleading))
(13)
14

---

Table Overview of Tasks and Metrics Used for Each Task. The table presents original and corrupted examples along with the expected output token IDs for six tasks: Indirect Object Identification (IOI), Subject- Verb Agreement (SVA), Gender Bias, Capital-Country, Hypernymy, and Greater-Than. The "Example Prompt" column provides representative original and corrupted inputs for each task.
The "Output" column displays the expected output token ID, and the "Metric" column specifies the evaluation metric used for the corresponding task.
TASK
EXAMPLE PROMPT
OUTPUT
METRIC
101
"WHEN AMY AND LAURA GOT SNACK THE HOUSE, LAURA DECIDED TO GIVE TO"
"14235" "16753"
LOGIT ENCE
DIFFER-
"WHEN AMY AND LAURA GOT SNACK AT THE HOUSE, NICHOLAS DECIDED TO GIVE IT TO"
SVA
"THE SONG THAT THE CHEF LIKES" "THE SONGS THAT THE CHEF LIKES"
"0"
PROBABILITY DIFFERENCE
"0"
GENDER-BIAS
"THE POET WAS PROMOTED BECAUSE"
"673"
LOGIT DIFFER-
"THE MAN WAS PROMOTED BECAUSE"
"339"
ENCE
HYPERNYMY
GEMSTONES AND OTHER" VICE PRESIDENTS AND OTHER"
"[16840,
PROBABILITY
23685]"
DIFFERENCE
"[7018,
7602]
CAPITAL-COUNTRY
"KABUL, THE CAPITAL OF "LONDON, THE CAPITAL OF"
"8037"
LOGIT DIFFER
"1578"
ENCE
GREATER HHEATER-THAN
"THE CONTRACT LASTED FROM THE YEAR
"52"
PROBABILITY
1352 TO THE YEAR 13"
"52"
DIFFERENCE
"THE CONTRACT LASTED FROM THE YEAR 1301 TO THE YEAR 13"
which measures the difference in log probabilities between the correct and misleading name/pronoun. For SVA, Greater- Than, and Hypernymy, we use Probability Difference, defined as:
Σ P(ycomea)) - Σ P(lincorrea),
(14)
which compares the probability of the correct answer with the sum of the probabilities of incorrect answers.
Table 2: Original and Corrupted Baseline Performance of GPT-2 small across tasks, Clean Baseline
refers to 64, while the Corrupted Baseline refers to 8_.
Task
Metric Clean Baseline
Corrupted Baseline
IOI
logit diff
3.80
0.03
SVA
prob diff
0.154
-0.157
Gender-Bias
logit diff
0.88
-3.22
Hypernymy
prob diff
23,43
-3,482
Supital-Countyy
logit diff
0.25
-0.28
Greater- Than
prob diff
0.814
-0,456
A.2 More results
In this section, we also test the runtime of the three methods on the 1OI and Greater- Treater-Thhn datasets with 97.5% edge sparsity (see Table 3). EAP-GP is approximately five times slower than EAP- IG. However, this is not only due to the & forward and backward passes over the data but also because constructing the intermediate points of the integration path requires an additional forward and backward pass over the activations, further contributing the overall runtime.
15

---

Table 3: Comparison of different methods' performance based 97.5% sparsity. NES represents the Normalized Faithfulness Score, and Times represents the computation time for different methods. A higher Normalized Faithfulness Score and shorter computation time indicate better performance.
Method
Sparsity (%)
I0I
Sreater-Than
NFS( %)) 1
Time (8) +
NFS ()5(%) t
Time (s) &
EAP
97.5 0.01
56.9
12.6
96.3
11.7
EAP-IG
0..01
62.4
49.7
97.6
44.3
EAP-GP
97.5 + 0.01
80.1
232.5
99.8
210.7
101
Greater-Than
Gender-Biae
EARNG
DAN-C D4P-2F
EAP42
EAP-CP
07.0 27.5
96.3
80.
56. 110
21.0
972
563
535 1953
Edge Sparaity (%)
Edge Sparaity 1%)
Edge Spansty (5)
SVA
Country-Captall
Hypemymy
100
Marhed
Mixiad CAP
Marthd
22.
20.3
80.
00.5
212
Figure 5: Comparison of circuit performance across different methods on GPT-2 Medium. In all plots, a higher value indicates better performance. EAP-GP identifies circuits that outperform other methods across all six tasks.
also perform experiments GPT-2 Medium (345M) (see Figure and GPT-2 XL (1.SB) (sec Figure(6) across six tasks and report the faithfulness the identified circuits. Our results on both GPT- 2 Medium and GPT-2 XL confirm our earlier findings. In both models, when there are discernible differences the faithfulness of the identified circuits, EAP-GP outperforms both EAP and EAP-IG.
Additionally, we present example circuit diagrams of the circuits found by EAP-GP. However, these come with one caveat: the typical circuits we found still contained too many edges to be displayed in reasonably sized figure. Therefore, we only provide visualizations for the Greater-Thee task with 99. 99.9% sparsity (such those reported in Figure 7).
16

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Table 4: Normalized faithfulness for Six Tasks in GPT2-Small.
Task
Edge Sparsity (%)
EAP (%)
EAP-IG (%)
EAP-GP (%)
99.30%
0.03%
25.53%
29.18%
99.00%
0.05%
42.51%
41.05%
98.70%
35.41% %
45.10%
44.76%
98.40%
53.05%
49.68%
59.93%
98.10%
50.21%
65.12%
65.23%
I01
97.80%
47.56%
66.18%
73.52%
97.50%
56.94%
62.47%
80.08%
99.30%
0.00%
5.79%
9.97%
99.00%
0.00%
13.83%
36.66%
98.70%
21.54%
46.95%
69.77%
98.40%
34.41%
72.03%
82.64%
98.10%
47.59%
80.06%
91.32%
SVA
97.80%
72.03%
84.57%
95.50%
97.50%
75.88%
84.57%
96.14%
99.30%
55.57%
70.06%
68.76%
99.00%
80.00%
73.91 %
78.91%
98.70%
84.91%
85.00%
88.44%
98.40%
79.61%
88.76%
90.10%
18%
81.76%
90.47%
90.73%
Gender-Bias
97.80%
89.54%
90.88%
91.17%
97.50%
90.05%
90.95%
91 .1.%
99.30%
-0.37%
52.89%
65.36%
99.00%
13.22%
75.42%
82.50%
98.70%
21.23%
82.31%
90.32%
98.40%
30.35%
86.41%
91.62%
98.10%
35.57%
90.50%
90.32%
Country-Capite
97.80%
57.54%
91.43%
91.81%
97.50%
60.52%
91.62%
93.67%
99.30%
7.41%
10.11%
14.01%
99.00%
10.30%
17.26%
24.32%
98.70%
17.11%
29.28%
38.27%
98.40%
29.57%
38.57%
46.22%
98.10%
35.51%
47.27%
54.93%
Hypemymy
97.80%
40.31%
53.07%
59.48%
97.50%
45.58%
55.62%
67.24%
99.30%
70.24%
81.89%
85.83%
99.00%
92.52%
95.35%
94.88%
98.70%
94.41%
98.43%
97. 97.95%
98.40%
95.43%
98.03%
98.989
98.10%
95.12%
98.66%
99.69%
Greater-Than
97.80%
95.98%
100.00%
99.53%
97.50%
96.38%
99.45%
98.98%
17

---

Table 5: Normalized faithfulness for Six Tasks in GPT2-Medium.
Task
Edge Sparsity (%)
EAP (%)
EAP-IG (%)
EAP-GP (%)
98.38%
46.71%
60.03%
64.75%
97.98%
57.24%
62.95%
70.04%
97.58%
62.44%
69.54%
72.94%
97.19%
65.75%
75.52%
76.83%
I0I
96.79%
70.70%
77.67%
78.03%
99.17%
82.11%
91.05%
93.37%
98.77%
89.52%
94.33%
98.19%
98.38%
94.56%
96.08%
98.81%
97.98%
95.40%
97.09%
99.09%
97.58%
96.16%
98.82%
98.40%
SVA
97.19%
96.26%
99.00%
98.73%
96.79%
96.62%
99.14%
98.89%
99.
77.20%
80. 10.17%
83.28%
98.77%
77.63%
81.86%
85.46%
98.38%
81.46%
86.47%
88.69%
97.98%
85.61%
90.92%
90.74%
97.58%
88.74%
91.42%
92.85%
Cender-Bias
97.19%
90.87%
94.11% %
95.52%
96.79%
94.62%
98.30%
97.82%
99.17%
42.73%
71.34%
75.24%
98.77%
54.78%
75.72%
78.88%
98.38%
62.91%
78.74%
84.78%
97.98%
71.47%
81.36%
85.25%
97.58%
75.52%
84.19%
87.35%
Country-Capital
97.19%
79.23%
85.58%
87.76%
96.79%
80.45%
86.16%
88.16%
99.17%
33.42%
42.16%
54.82%
98.77%
41.45%
52.54%
64.08%
98.38%
51.24%
59.53%
72.10%
97.98%
56.07%
65.81% %
76.61%
97.58%
61.14%
69.87%
79.55%
Hypernymy
97.19%
64.88%
74.83%
82.08%
96.79%
68.53%
77.98%
87.02%
99.17%
79.90%
83.23%
87.96%
98.77%
82.99%
87.50%
91.78%
98.38%
84.00%
89.47%
94.71%
97.98%
89.84%
91.60%
95.15%
97.58%
91.63%
93.96%
97.90%
Greater-Ther Than
97.19%
97.64%
92.85%
99.19%
96.79%
96.68%
95.76%
99.16%
18

---

Table 6: Normalized faithfulness for Six Tasks in GPT2-XL.
Task
Edge Sparsity (%)
EAP (%)
EAP-IG (%)
EAP-GP (%)
99.19%
55.63%
60.02%
61.43%
98.79%
64.71%
69.69%
68.59%
98.39%
73.07%
74.77%
74.51%
97.99%
78.55%
77.99%
80.24%
97.59%
82.27%
81.33%
82.97%
IOI
97.19%
83.91%
84.90%
86.08%
96.79%
85.20%
85.52%
88.14%
99.20%
90.17%
93.69%
96.22%
98.80%
94.28%
96.27%
98.00%
98.40%
96.30%
97.73%
98.30%
98.00%
97.10%
98.66%
98.25%
97.60%
97.53%
98.97%
98.57%
SVA
97.20%
98.01%
99.18%
98.75%
96.80%
98.38%
99.39%
99.06%
98.80%
98.26%
98.96%
99.58%
98.40%
98.85%
99.36%
99.91%
98.00%
99.25%
99.63%
100%
97.60%
99.67%
100%
100%
97.20%
99.67%
100%
100%
Gender-Bind Bias
96.80%
99.58%
100%
100%
99.20%
43.96%
74.92%
83.46%
98.80%
60.10%
81.29%
86.78%
98.40%
72.07%
85.23%
89.97%
98.00%
78.09%
88.18%
91.28%
97.60%
80.66%
89.28%
92.42%
Country-Capital
97.20%
85.00%
90.91% %
93.49%
96.80%
87.06%
92.03%
94.17%
99.20%
55.16%0 16.1
60.54%
74.73%
98.80%
68.55%
73.93%
84.02%
98.40%
76.64%
82.15%
88.42%
98.00%
82.60%
86.41 %
91.24%
97.60%
86.50%
88.67%
93.61%
Hypernymy
97.20%
88. 79%
90.94%
95.23%
96.80%
90.71%
92.79%
95.92%
98.80%
97.96%
98.15%
98.68%
98.40%
98.30%
98.75%
98.91%
98.00%
98.15%
98.74%
99.08%
97.60%
98.47%
98.61%
99.11%
97.20%
98.53%
98.75%
99.13%
Greater-Thar
96.80%
99.31%
98.89%
99.45%
19

---

Greater
Gender
$6.0
$8.5
1300
Mechal
CAP-GP
SAP-1
EAP-07
EAP-1
875
ZAP-O
CAP-3P
07.
902
Edgg Spansity (S)
Edge Spansty (7))
Edge Spannity (%)
SVA
Country- Capital
Hypemymy
Method
CAP
EAP
ZA0
Edge Spanstty
Edge Spanity
Edge Spansit (%)
Figure 6: Comparison of circuit performance across different methods on GPT-2 XL. In all plots, higher value indicates better performance. EAP-GP identifies circuits that outperform other methods across all six tasks.
Ext
Issai
aValo1V)
hight
Figure A circuit for Greater-Then with 99.9% sparsity, found by EAP-GP.
20

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Reviews:
[{"review_id": "fhucZZThny", "reviewer": "Reviewer_pkLe", "summary": "This paper concerns methods for circuit discovery, that is, finding the minimal, complete and faithful subgraph of the NN's computational graph which is sufficient to perform the task. It identifies a shortcoming of the existing most popular method: EAP-IG. EAP-IG computes the gradient with respect to computational graph components, at various points in the straight line between activations at the clean input x and at corrupted input x', and uses the gradient's average as the \"attribution score\". Components with the highest attribution score are taken as the relevant subgraph, that is, the circuit.\n\nThe problem is that at many of these intermediate straight-line points, in LLMs, the gradient is saturated to zero. As a result, the attribution scores for many of the subgraph components is too low. The authors propose to instead take gradient descent steps from the clean towards the corrupted input, which has fewer saturation problems. As a result, they are able to improve the faithfulness scores (\"loss recovered\") by 10-17% (depending on the task)", "questions": "The paper should compare with AtP*, which also deals with saturation; explain why it's OK for the line to not be between x and x' and instead be something else, and empirically show that the method works because of why they say it works.\n\n\nAlso:\n- What is the variability between runs in Figures 3 and 4? It is impossible to say if the current method is an improvement if there is a lot of variation based on e.g. random seeds and the exact selection of training points.\n- Are the quantities in Figure 3 evaluated on test datasets? They should be.\n\n\nI'm willing to accept this paper if it satisfactorily addresses all the 5 things above.\n\n## Minor questions\n- Where exactly does the 17.7% figure for the \"improvement up to 17.7%\" in the abstract come from? Is it the largest gap between EAP-GP and the next method in Figure 3?\n- How did you choose the circuit edge for Fig. 1? In L165 it just says \"we analyze a circuit edge\".\n- Presentation tips:\n  - Showing the sparsity in %s close to 100% in Fig. 2 and 3 was confusing to me. I'm used to low % (so the % is the amount of nonzero things) or straight up counting. That way you can also space your datapoints in a log-space.\n  - It would be nice if the caption of Fig. 1 linked to Section 4, which discusses it, since it appears 3 pages later. I was looking for an explanation of the figure in the same and next page and could not find it, leaving me a bit confused.\n  - use \\left( and \\right) in equations like eq. 7 to make the brackets as high as the thing they're bracketing (the fraction)", "limitations": "Not for factual limitations, see my point about a misleading Fig. 1 (and text, which is also misleading) above.\n\nTheir work should be generally of societal positive impact, though it's fairly basic research so the impacts are not near.", "rating": 2, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strength\n\nThe paper addresses an important problem (circuit discovery), makes a correct observation about where the most popular method falls short (saturation of gradients) and makes a nice algorithmic contribution (why bother following the straight line?). It also shows an improvement in the benchmarks. It's well written and easy to understand, and overall a pretty good paper.\n\nEven though the following \"weaknesses\" section is very long, I think this paper is a good idea with a fair execution, so overall it's a decent paper. It's just my job as a reviewer to point out mistakes! Together we can make it a good paper.\n\n# Weaknesses:\n\nThe paper has several weaknesses, which I will now point out. I think they're all addressable, though some of them might require more substantial changes than are doable in one round of rebuttals.\n\n## Figure 1 (right) is misleading: this method does not end up at corrupted x'\n\nOne core thread that has unified all circuit discovery algorithms until now is: we want to check what happens when we move edges from their value on clean activations at original input x, to corrupted activations at x'.\n\nThis paper instead optimizes \\gamma (belonging to NN inputs) using gradient descent on ||Model(\\gamma) - Model(x_corrupted)||_2^2 (eq. 8), and uses the iterates of this optimization to evaluate the gradient of outputs withe respect to circuits. Figure 1 (right) says that this method, which starts at x, ends at x_corrupted: the arrow goes from the original to the corrupted point. The text also says so. However, making Model(\\gamma) = Model(x_corrupted) does NOT guarantee that \\gamma = x_corrupted.\n\nIs it actually sufficient for attribution that we are at an input which is as bad at the behavior as x_corrupted (x')? Perhaps, but this discrepancy should be made explicit and discussed. Figure 1(left) clearly shows that the gradients are *not* the same for x_corrupted (x') and for the found point via EAP-GP: the right-most points have gradient ~2.00 for EAP-GP, and ~0.00 for EAP-IG (which is guaranteed to end up at x').\n\nThis discrepancy needs to be explicitly written down or I cannot in good conscience accept the paper.\n\n## No explicit exploration of whether the method is better due to dealing with saturation, or some other reason\n\nThere's anecdotal evidence in Fig. 1, but nothing systematic. Showing something like the average norm of gradients during the path integration, and comparing between EAP-GP and EAP-IG, would go some way to show that.\n\nYou cannot claim that your method is better because it reduces gradient saturation, without actually showing it empirically. This also needs addressing\n\n## Syed et al.'s benchmark is not representative of modern models.\n\nIn 2023, when people were working on circuit discovery for the first time, it was understandable to use the circuits in GPT-2 small as the targets of the benchmark. Nowadays, however, the models used have changed a lot in size and a little bit in architecture: using rotary embeddings (RoPE) instead of purely learned embeddings, and RMSNorm instead of LayerNorm. There have also been published benchmarks such as the [Mechanistic Interpretability Benchmark, which has a circuit discovery track](https://arxiv.org/abs/2504.13151). Why not use those, and instead stick to the relatively unreliable evaluations from Syed et al?\n\nThis is should ideally be addressed too, but I'm willing to budge on this point.\n\n## Prior art on saturation: AtP* from early 2024\n\nThere is key prior art on dealing with saturated activations, specifically caused because of the softmax on the QK: AtP*, from early 2024 (https://arxiv.org/pdf/2403.00745). See especially Figure 3 in that paper. This present paper does not compare with AtP* at all, even though they also present a method to deal with the saturation.\n\nIn comparison with AtP*, the present paper is more generally applicable because it makes no assumptions about the architecture of the model. But, being applied to transformers, the saturation is almost certainly also because of the softmaxes, so all of the experiments in the paper are in the domain of applicability of AtP*. A comparison between the two methods on how well they deal with saturated inputs is important. Which one should I use? AtP* is fairly computationally cheap, even if you apply it for each intermediate part of the gradient integration. Actually, both methods could be combined because they make incremental improvements.\n\nThis paper needs to compare with AtP*.", "was_revised": true, "final_justification": "I still would like to recommend rejection, due to substantial errors the authors make in the properties of the method they present, poor evaluation, and continued resistance to correcting these two.\n\nSubstantial errors: the authors mistakenly believe that their gradient-descent procedure always ends up at the corrupted point in practice, but that is contradicted by the math and also by the graph in Figure 1 (the gradient should be ~zero at the corrupted point if this was so, but it is high)\n\nPoor evaluation: did not compare with AtP*, an existing method that also try to address gradient saturation, only used a very old and small language model (GPT-2 small was released in 2019, 6 years ago, and is differnet from current models), and the lack of error bars in their evaluation makes it difficult to say that the method improves over things.", "rebuttal": "**Weaknesses:**\n> W1: Figure 1 (right) is misleading: this method does not end up at corrupted x' \n\nA1: Thank you for your careful reading and insightful comments. We agree that Figure 1 is currently misleading, and we appreciate you pointing this out.\n\nIn our actual setup, the start and end points of the integration path are explicitly fixed as the clean input x and the corrupted input x', respectively, to ensure the path lies between them. The intermediate values of $\\gamma$ are computed by minimizing the loss\n$$\n\\|\\text{Model}(\\gamma) - \\text{Model}(x_{\\text{corrupted}})\\|_2^2\n$$\nand are then used for attribution analysis.\n\nTherefore, Figure 1 only includes intermediate points along the integration path, excluding the clean and corrupted inputs themselves. The plotted values represent the gradients at those intermediate points. We will revise Figure 1 to more accurately reflect this setup and include an explicit clarification in the manuscript, as suggested. Thank you again for highlighting this important issue.\n\n> W2: No explicit exploration of whether the method is better due to dealing with saturation, or some other reason\n\nA2: Thank you for raising this important point. We agree that the claim regarding gradient saturation needs empirical support.\n\n|Step|Method|Mean|Method|Mean|\n|-|-|-|-|-|\n|1|EAP-GP|1.949|EAP-IG|1.949|\n|2|EAP-GP|1.294|EAP-IG|0.019|\n|3|EAP-GP|0.467|EAP-IG|0.160|\n|4|EAP-GP|0.225|EAP-IG|0.076|\n|5|EAP-GP|0.123|EAP-IG|0.123|\n\nTo address this, we conducted additional experiments on the IOI task to measure the average gradient norm  of all edges within a selected circuit during attribution. As shown in the supplementary table, EAP-IG tends to follow integration paths that pass through saturated regions, resulting in low gradient magnitudes and less accurate attributions. In contrast, our proposed EAP-GP avoids these saturated areas by adaptively selecting informative paths, leading to higher gradient norms and more faithful circuit discovery.\n\n>W3: Syed et al.'s benchmark is not representative of modern models\n\nA3: Thank you for the insightful suggestion. We recognize the importance of rigorous and representative benchmarks such as the Mechanistic Interpretability Benchmark (MIB). According to the NeurIPS 2025 policy, “For the purpose of the reviewing process, papers that appeared online after March 1st, 2025 will generally be considered 'contemporaneous' in the sense that the submission will not be rejected on the basis of the comparison to contemporaneous work.” Since MIB was released in April 2025, we consider it contemporaneous work for the purposes of this submission.\n\nIn the context of circuit discovery, our primary objective is to approximate both the process and quality of manual circuit identification. Given that both manual and automated approaches rely on shared evaluation metrics (e.g., logit difference), qualitative analysis as exemplified by Syed et al.'s benchmark remains a key tool for assessing alignment.\n\nWhile we acknowledge MIB’s potential as a rigorous evaluation framework, its current implementation supports only a limited set of HuggingFace-compatible models (e.g., Gemma-2 2B, LLaMA-3.1-8B). Our EAP-GP method is built on a custom tracing framework with edge-level hook mechanisms, which are not directly compatible with MIB’s interface. Additionally, intervention-based evaluation on MIB-supported models requires substantial computational resources that exceed our current hardware capacity.\n\nThat said, we fully recognize the value of MIB and plan to gradually adapt our implementation for compatibility with it in future work. We will also incorporate a discussion of this contemporaneous benchmark and its relevance in the final version.\n\n>W4: Prior art on saturation: AtP* from early 2024\n\nA4: Thank you for the suggestion. We respectfully argue that AtP is not a suitable quantitative baseline for EAP-GP, due to the following key differences:\n\n1. **Different Saturation Problems and Solutions:** While both AtP∗ and EAP-GP address saturation effects, they do so in fundamentally different contexts. AtP∗ targets softmax saturation in attention layers and addresses it via QK-Fix, which recomputes attention weights before applying gradient-based approximation. In contrast, EAP-GP tackles gradient saturation along arbitrary edges (including MLPs and cross-layer paths) through gradient projection and rescaling, enabling recovery of deeply embedded causal edges. The saturation types and corrective mechanisms are not comparable.\n\n2. **Granularity Mismatch（Component vs. Edge）：**  AtP∗ provides component-level attribution, assigning importance scores to attention heads or MLP units. EAP-GP, on the other hand, performs edge-level attribution, identifying specific information flows between components. Since our goal is to extract interpretable subgraphs by selecting high-contributing edges, AtP∗ cannot serve as a directly comparable baseline.\n\n3. **No Public Implementation:** As of submission, the full implementation of AtP∗ has not been open-sourced. Although the methodology is described, faithful and efficient reproduction remains challenging. In contrast, all our baselines are fully reproducible, ensuring a fair evaluation framework.\n\nDespite the above, we devoted considerable effort to re-implement AtP∗ based on the paper description and conducted a qualitative comparison on the IOI dataset. The top components identified by AtP∗ are as follows:\n\nTop 10 Attention Heads (contribution score):\n\nLayer 10, Head 7: 0.0424\nLayer 11, Head 10: 0.0359\nLayer 9, Head 9: 0.0219\nLayer 5, Head 5: 0.0147\nLayer 10, Head 0: 0.0116\nLayer 9, Head 6: 0.0110\nLayer 11, Head 2: 0.0069\nLayer 10, Head 10: 0.0067\nLayer 10, Head 6: 0.0060\nLayer 6, Head 9: 0.0049\n\nTop 5 MLP Layers (mean contribution):\n\nLayer 0: 0.0189\nLayer 5: 0.0069\nLayer 10: 0.0069\nLayer 7: 0.0066\nLayer 9: 0.0064\n\nThese components substantially overlap with those identified in the causal circuit recovered by EAP-GP:\ninput, m0, a3.h0, m4, a5.h5, a6.h9, a7.h9, a8.h6, a8.h10, a9.h9, a10.h0, a10.h6, a10.h7, a10.h10, m10, a11.h2, a11.h10, logits\n\nSpecifically, 10 out of AtP∗’s top 10 attention heads (100%) appear in the EAP-GP circuit, and 2 out of the top 5 MLP layers (40%) are also shared.This strong alignment confirms the consistency of the two methods at the component level, while EAP-GP additionally reveals the directed causal structure via fine-grained edge-level attribution.\n\n**Questions:**\n\n>Q1-3:The paper should compare with AtP*, which also deals with saturation; explain why it's OK for the line to not be between x and x' and instead be something else, and empirically show that the method works because of why they say it works.\n\nA5: Thank you for the Question. Please refer to our response to W1-4 for details.\n\n>Q4: What is the variability between runs in Figures 3 and 4? It is impossible to say if the current method is an improvement if there is a lot of variation based on e.g. random seeds and the exact selection of training points.\n\nA6: Thank you for pointing this out. We agree that assessing the variability across runs is essential for evaluating the robustness of our method. We have conducted additional experiments using different random seeds and training samples to assess the variability across runs. The standard deviation of performance across five runs is approximately 3% for IOI, around 3% for SVA and Hypernymy, and about 1% for Gender-Bias, Country-Capital, and Greater-Than. For instance, the following table reports the detailed faithfulness scores on the IOI task:\n\n|EdgeSparsity(%)|EAP(%)|EAP-IG(%)|EAP-GP(%)|\n|-|-|-|-|\n|99.30%|0.03%|25.53%|29.18%±1.2%|\n|99.00%|0.05%|42.51%|41.05%±1.6%|\n|98.70%|35.41%|45.10%|44.76%±1.1%|\n|98.40%|53.05%|49.68%|59.93%±2.6%|\n|98.10%|50.21%|65.12%|65.23%±2.9%|\n|97.80%|47.56%|66.18%|73.52%±3.4%|\n|97.50%|56.94%|62.47%|80.08%±3.1%|\n\nIn the revised version of the paper, we will include error bars in Figures 3 and 4 to reflect this variability and report detailed standard deviations in the appendix to ensure transparency and reproducibility.\n\n>Q5: Are the quantities in Figure 3 evaluated on test datasets? They should be.\n\nA7: Thank you for the question. In our setting, Figure 3 presents the evaluation results on the test datasets.\n\n**Minor questions**\n\n>Q6: Where exactly does the 17.7% figure for the \"improvement up to 17.7%\" in the abstract come from? Is it the largest gap between EAP-GP and the next method in Figure 3?\n\nA8: Yes, the 17.7% improvement refers to the largest performance gap between EAP-GP and the next-best method shown in Figure 3. We also provide the detailed faithfulness scores of the discovered circuits in the appendix for reference.\n\n>Q7: How did you choose the circuit edge for Fig. 1? In L165 it just says \"we analyze a circuit edge\".\n\nA9: Thank you for the question. In Figure 1, We report the average gradient norm of all edges within a selected circuit, rather than focusing on a single edge. We will clarify this in the manuscript to avoid confusion.\n\n>Q8: Showing the sparsity in %s close to 100% in Fig. 2 and 3 was confusing to me. I'm used to low % (so the % is the amount of nonzero things) or straight up counting. That way you can also space your datapoints in a log-space.\n\nA10: Thank you for the suggestion. We will consider using nonzero ratios spacing for the sparsity axis to improve clarity.\n\n>Q9: It would be nice if the caption of Fig. 1 linked to Section 4, which discusses it, since it appears 3 pages later. I was looking for an explanation of the figure in the same and next page and could not find it, leaving me a bit confused.\n\nA11: Thank you for the suggestion. We will revise the Figure 1 caption to reference Section 4 for clarity.\n\n>Q10: use \\left( and \\right) in equations like eq. 7 to make the brackets as high as the thing they're bracketing (the fraction)\n\nA12: Thank you for the suggestion. We will update the equations to use properly sized brackets with \\left and \\right."}, {"review_id": "hlVxa6gi5b", "reviewer": "Reviewer_ptDW", "summary": "This work introduces Edge Attribution Patching with GradPath (EAP-GP), an improvement to an existing circuit discovery algorithm, EAP-IG. This work identifies a problem with EAP-IG (i.e., that integrated gradients pushes the model along a path that may traverse through a region of near-zero gradient) which hinders its attributions to connections between model components, and then introduces a simple solution to that problem. Across several evaluations, EAP-GP outperforms existing methods in both faithfulness and consistency with manually annotated circuits.", "questions": "Why does EAP-GP not still produce performance gains at very high sparsities if these tasks are basically solved by simple feature extraction?\n\nHow ubiquitous is the saturation effect within a model, across models, across tasks?", "limitations": "Limitations are discussed at the end of the results section, but should be put in a limitations section, with a disclaimer that the method is sensitive to hyperparameters", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "The problem that authors identify with EAP-IG is reasonable, as is their solution. Though the method empirically outperforms across a variety of tasks, I am left wondering how ubiquitous the saturation effects are. Section 4 plots only one edge in the IOI task, and could be improved by including similar plots aggregated over all tasks, or more comprehensive discussions of e.g., how many edges face these saturation effects.\n\nAdditionally, further discussion of the greater-than and gender-bias results is warranted. Why does EAP-GP not still produce performance gains at very high sparsities if these tasks are basically solved by simple feature extraction?\n\nWriting: \nThe \"zero-gradients problem\" is introduced early on, but not explicitly defined at that point. This will confuse some readers, so please define.\n\nFinally, limitations are discussed at the end of the results section, but should be put in a limitations section, with a disclaimer that the method is sensitive to hyperparameters", "was_revised": true, "final_justification": "The authors promised the most important revisions/clarifications that I requested during the initial review, and have conducted additional analyses to address my concern regarding the ubiquity of saturation effects.", "rebuttal": ">W1: how ubiquitous the saturation effects are?\n\nA1: Thank you for the Question. Please refer to our response to Q2 for details.\n\n>W2: further discussion of the greater-than and gender-bias results is warranted\n\nA2: Thank you for the Question. Please refer to our response to Q1 for details.\n\n>W3: Writing: The \"zero-gradients problem\" is introduced early on, but not explicitly defined at that point. This will confuse some readers, so please define.\n\nA3: Thank you for the suggestion. We will revise the manuscript to include an explicit definition of the “zero-gradients problem” when it is first introduced, to avoid potential confusion for readers.\n\n>W4: limitations are discussed at the end of the results section, but should be put in a limitations section, with a disclaimer that the method is sensitive to hyperparameters\n\nA4: Thank you for the suggestion. Please refer to our response to L1 for details.\n\n\n\n\n>Q1: Why does EAP-GP not still produce performance gains at very high sparsities if these tasks are basically solved by simple feature extraction?\n\nA5: Thank you for your thoughtful question. We agree that tasks like Greater-Than and Gender-Bias are largely solvable via simple feature extraction mechanisms. As shown in Figure 3 and Table 4 of our paper, the faithfulness scores of all three methods (EAP, EAP-IG, EAP-GP) are indeed relatively close under high sparsity regimes in these tasks. However, there are a few important considerations explaining why EAP-GP does not yield further substantial gains in such cases:\n\n**Ceiling Effect due to Task Simplicity:** These tasks involve relatively shallow reasoning and are dominated by localized features (e.g., profession-to-pronoun or numeric increments). Consequently, even a small number of edges are sufficient to recover most of the task-relevant signal. Thus, all methods tend to converge to similarly high faithfulness scores under high sparsity, leaving limited headroom for improvement.\n\n**Circuit Saturation vs. Attribution Saturation:** EAP-GP is designed to mitigate saturation effects in attribution scores, not to discover more complex circuits where none are needed. In tasks that do not require long-range or compositional reasoning, even naive edge selection strategies may yield circuits that already match the model's behavior well. Hence, while EAP-GP still helps ensure robustness, its advantage becomes less pronounced.\n\n**Sensitivity to Sparsity Thresholds:** At extremely high sparsity (e.g., >99.5%), all methods can become sensitive to small attribution variations, as shown in Figure 2. EAP-GP’s step size dynamics (see Section 6.2) may also amplify noise due to gradient instability near the baseline, which can slightly hurt performance compared to moderate sparsity.\n\nIn summary, the marginal gains of EAP-GP in simple tasks under high sparsity are bounded not by its capability, but by the simplicity of the task structure itself. We believe this aligns with the broader finding that gradient saturation effects are more critical in complex tasks such as IOI and Hypernymy, where EAP-GP shows the most substantial improvements.\n\n\n\n\n>Q2: How ubiquitous is the saturation effect within a model, across models, across tasks?\n\nA6: We thank the reviewer for raising this important point regarding the generality of saturation effects. Our investigation reveals that the saturation effect is a widespread and recurring phenomenon, as detailed below:\n\n**Within a Model:** As shown in Figure 1 and Section 4, we observe saturation effects on edge gradients even within a single circuit in the IOI task. Specifically, the straight-line path used by EAP-IG frequently traverses regions where the gradient of the loss ∂L/∂x becomes nearly zero. These regions occur at both the start and end of the interpolation path, regardless of the specific edge being evaluated. This indicates that saturation is not limited to individual edges but affects broad regions of the activation space.\n\n\n| Step | Method  | Mean    | Method  | Mean   |\n|------|---------|---------|---------|--------|\n|   1  | EAP-GP  | 1.949   | EAP-IG  | 1.949  |\n|   2  | EAP-GP  | 1.294   | EAP-IG  | 0.019  |\n|   3  | EAP-GP  | 0.467   | EAP-IG  | 0.160  |\n|   4  | EAP-GP  | 0.225   | EAP-IG  | 0.076  |\n|   5  | EAP-GP  | 0.123   | EAP-IG  | 0.123  |\n\nTo address this, we conducted additional experiments on the IOI task to measure the average gradient norm across all circuit edges during attribution. As shown in the supplementary table, EAP-IG tends to follow integration paths that pass through saturated regions, resulting in low gradient magnitudes and less accurate attributions. In contrast, our proposed EAP-GP avoids these saturated areas by adaptively selecting informative paths, leading to higher gradient norms and more faithful circuit discovery.\n\n**Across Tasks:** Figure 3 and Table 4 show that saturation effects are especially detrimental in complex reasoning tasks such as IOI, Hypernymy, and SVA. In these tasks, EAP-IG shows a noticeable drop in faithfulness compared to EAP-GP as sparsity increases, suggesting that saturation limits its ability to select faithful edges. In contrast, in simpler tasks like Greater-Than and Gender-Bias, where feature extraction is more direct, the saturation effect has less impact—but is still measurable (e.g., Table 4 shows 1–2% gains by EAP-GP at 99% sparsity).\n\n**Across Models:** As shown in Figures 5 and 6 (Appendix A.2), the saturation effect persists across GPT-2 Small, Medium, and XL. In particular, EAP-GP consistently outperforms EAP-IG across all model sizes, demonstrating that the issue is not alleviated by larger capacity or more parameters. In fact, larger models often exhibit more pronounced saturation due to their increased nonlinearity and overparameterization, further motivating the need for path-aware methods like EAP-GP.\n\nIn conclusion, saturation is a general and systematic problem that arises across architectures, tasks, and layers. Our method mitigates this problem by dynamically adjusting the gradient path to avoid such regions, which proves effective and robust in a variety of experimental settings.\n\n\n>L1:Limitations are discussed at the end of the results section, but should be put in a limitations section, with a disclaimer that the method is sensitive to hyperparameters\n\nA7: Thank you for the suggestion. We agree that the paper would benefit from a clearer presentation of its limitations. To address this, we will move the current limitations discussion from the end of Section 6.2 into a new section titled Limitations and Future Work. This section will also mention that EAP-GP is somewhat sensitive to its main hyperparameter k, which controls the number of integration steps."}, {"review_id": "ux3KUsSLaZ", "reviewer": "Reviewer_vD2V", "summary": "This paper presents an improvement to the gradient-based automatic circuit discovery method EAP and its follow-up, EAP-IG. These methods identify limitations in prior gradient-based approaches to circuit discovery. In particular, such methods compute an edge's importance by multiplying the gradient with the change in activation, and, therefore, EAP suffers from the zero-gradient problem: when the gradient approaches zero, the importance score also approaches zero, regardless of the actual significance of the edge. EAP-IG was proposed to mitigate this issue by using integrated gradients and achieved some improvements. However, it remains affected by gradient saturation: if the corrupted input enters a \"saturation zone,\" the gradient again becomes nearly zero.\n\nThe authors proposed GradPath to mitigate this issue. EAP-IG can be seen as applying a \"big jump\" along a straight line, which may lead the method into a saturation region, resulting in a small gradient. Instead of integrating in one step, the authors' method iteratively follows the steepest steps one at a time, producing a \"GradPath\" that mitigates the saturation effect. As a result, EAP-GP achieves better performance than both EAP and EAP-IG.", "questions": "- What do you think the better performance of EAP-GP can bring for the interpretability community?\n\n- Can any misconceptions be refuted, or previously overlooked points revealed, based on the improved performance? You do not need to do new experiments, but please pointing out some possible directions.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Overall, this paper presents a novel and effective improvement to gradient-based automatic circuit discovery methods, offering a useful mitigation strategy for the saturation effect. The main limitation is that it does not provide any new insights into the interpretation of LMs, which should be the primary goal of circuit discovery. This is concerning, as such work risks turning automatic circuit discovery into a leaderboard benchmarking task, drifting away from its original purpose: understanding the internal workings of LLMs. Nonetheless, this work provides a new tool to the community that shows promise as a generalisable approach. I believe it can support further research and help others develop more effective interpretations in the future.\n\nStrength\n- This paper is very well written. The presentation of the paper is clear and easy to follow. \n- The authors identify that the saturation effect for EAP-IG, which suggests that a less severe version of the zero gradient problem also exists for EAP-IG.\n- This work presents solid performance-based evaluation and showcased the state-of-the-art performance.\nWeakness\n- Although this work concerns interpretability, the paper does not offer new insights into the interpretation of the LM. This is acceptable for the this work, but it would still be beneficial to include at least a discussion of the interpretability aspect. The paper would be significantly stronger if the authors could use EAP-GP's new, improved result to refute previous misconceptions or reveal previously overlooked points caused by the limitation of EAP or EAP-IG.", "was_revised": true, "final_justification": "Thanks for the response. I am satisfied with the elaboration. Please incorporate them in the updated draft. I will maintain my positive assessment.", "rebuttal": ">Q1: What do you think the better performance of EAP-GP can bring for the interpretability community?\n\nA1: Thank you for the constructive question. We believe the improved performance of EAP-GP has several important implications for the interpretability community:\n\n**More Reliable Circuits Under Sparsity Constraints:** EAP-GP consistently discovers more faithful circuits under high sparsity levels (see Table 4), particularly in complex reasoning tasks. This enables researchers to analyze much smaller subgraphs without sacrificing interpretability fidelity, which is critical for scaling interpretability to larger models.\n\n**Recognizing Saturation as a General Challenge:** By identifying and addressing saturation effects, EAP-GP highlights a previously under-discussed failure mode in mechanistic interpretability methods. While saturation has been noted in other contexts, to our knowledge, this is the first work to explicitly observe and address it within circuit discovery. This finding may prompt a broader re-examination of gradient-based attribution tools used throughout mechanistic interpretability.\n\n**Towards Path-Adaptive Attribution Methods**    EAP-GP offers a new perspective on attribution by introducing a general design principle: adapting the integration path to the model’s local gradient landscape. This perspective encourages future research into dynamic, model-aware attribution strategies that are better equipped to handle common issues such as saturation and vanishing gradients.\n\n\n> Q2: Can any misconceptions be refuted, or previously overlooked points revealed, based on the improved performance? You do not need to do new experiments, but please pointing out some possible directions.\n\n\nA4: Thank you for the insightful suggestion. We conducted a qualitative comparison of the circuits discovered by EAP, EAP-IG, and EAP-GP on the IOI task. Below are representative circuits extracted by each method. \n\n**EAP:** input-&gt;a0.h1&lt;v&gt;,input-&gt;m0,a0.h1-&gt;m0,a0.h1-&gt;m1,m0-&gt;m1,a0.h1-&gt;m2,m0-&gt;m2,m1-&gt;m2,m0-&gt;m3,m2-&gt;m3,m1-&gt;a6.h9&lt;v&gt;,a0.h1-&gt;a7.h10&lt;v&gt;,m0-&gt;a7.h10&lt;v&gt;,m2-&gt;a7.h10&lt;v&gt;,m0-&gt;a8.h8&lt;v&gt;,m0-&gt;a8.h11&lt;v&gt;,a6.h9-&gt;m8,a7.h10-&gt;m8,a8.h8-&gt;m8,a8.h11-&gt;m8,a0.h1-&gt;a9.h1&lt;v&gt;,m0-&gt;a9.h1&lt;v&gt;,m1-&gt;a9.h1&lt;v&gt;,m2-&gt;a9.h1&lt;v&gt;,m3-&gt;a9.h1&lt;v&gt;,a7.h10-&gt;m9,a8.h11-&gt;m9,m8-&gt;m9,a9.h1-&gt;m9,m0-&gt;a10.h7&lt;v&gt;,a7.h10-&gt;m10,a8.h11-&gt;m10,m8-&gt;m10,a9.h1-&gt;m10,m9-&gt;m10,m8-&gt;m11,m9-&gt;m11,m10-&gt;m11,m8-&gt;logits,a9.h1-&gt;logits,m9-&gt;logits,a10.h7-&gt;logits,m10-&gt;logits,m11-&gt;logits\n\n\n**EAP-IG:** input-&gt;a0.h1&lt;v&gt;,input-&gt;a0.h10&lt;v&gt;,input-&gt;m0,a0.h1-&gt;m0,a0.h10-&gt;m0,m0-&gt;m1,m0-&gt;m2,m1-&gt;m2,m0-&gt;m3,m1-&gt;m3,m0-&gt;a5.h1&lt;v&gt;,m0-&gt;a5.h5&lt;v&gt;,a0.h1-&gt;a6.h9&lt;v&gt;,m0-&gt;a6.h9&lt;v&gt;,m1-&gt;a6.h9&lt;v&gt;,a0.h1-&gt;a7.h10&lt;v&gt;,m0-&gt;a7.h10&lt;v&gt;,m2-&gt;a7.h10&lt;v&gt;,m0-&gt;a8.h8&lt;v&gt;,m0-&gt;a8.h11&lt;v&gt;,a5.h1-&gt;m8,a6.h9-&gt;m8,a7.h10-&gt;m8,a8.h8-&gt;m8,a8.h11-&gt;m8,a0.h1-&gt;a9.h1&lt;v&gt;,m0-&gt;a9.h1&lt;v&gt;,m1-&gt;a9.h1&lt;v&gt;,m2-&gt;a9.h1&lt;v&gt;,m3-&gt;a9.h1&lt;v&gt;,m8-&gt;a9.h1&lt;q&gt;,a5.h5-&gt;m9,a6.h9-&gt;m9,a7.h10-&gt;m9,a8.h11-&gt;m9,m8-&gt;m9,a9.h1-&gt;m9,a6.h9-&gt;m10,a7.h10-&gt;m10,m8-&gt;m10,a9.h1-&gt;m10,m9-&gt;m10,m8-&gt;m11,m9-&gt;m11,m10-&gt;m11,m8-&gt;logits,a9.h1-&gt;logits,m9-&gt;logits,m10-&gt;logits,m11-&gt;logits\n\n\n**EAP-GP:** input-&gt;a0.h1&lt;v&gt;,input-&gt;a0.h10&lt;v&gt;,input-&gt;m0,a0.h1-&gt;m0,a0.h10-&gt;m0,a0.h1-&gt;m1,m0-&gt;m1,m0-&gt;m2,m1-&gt;m2,m0-&gt;a5.h1&lt;v&gt;,m0-&gt;a5.h5&lt;v&gt;,a0.h1-&gt;a6.h9&lt;v&gt;,m0-&gt;a6.h9&lt;v&gt;,m1-&gt;a6.h9&lt;v&gt;,a0.h1-&gt;a7.h10&lt;v&gt;,m0-&gt;a7.h10&lt;v&gt;,m2-&gt;a7.h10&lt;v&gt;,m0-&gt;a8.h8&lt;v&gt;,m0-&gt;a8.h11&lt;v&gt;,a5.h1-&gt;m8,a5.h5-&gt;m8,a6.h9-&gt;m8,a7.h10-&gt;m8,a8.h8-&gt;m8,a8.h11-&gt;m8,a0.h1-&gt;a9.h1&lt;v&gt;,m0-&gt;a9.h1&lt;v&gt;,m1-&gt;a9.h1&lt;v&gt;,m2-&gt;a9.h1&lt;v&gt;,m8-&gt;a9.h1&lt;q&gt;,a5.h5-&gt;m9,a6.h9-&gt;m9,a7.h10-&gt;m9,a8.h11-&gt;m9,m8-&gt;m9,a9.h1-&gt;m9,a6.h9-&gt;m10,a7.h10-&gt;m10,m8-&gt;m10,a9.h1-&gt;m10,m9-&gt;m10,m8-&gt;m11,m9-&gt;m11,m10-&gt;m11,m8-&gt;logits,a9.h1-&gt;logits,m9-&gt;logits,m10-&gt;logits,m11-&gt;logits\n\n\nThe circuits discovered by EAP, EAP-IG, and EAP-GP on the IOI task demonstrate progressively more advanced patterns of information flow and integration. EAP identifies a sparse, mostly linear circuit centered on a single attention head, resulting in limited feature fusion and low redundancy. EAP-IG builds upon this by introducing multiple attention heads and localized modular interactions, enabling richer internal connectivity and the early use of query-based aggregation. EAP-GP further advances these capabilities by leveraging its gradient-guided path integration design to identify attribution paths that avoid saturated or misleading gradients. As a result, it discovers circuits involving a broader set of attention heads across multiple layers, centralizes information through a key convergence node (e.g., m8), and forms deep, multi-branch structures with extensive cross-layer integration. This reflects EAP-GP's ability to uncover more faithful and causally grounded circuits. As a result, the discovered structures exhibit significantly higher structural complexity, redundancy, and robustness. These properties enable the final logits to be influenced by diverse and complementary sources of information."}, {"review_id": "hwdYeCBxYW", "reviewer": "Reviewer_LBjM", "summary": "This work focuses on improving gradient-based circuit discovery techniques that aim to reverse engineer neural networks by analyzing their computational graph. In particular, the authors propose Edge Attribution Patching with GradPath (EAP-GP), which improves over existing techniques such as EAP and EAP-IG by avoiding zones of gradient saturation. The paper reports improvements of up to 17% in circuit faithfulness.", "questions": "Improve motivation of the work: What is the theory of impact for this work? What is the utter goal of having more faithful circuits?\n\nCan we make EAP-GP faster so that it's more competitive against EAP-IG?\n\nAre there any limitations on using manually found ground-truth circuits as a part of a quantitative experiment?\n\nDoes it make sense to do a qualitative analysis of the circuits found by these techniques?", "limitations": "Authors have addressed some limitations in the Experiments section, but I think the paper would benefit from having a dedicated section. As mentioned above in the review, authors should also make explicit that EAP-GP is way more costly than EAP-IG (i.e., there's a tradeoff compute/accuracy between techniques).", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The work seems very relevant for the field of Mechanistic Interpretability: Circuit Discovery techniques are constrained by the quality and cost of the metrics for measuring the importance of each edge/node in the neural network computational graph.\n- EAP-GP seems to be a sound proposal that improves over the state of the art (EAP and EAP-IG)\n- The work includes a solid experimental setup measuring EAP-GP vs EAP and EAP-IG on 6 different tasks and 3 different variants of GPT-2 (small, medium, and XL)\n- The authors also compare the computation time for EAP-GP vs EAP and EAP-IG, which is important to understand the tradeoffs between these techniques\n- Writing is very clear and concise for the most part\n\nWeaknesses:\n- No mention of limitations or future work. Are there any edge cases that might be problematic for EAP-GP? Can we make EAP-GP cheaper to run (since it seems to be ~4x more expensive than EAP-IG)? Etc.\n- Unclear if the ground-truth circuits used for comparison (Syed et al) provide a good signal or not on the quality of the circuits found automatically. I.e., if these ground-truth circuits are not very faithful, then EAP-GP having less precision/recall than EAP-IG might be good.\n- A qualitative analysis of some of the circuits found (e.g., for IOI) would be nice. Does EAP-GP find attention heads or MLPs that are interesting or relevant for the circuit and haven't been analysed before?\n- Unclear what the practical applications of having more faithful circuits for AI Safety are. Also, circuit discovery might not scale to bigger SOTA models.\n\nMinor issues and typos:\n- The main body should reference the compute analysis in Table 3, which seems to suggest that EAP-GP is ~4x more expensive to run than EAP-IG.\n- Maybe rename Section 6 to \"Evaluation\" instead of \"Experiments\"\n- Missing an explicit mention of the AUCs for all methods in the precision-recall curves of Fig. 4. \n- Paper goes back and forth with these terms: baseline input, clean input, corrupted input, original input, . Please choose two and go with them, otherwise is quite confusing for the reader.\n- Faithfulness of circuits is talked about in intro (line 51), way before it's defined in the paper, which is slightly confusing if you don't know before hand what it means.\n- Typo in line 125, should be \"graph\" instead of \"subgraph\". I.e., \"Given a model G, which can be represented as a computational **graph**\"\n- IOI dataset is mentioned for the first time in line 165, without any cite. Please add the cite or reference to the appropriate section where this is explained.\n- Typo in line 211: \"iteratively\" twice in the same sentence.", "was_revised": true, "final_justification": "The authors have compellingly addressed my concerns on the ground-truth circuits used for comparison. They will also improve the final work by further discussing limitations and future work (such as making EAP-GP cheaper to run), and by including qualitative analysis of some of the circuits found (which they already did for the rebuttal). I remain positive about this paper and believe it is a technically solid advance on the field of Mechanistic Interpretability.", "rebuttal": ">W1: No mention of limitations or future work. Are there any edge cases that might be problematic for EAP-GP? Can we make EAP-GP cheaper to run (since it seems to be ~4x more expensive than EAP-IG)? Etc.\n\n\nA1: Thank you for the thoughtful comments. We acknowledge that EAP-GP introduces additional computational cost (∼4× slower than EAP-IG, as shown in Table 3), primarily due to the dynamic construction of model-dependent integration paths. In future work, we plan to explore efficiency improvements such as low-rank approximations, early stopping based on gradient convergence, and path simplification techniques.\n\nAs for limitations, EAP-GP may underperform in cases where gradients near corrupted inputs are highly unstable or noisy—especially in tasks with weak supervision signals. We view this as an opportunity for further robustness improvements, such as incorporating gradient smoothing or hybrid attribution strategies. We will add a dedicated section at the end of the paper to discuss these limitations and future directions.\n\n\n>W2: Unclear if the ground-truth circuits used for comparison (Syed et al) provide a good signal or not on the quality of the circuits found automatically. I.e., if these ground-truth circuits are not very faithful, then EAP-GP having less precision/recall than EAP-IG might be good.\n\n\nA2: Thank you for the insightful suggestion. In the context of circuit discovery, the primary goal of automatic methods is to approximate both the process and the quality of manual circuit discovery. Since both approaches rely on the same evaluation metrics (e.g., logit difference) to identify circuits, it is natural to validate their consistency through qualitative analysis. By qualitatively comparing the circuits discovered by automatic methods with those obtained manually, we can assess whether they capture the same interpretable mechanisms. This offers further evidence that automatic circuit discovery can faithfully reproduce the insights of manual analysis and scale to more complex settings, making it a practical and effective alternative.\n\n\n>W3: A qualitative analysis of some of the circuits found (e.g., for IOI) would be nice. Does EAP-GP find attention heads or MLPs that are interesting or relevant for the circuit and haven't been analysed before?\n\n\nA3:Thank you for the insightful suggestion. We conducted a qualitative comparison of the circuits discovered by EAP, EAP-IG, and EAP-GP on the IOI task. Below are representative circuits extracted by each method. \n\n**EAP:** input-&gt;a0.h1&lt;v&gt;,input-&gt;m0,a0.h1-&gt;m0,a0.h1-&gt;m1,m0-&gt;m1,a0.h1-&gt;m2,m0-&gt;m2,m1-&gt;m2,m0-&gt;m3,m2-&gt;m3,m1-&gt;a6.h9&lt;v&gt;,a0.h1-&gt;a7.h10&lt;v&gt;,m0-&gt;a7.h10&lt;v&gt;,m2-&gt;a7.h10&lt;v&gt;,m0-&gt;a8.h8&lt;v&gt;,m0-&gt;a8.h11&lt;v&gt;,a6.h9-&gt;m8,a7.h10-&gt;m8,a8.h8-&gt;m8,a8.h11-&gt;m8,a0.h1-&gt;a9.h1&lt;v&gt;,m0-&gt;a9.h1&lt;v&gt;,m1-&gt;a9.h1&lt;v&gt;,m2-&gt;a9.h1&lt;v&gt;,m3-&gt;a9.h1&lt;v&gt;,a7.h10-&gt;m9,a8.h11-&gt;m9,m8-&gt;m9,a9.h1-&gt;m9,m0-&gt;a10.h7&lt;v&gt;,a7.h10-&gt;m10,a8.h11-&gt;m10,m8-&gt;m10,a9.h1-&gt;m10,m9-&gt;m10,m8-&gt;m11,m9-&gt;m11,m10-&gt;m11,m8-&gt;logits,a9.h1-&gt;logits,m9-&gt;logits,a10.h7-&gt;logits,m10-&gt;logits,m11-&gt;logits\n\n\n**EAP-IG:** input-&gt;a0.h1&lt;v&gt;,input-&gt;a0.h10&lt;v&gt;,input-&gt;m0,a0.h1-&gt;m0,a0.h10-&gt;m0,m0-&gt;m1,m0-&gt;m2,m1-&gt;m2,m0-&gt;m3,m1-&gt;m3,m0-&gt;a5.h1&lt;v&gt;,m0-&gt;a5.h5&lt;v&gt;,a0.h1-&gt;a6.h9&lt;v&gt;,m0-&gt;a6.h9&lt;v&gt;,m1-&gt;a6.h9&lt;v&gt;,a0.h1-&gt;a7.h10&lt;v&gt;,m0-&gt;a7.h10&lt;v&gt;,m2-&gt;a7.h10&lt;v&gt;,m0-&gt;a8.h8&lt;v&gt;,m0-&gt;a8.h11&lt;v&gt;,a5.h1-&gt;m8,a6.h9-&gt;m8,a7.h10-&gt;m8,a8.h8-&gt;m8,a8.h11-&gt;m8,a0.h1-&gt;a9.h1&lt;v&gt;,m0-&gt;a9.h1&lt;v&gt;,m1-&gt;a9.h1&lt;v&gt;,m2-&gt;a9.h1&lt;v&gt;,m3-&gt;a9.h1&lt;v&gt;,m8-&gt;a9.h1&lt;q&gt;,a5.h5-&gt;m9,a6.h9-&gt;m9,a7.h10-&gt;m9,a8.h11-&gt;m9,m8-&gt;m9,a9.h1-&gt;m9,a6.h9-&gt;m10,a7.h10-&gt;m10,m8-&gt;m10,a9.h1-&gt;m10,m9-&gt;m10,m8-&gt;m11,m9-&gt;m11,m10-&gt;m11,m8-&gt;logits,a9.h1-&gt;logits,m9-&gt;logits,m10-&gt;logits,m11-&gt;logits\n\n\n**EAP-GP:** input-&gt;a0.h1&lt;v&gt;,input-&gt;a0.h10&lt;v&gt;,input-&gt;m0,a0.h1-&gt;m0,a0.h10-&gt;m0,a0.h1-&gt;m1,m0-&gt;m1,m0-&gt;m2,m1-&gt;m2,m0-&gt;a5.h1&lt;v&gt;,m0-&gt;a5.h5&lt;v&gt;,a0.h1-&gt;a6.h9&lt;v&gt;,m0-&gt;a6.h9&lt;v&gt;,m1-&gt;a6.h9&lt;v&gt;,a0.h1-&gt;a7.h10&lt;v&gt;,m0-&gt;a7.h10&lt;v&gt;,m2-&gt;a7.h10&lt;v&gt;,m0-&gt;a8.h8&lt;v&gt;,m0-&gt;a8.h11&lt;v&gt;,a5.h1-&gt;m8,a5.h5-&gt;m8,a6.h9-&gt;m8,a7.h10-&gt;m8,a8.h8-&gt;m8,a8.h11-&gt;m8,a0.h1-&gt;a9.h1&lt;v&gt;,m0-&gt;a9.h1&lt;v&gt;,m1-&gt;a9.h1&lt;v&gt;,m2-&gt;a9.h1&lt;v&gt;,m8-&gt;a9.h1&lt;q&gt;,a5.h5-&gt;m9,a6.h9-&gt;m9,a7.h10-&gt;m9,a8.h11-&gt;m9,m8-&gt;m9,a9.h1-&gt;m9,a6.h9-&gt;m10,a7.h10-&gt;m10,m8-&gt;m10,a9.h1-&gt;m10,m9-&gt;m10,m8-&gt;m11,m9-&gt;m11,m10-&gt;m11,m8-&gt;logits,a9.h1-&gt;logits,m9-&gt;logits,m10-&gt;logits,m11-&gt;logits\n\nThe circuits discovered by EAP, EAP-IG, and EAP-GP on the IOI task demonstrate progressively more advanced patterns of information flow and integration. EAP identifies a sparse, mostly linear circuit centered on a single attention head, resulting in limited feature fusion and low redundancy. EAP-IG builds upon this by introducing multiple attention heads and localized modular interactions, enabling richer internal connectivity and the early use of query-based aggregation. EAP-GP further advances these capabilities by leveraging its gradient-guided path integration design to identify attribution paths that avoid saturated or misleading gradients. As a result, it discovers circuits involving a broader set of attention heads across multiple layers, centralizes information through a key convergence node (e.g., m8), and forms deep, multi-branch structures with extensive cross-layer integration. This reflects EAP-GP's ability to uncover more faithful and causally grounded circuits. As a result, the discovered structures exhibit significantly higher structural complexity, redundancy, and robustness. These properties enable the final logits to be influenced by diverse and complementary sources of information.\n\n\n\n>W4: Unclear what the practical applications of having more faithful circuits for AI Safety are. Also, circuit discovery might not scale to bigger SOTA models.\n\nA4:Thank you for raising these concerns. We believe that improving circuit faithfulness has important implications for AI safety. Faithful circuits allow researchers to uncover the true causal mechanisms behind model behavior, which is essential for tasks such as auditing, detecting spurious correlations, and ensuring behavioral alignment in high-stakes applications (e.g., content moderation, planning, or question answering).\n\nImportantly, much of mechanistic interpretability is grounded in attribution analysis, and our work reveals saturation as a previously underappreciated failure mode of gradient-based attribution in circuit discovery. This issue may also affect other attribution-based tools widely used in AI safety and interpretability, highlighting the need for methods that produce faithful and robust causal explanations. Without such faithfulness, interventions or explanations may be misleading or ineffective.\n\nRegarding scalability, earlier circuit discovery approaches relied heavily on manual inspection. Recent advances, including our proposed EAP-GP, demonstrate that gradient-based methods are capable of scaling to larger models. We acknowledge that challenges remain for frontier-scale systems, but view our work as a meaningful step toward scalable and reliable mechanistic interpretability.\n\n\n> Minor issues and typos:\n\nA5: Thank you for your careful reading and constructive suggestions. We will revise the paper accordingly. Specifically, we will reference the compute analysis in Table 3 to highlight the ~4× cost of EAP-GP, rename Section 6 to “Evaluation,” include AUC values in Fig. 4, and standardize terminology to “clean input” and “corrupted input” for clarity. We will also clarify the definition of circuit faithfulness earlier in the text, fix the typo in line 125 (“graph”), add a citation or reference for the IOI dataset at its first mention, and remove the duplicated “iteratively” in line 211. Your feedback is much appreciated and will help improve the overall clarity and consistency of the paper.\n\n\n\n\n\n>Q1: Improve motivation of the work: What is the theory of impact for this work? What is the utter goal of having more faithful circuits?\n\nA6: Thank you for the Question. Please refer to our response to W4 for details.\n\n>Q2:Can we make EAP-GP faster so that it's more competitive against EAP-IG?\n\nA7: Thank you for the Question. Please refer to our response to W1 for details.\n\n>Q3: Are there any limitations on using manually found ground-truth circuits as a part of a quantitative experiment?\n\nA8: Thank you for the Question. Please refer to our response to W2 for details.\n\n>Q4:Does it make sense to do a qualitative analysis of the circuits found by these techniques?\n\nA9: Thank you for the Question. Please refer to our response to W3 for details."}]

Author rebuttal:

Meta-review: The paper proposes Edge Attribution Patching with GradPath (EAP-GP), a modification to gradient-based circuit discovery methods that addresses saturation effects encountered in integrated gradients approaches. The method adaptively follows gradient paths to avoid saturated regions, leading to improved attribution reliability and more faithful circuit identification across several GPT-2 models and tasks.

Reviewers agreed that the paper tackles an important problem in mechanistic interpretability with a clear and well-motivated algorithmic idea. The method shows consistent empirical gains, and the paper is well written. Weaknesses identified include: (1) potential misleading presentation of the method in Figure 1; (2) insufficient empirical evidence that improvements stem specifically from reduced saturation; (3) reliance on older benchmarks rather than newer ones; (4) lack of direct comparison with relevant prior work (AtP*); (5) relatively limited discussion of interpretability insights and practical applications, with some reviewers also noting higher computational cost.

The rebuttal was deemed constructive. The authors clarified the Figure 1 issue, provided new experiments quantifying gradient norms to demonstrate the role of saturation, and reported variability across runs. They also explained why newer benchmarks (MIB) were not used and attempted a partial AtP* comparison. Additional analyses on task-specific behaviors and qualitative circuit comparisons strengthened the paper. Nonetheless, one reviewer remained unsatisfied with how the endpoint definition in Figure 1 was handled and continued to press for stronger AtP* comparisons, though they acknowledged improvements and indicated willingness to raise their score to borderline accept.

Overall, three reviewers (ptDW, vD2V, LBjM) found the rebuttal convincing and maintained or increased their already positive scores, highlighting that the paper makes a technically solid contribution and addresses key weaknesses. One reviewer remained skeptical about specific methodological claims and withheld a full endorsement, although their position softened somewhat after discussion. Overall, the majority of reviewers view the contribution positively, with concerns largely centered on presentation and comparisons rather than fundamental correctness. Given all this, the AC recommends the paper to be accepted. The authors are encouraged to carefully revise the presentation of the integration path (e.g., correcting Figure 1 and Algorithm 1), strengthen the discussion of AtP* and related prior work, and expand the interpretability implications in the camera-ready version.
Decision: Accept (poster)