We sincerely thank the reviewer for recognizing our insight that MSA layers are the primary knowledge locus in ViTs, as well as the principled and effective two‑stage design of RefineViT. Below, we address all weaknesses and questions, supplemented with new experiments for further support.

W1. Ablation studies to clarify the individual impact of each component: 1.ablate without learning P in multi-label setting. 2. training P without zeroing heads

We conducted two ablation experiments to assess the individual impact of the two stages:

1. Ablation without learning P: We disable Stage Two and directly ablate the identified heads. On the ViT Natural Image benchmark (class 954_582), this results in a sharp drop in Locality Rate (LR) as more heads are ablated, confirming that learning P is critical for preserving locality (see table below).

N_ablated	0	3	6	9	12
LR(%)	100	46.16±2.09	38.08±4.91	32.94±8.55	29.03±10.37
GR(%)	0	73.78±13.08	86.67±2.30	84.89±2.03	84.44±2.78

2. Training P without zeroing heads: This is already shown in Figure 9 (Appendix, Page 20). Without Stage One (head zeroing), the GR gains largely vanish, highlighting its role in guiding P's learning.

Together, these results demonstrate that both stages are essential and complementary.

W2.Computation Complexity: $\mathcal{O}(L! \times H)$ forward passes per sample?

In practice, we perform only one forward pass per sample. The required components for computing head utilities (i.e., the decomposition of the backbone output) are stored and reused. This design avoids the $\mathcal{O}(L! \times H)$ cost and keeps our method computationally efficient. A detailed description of the head‑selection procedure is provided in Appendix (p.14, Summary of the Procedure).

Q1.More intuition or theoretical argument why MSA are more critical?

The intuition is that in ViT architectures, the lower layers primarily focus on extracting local features from individual patches (e.g., parts of an object like a wing or a head), while higher layers integrate these local features into composite concepts (e.g., recognizing a bird as a combination of head, wings, claws, and tail).

Since MSA layers capture relationships between patches, errors in these layers can significantly disrupt the formation of composite concepts, leading to a larger impact on prediction accuracy. In contrast, MLP layers mainly refine the information extracted by MSA but do not directly capture inter‑patch relationships, making their impact comparatively less critical.

Q2. If repeating stage 1 using different samples, how consistent are the resulting top-K list?

We conduct an experiment where we randomly selected two images from the ViT editing benchmark (class 954_582) and measured the overlap in their top-K head selections. We repeated this process 100 times and averaged the results to minimize randomness. The results show that the top-K lists have an average overlap of over 65%, indicating good consistency. Specifically, the overlap percentages for different values of K are as follows:

Top-K	K=1	K=3	K=6	K=9	K=12	K=15
Overlap (%)	73.0	81.33	68.67	65.11	66.92	69.87

These findings demonstrate that our method produces consistent top-T lists even when using different misclassified examples from the same class.

Q3. Why ROME (update last layer of MLP) performs really well on locality? Does it contradicts the core finding of this paper (MSA plays a more important role in preserving the model's capability).

No, it does not contradict.

• Locality measures how well predictions are preserved on unrelated data. ROME edits only the MLP layer and leaves the MSA modules untouched, so the model's core representations are largely preserved, leading to a higher Locality Rate (LR).
• However, its high locality can come at the cost of weak edits. As shown in Figure 4, ROME has a relatively low Generalization Rate (GR), indicating limited editing success. In fact, if no editing were performed, the Locality Rate would remain at 100%, highlighting the trade-off between locality and effective editing.

Thus, our core insight remains valid: MSA modules are central to knowledge preservation and effective editing.

Q4.L202: "This allows updates in under 0.3 seconds for 50 epochs". Does that include the time to find the ablation matrix A?

The reported update time of under 0.3 seconds for 50 epochs does not include the time to compute the ablation matrix A. However, as noted in our response to W2, Stage One requires only a single forward pass per sample, after which the backbone’s output is stored. Subsequent steps involve only matrix multiplications (for CLIP-ViT) or classifier-head-only forward passes, making them extremely fast with negligible time cost. Thus, the overall process remains highly efficient.

We sincerely thank the reviewer for recognizing the practical importance, MSA‑focused design, and strong experimental results of our RefineViT framework. Below, we address all weaknesses and questions, supplemented with new experiments for further support.

Q1. Does this method generalize to scenarios where multiplex edits are required? dynamic and continuously? cumulative effects or degradation?

Yes, our method supports multiple editing and demonstrates strong performance in such scenarios.

• We evaluate this on the ViT benchmark by sequentially editing three target classes, each involving a single misclassified example.
  • We compare our approach against the state-of-the-art method (WTE) and standard fine-tuning with $l_{2}$ regularization.
  • At each step, we measure both Generalization Rate (GR), i.e., accuracy on target classes, and Locality Rate (LR), i.e., performance on unrelated data. Importantly, we track GR for both the current (e.g., CLS_3 for the Editing 3) and all previously edited target classes (e.g., CLS_1 and CLS_2) to assess edit retention. The results are shown in the following tables.

GR	Edit 1	Edit 2	Edit 2	Edit 3	Edit 3	Edit 3
	CLS_1	CLS_1	CLS_2	CLS_1	CLS_2	CLS_3
RefineViT(ours)	92.0	92.0	98.54	90.67	98.54	96.1
WTE	73.61	73.61	84.21	73.61	84.21	96.54
Std.F.T	38.89	0	37.84	5.55	5.26	98.77

LR	Edit 1	Edit 2	Edit 3
RefineViT(ours)	91.79	88.12	84.69
WTE	90.48	86.52	85.176
Std.F.T	95.99	83.84	83.88

• Compared to the SOTA method (WTE) and standard fine-tuning with $l_2$ regularization, our approach consistently maintains higher GR and LR across all edits. This indicates that RefineViT better preserves previous edits while maintaining locality, showcasing its effectiveness in multiple editing settings.

Q2 & W1. Can the method be adapted for more complex vision tasks such as object detection, instance/semantic segmentation? What are the main challenges or required modifications?

Extending model editing to complex tasks like object detection or segmentation presents several challenges:

1. These tasks involve different error types and outputs (e.g., bounding boxes or masks rather than class labels).
2. Unlike classification, which primarily uses the CLS token, detection/segmentation rely on all patch tokens, making attribution and decomposition more difficult.
3. There is currently no established benchmark or protocol for model editing in these settings, making standardized evaluation difficult.

Despite these challenges, we demonstrate the potential of our method beyond classification by applying it to a CLIP-based segmentation task, following the setup in [4]. Using a single edit sample, we observe improved pixel-wise accuracy on similar images and a slight improvement in overall performance:

Avg. Pixel-Wise Accuracy	Similar Data	Overall
Original CLIP-ViT	72.29%	76.78%
CLIP-ViT-Edited (Ours)	74.50%	77.01%

This shows initial promise for adapting our framework to segmentation tasks. We plan to explore this direction further and develop benchmarks and methods for model editing in segmentation.

[4] Yossi Gandelsman, Alexei A. Efros, and Jacob Steinhardt. Interpreting clip’s image represen- tation via text-based decomposition.

We sincerely thank the reviewer for recognizing our clear presentation, extensive experiments, and the effectiveness of the lightweight projection on localized MSA layers. Below, we address all weaknesses, supplemented with new experiments for further support.

w1. Figures 3 and 4 could benefit from clearer and more informative visualizations.

A: Thanks for your suggestion. We will revise them.

W2. Include a comparison where a random subset of MSA layers is used to optimize the projection matrix?

A: Thank you for the suggestion. We conducted this comparison using the Waterbirds dataset and ViT-L-14. The results are summarized below:

GR	Epoch 0	Epoch 20	Epoch 40	Epoch 60	Epoch 80
RefineViT	72.64	80.62±1.20	82.82±1.25	83.35±1.41	83.58±1.25
Random Subset	72.64	79.41±1.72	81.65±1.56	82.47±1.81	82.59±2.09

LR	Epoch 0	Epoch 20	Epoch 40	Epoch 60	Epoch 80
RefineViT	92.65	91.43±0.25	91.36±0.27	90.96±0.54	90.18±0.89
Random Subset	92.65	91.32±0.17	90.59±0.16	90.97±0.47	90.62±0.46

We find that randomly selecting MSA layers for projection matrix optimization leads to consistently lower GR across training epochs compared to our structured selection, underscoring the importance of the identified heads for effective model editing.

Furthermore, Figure 9 (page 20) presents additional ablations on stage 1 of RefineViT, further demonstrating the value of our head selection mechanism. Taken together, these results confirm that our design choices are essential for achieving strong generalization while preserving locality.

W3. The decomposition of residual tokens into contributions from MSA and MLP layers is not novel.

A: We clarify that the decomposition of ViT representations is not presented as a novel contribution of our work. It appears in the Preliminaries section with proper citations, serving only to establish the foundation for our method. Our main contribution lies in the editing framework and targeted refinement strategy, which go beyond these prior analyses.

We will also include a citation to the paper you mentioned in the related work.

We thank the reviewer for the thoughtful feedback. We would like to clarify the specific contribution of our attention head identification step.

1. Attention Head Identification Improves Generalization Rate (GR) Without Fine-Tuning:
   As shown in the table below, ablating attention heads identified by our method leads to a significant increase in GR compared to both the base model and random subset ablation, without any fine-tuning. Specifically:

   Method	GR(%)	LR(%)
   Base	72.64	92.65
   RefineViT	83.48	88.19
   Random Subset	72.03 ± 0.72	90.98 ± 2.28

   Our method effectively removes attention heads that contributed to the error, resulting in improved GR. In contrast, random subset ablation performs similarly or slightly worse than the base model. The effectiveness of attention head identification is also supported by the empirical results in Table 1 of the paper.

2. Fine-Tuning Narrows Performance Gap:
   After fine-tuning, the gap between attention head identification and the random subset becomes less pronounced. This is partly because fine-tuning with an appropriate loss can itself be a strong model editing method, efficiently leveraging the information from the editing sample, as also shown in [A]. Thus, even random subset ablation followed by fine-tuning achieves competitive results. Nevertheless, our method consistently outperforms random subset ablation due to the additional information provided by attention head identification.

3. Necessity of Attention Head Identification:
   These findings suggest that attention head identification is particularly valuable without fine-tuning, providing consistent GR improvement. While fine-tuning can compensate for suboptimal ablation, the localization step remains important for achieving better results.

We hope this clarifies the unique role and necessity of our attention head identification step.

[A] Gangadhar, Govind, and Karl Stratos. "Model editing by standard fine-tuning." Findings of ACL 2024.

We sincerely thank the reviewer for the positive feedback, particularly recognizing the technical soundness, clear presentation, and the novelty and timeliness of our ViT model editing approach. Below, we address all questions and weaknesses, supplemented with new supporting experiments.

Q1 & W1: Given its reliance on utility-based heuristics. (1) Are there adversarial cases where this could be misleading? (2) Can the head attribution process be made more robust? (3) How interpretable?

A: Point‑by‑point response: (1) Potential misleading cases. Our method is inherently data-driven and thus sensitive to the quality of the editing sample, especially in the one-sample setting. Ambiguous or mislabeled samples can reduce the reliability of head attribution and the resulting edits.

To illustrate this, we conducted a new Waterbirds experiment comparing edits using a correct (“real”) misclassified sample versus an incorrect (“fake”) one. Editing with a real sample improves both average and worst-group accuracy, whereas a fake sample significantly degrades performance:

	Avg. Acc (%)	Wst. Acc (%)
Original CLIP-ViT	92.06	45.71
One 'Real' sample	92.8 ± 1.18	53.9 ± 3.10
One 'Fake' sample	78.53 ± 3.52	14.04 ± 12.36

This demonstrates the expected limitations under weak supervision while confirming that the method behaves sensibly—improving with informative signals and degrading with misleading ones.

(2) Robustness. In scenarios where multiple samples are available, we mitigate brittleness by leveraging four complementary utility scores (Utility A–D, Appendix A, p.13) capturing different aspects of attention behavior. In the Waterbirds experiment (Appendix C, p.16), Grad-CAM visualizations and TextSpan-generated descriptions validate that the selected heads align with the intended utility functions.

(3) Interpretability. On Waterbirds, which contains strong spurious correlations (water/land backgrounds for bird-species classification), our utility scores consistently identify heads focusing on these background cues, as confirmed by TextSpan descriptions (Tables 4 & 5) and Grad-CAM visualizations (Fig. 7). These analyses demonstrate that our utility-based heuristics are both effective and interpretable.

W2. The method requires at least one labeled misclassified instance per error type, which may be non-trivial in open-set or online deployment settings.

A: We acknowledge the need for at least one labeled misclassified instance to guide editing.

• However, this is a minimal data requirement in the field of model editing. As far as we know, there are no zero-shot model editing methods. Our method achieves effective editing using just a single such instance.
• In practice, model errors are typically discovered through observed prediction failures, making such instances naturally available. Hence, this requirement is reasonable and aligns with real‑world deployment scenarios.

W3. & Q6. Can the method generalize to tense prediction tasks such as object detection or segmentation?

A: Thank you for the suggestion. Yes, it can.To assess generalization beyond classification, we follow the setup in [4] and apply our method to a segmentation task using a single edit sample.

• As shown in the table below, our method improves pixel-wise accuracy on similar images and even slightly boosts overall performance on the full dataset:

Avg. Pixel-Wise Accuracy	Similar Data	Overall
Original CLIP-ViT	72.29%	76.78%
CLIP-ViT-Edited (Ours)	74.50%	77.01%

• To our knowledge, there are currently no established model editing methods for segmentation. This result serves as an initial demonstration of our method in this setting. In future work, we plan to build a benchmark for model editing in segmentation and explore more effective methods tailored to dense prediction tasks.

Q2. Can the proposed method be generalized to multi-modal architectures like Flamingo or BLIP-2?

A: Our method focuses on editing visual transformers with standalone visual encoders. For multi-modal models like CLIP-ViT, which include an independent visual encoder, our method can be directly applied to the visual component.

In contrast, models such as BLIP-2 and Flamingo deeply fuse vision and language features via cross-attention, and their visual modules are typically frozen during training. Editing these tightly integrated architectures aligns more closely with large language model (LLM) editing than with visual transformer editing.

Therefore, adapting our method to these models is non-trivial and represents an interesting direction for future research.

Q3. How is performance affected by changing the number of attention heads ablated?

A: We evaluated the effect of ablating different numbers of attention heads using the ViT Natural Image benchmark (class 954_582). As shown below, GR (target-class performance) improves as more heads are ablated, peaks around 6 heads, and then slightly declines, showing that ablating the right heads matters more than simply ablating more heads:

N_ablated	3	6	9	12
GR(%)	73.78±13.08	86.67±2.30	84.89±2.03	84.44±2.78

Importantly, the number of heads ablated is not a fixed hyperparameter in our method.

• In single-sample settings, $T$ refers to the number of heads actually ablated. We select heads whose utility scores exceed a fixed threshold.
• In multi-sample settings (Appendix A, Page 13), $T$ denotes the size of the candidate pool, i.e., the number of top-ranked heads selected per utility score. The final ablation set is determined adaptively by applying a validation utility (as described in Appendix, Page 14, “Summary of the Procedure”), so the number ablated is typically smaller than $T$.

Furthermore, the sensitivity analysis in Figure 8 (Appendix) shows that performance stabilizes when $T ≥ 10$ in multi-sample settings, indicating that beyond this candidate pool size, increasing $T$ has minimal effect as the most impactful heads are already included.

Q4. The limitations of applying the projection matrix universally? Could it harm performance?

A: Applying a projection matrix universally may risk unintended changes, but our method is specifically designed to minimize such effects while maintaining strong edit performance.

• In model editing, three primary goals are typically considered: (1) edit success, (2) generalization, and (3) locality—the latter reflecting how well the edit preserves performance on unrelated data. In practice, edits often involve trade-offs, and to our knowledge, no method guarantees zero degradation on out-of-scope data.
• To address this, we introduce a locality loss to reduce such side effects explicitly. We report Locality Rate (LR) in Figures 4 and 5, showing that our method achieves a more favorable balance between edit success and preservation of unrelated behavior than prior approaches.
• Additionally, to assess the impact of using a projection matrix as the update mechanism, we compare it to LoRA, a commonly used alternative. As shown in Figure 14 (Appendix, Page 22), our projection-based strategy preserves both effectiveness and locality better than the LoRA-version baseline.

Q5. Can RefineViT serve as a debugging tool to discover spurious concepts?

A: Yes, it can. As shown in Appendix C (Page 16), we evaluate our method on the Waterbirds dataset, which contains strong spurious correlations between bird type and background. Tables 4 and 5 list the attention heads identified by our utility scores, along with descriptions from TextSpan. Grad-CAM visualizations in Figure 7 further confirm that these heads attend to background regions, indicating our method’s ability to identify spurious features driving incorrect predictions.

Thank you for reading our rebuttal. Did our response sufficiently address your concerns? We’d be happy to clarify or discuss any remaining questions you might have.

We would like to clarify a minor issue in our previous response to Q1 & W1. The accuracy values we initially reported were calculated using both the target classes from Waterbirds and unrelated ImageNet data. The correct approach is to compute accuracy using only the target classes.

Below, we provide the updated results. These results are consistent with our original claims and more clearly demonstrate our main point: mislabeled or ambiguous samples in the single-sample editing setting can reduce the reliability of attention head identification and the effectiveness of the resulting edits.

As a gentle reminder, we would also be grateful to know whether our responses have sufficiently addressed your concerns. Please let us know if there are any remaining concerns or if you would like further clarification.

We sincerely thank the reviewer for recognizing our conceptual contribution, practical two‑stage design, and strong empirical results supported by ablations. Below, we address all questions and weaknesses, supplemented with new experiments for further support.

W1 & Q2. The method relies on a linear decomposition of ViT representations. What are the limitations of this assumption, and in what cases might it lead to misidentification of faulty heads?

A: We acknowledge this simplification and discuss it in the Limitations section (page 23). Our decomposition focuses on the first‑order (direct) contributions of attention heads to the final representation, omitting higher‑order interactions across subsequent layers. While this does not fully capture the non‑linear and sequential dynamics of transformers, it provides a tractable and effective editing process.

We understand the reviewer’s concern that some heads may contribute to incorrect predictions primarily through higher‑order effects, or vice versa. However, our method modifies the final representation by removing only the direct (first‑order) contributions of identified heads, leaving their indirect effects intact. Therefore, the approach is generally robust to potential misidentification caused by omitting higher‑order effects.

Investigating higher‑order contributions is a promising future direction for achieving more fine‑grained and accurate interventions.

W2 & Q1. The L_locality term is a central part of the method for balancing success and locality. Why was it disabled for main benchmark in Figure 4?

A: We clarify that $L_{\text{locality}}$ is indeed a key component for balancing edit success and locality. However, in the experiments shown in Figure 4, only one misclassified sample is available, and no correctly predicted samples are present. Under such conditions, the standard form of $L_{locality}$ (Eq. 10) is not applicable.

Although an alternative regularization form (Eq. 11) could be used to reduce overfitting, we observed that our method already maintains strong locality without it. This aligns with our sensitivity analyses (Figures 10–13, Appendix), which shows that the success loss $L_{\text{success}}$ alone implicitly helps mitigate overfitting. Moreover, the small learning rates and few training epochs used in these experiments also help limit overfitting.

In practice, we find the optimal $\beta$ is significantly smaller than $\alpha$ in these specific experiments. Given the minor performance gap and for simplicity, we set $\beta = 0$ in these experiments.

W3. Limited discussion of when the proposed method might fail or its assumptions might be violated.

A: First, as we acknowledged in the Limitations section (Page 23), our method models only the first‑order, direct contributions of individual heads to the final representation and does not capture higher‑order or indirect effects; in scenarios where higher-order effects dominate, the proposed method cannot repair the corresponding errors.

Second, in the single‑sample editing setting, our method depends heavily on the quality of the provided misclassified sample. If the sample is ambiguous or mislabeled, the effectiveness of the edit will degrade.

We will include these discussions in the Limitation section.

Q3. Does this method generalize to scenarios where multiplex edits are required?

A: Yes, our method supports multiplex editing and shows strong performance in such scenarios.

• Evaluation setup: We test on the ViT benchmark by sequentially editing three target classes, each with a single misclassified sample.
  • We compare our approach against the state-of-the-art method (WTE) and standard fine-tuning with $l_{2}$ regularization.
  • At each step, we measure both Generalization Rate (GR), i.e. accuracy on target classes, and Locality Rate (LR), i.e. performance on unrelated data. Importantly, we track GR for both the current (e.g., CLS_3 for the 3rd Edit 3) and all previously edited target classes (e.g., CLS_1 and CLS_2) to assess edit retention. The results are shown in the following tables.

Generalization Rate (GR)	Edit 1	Edit 2	Edit 2	Edit 3	Edit 3	Edit 3
	CLS_1	CLS_1	CLS_2	CLS_1	CLS_2	CLS_3
RefineViT(ours)	92.0	92.0	98.54	90.67	98.54	96.1
WTE	73.61	73.61	84.21	73.61	84.21	96.54
Std.F.T	38.89	0	37.84	5.55	5.26	98.77

Locality Rate (LR)	Edit 1	Edit 2	Edit 3
RefineViT(ours)	91.79	88.12	84.69
WTE	90.48	86.52	85.176
Std.F.T	95.99	83.84	83.88

• Result: RefineViT consistently maintains higher GR and LR than WTE and standard fine-tuning, indicating it preserves previous edits while maintaining locality, which demonstrates strong effectiveness in multiplex editing scenarios.

We sincerely thank the reviewer for the thoughtful feedback.

You are correct that the main limitation of our method lies in the identification stage: our utility function is based only on the first-order (direct) contributions of attention heads. As you pointed out, this means it may miss heads whose main effect is indirect, acting through later layers.

We apologize for the confusion caused by the ambiguity in our previous response regarding this point. Our previous response focuses on the rectification stage. The rectification stage is minimally invasive, modifying only the direct contributions of selected heads and leaving indirect effects untouched. This design ensures that the edits do not introduce additional errors, but, as you noted, does not address errors from missed indirect contributors.

We believe the first-order identification is still useful in practice for two reasons:

• "Self-repair" in transformers makes indirect effects relatively weaker: Prior work [A, B] has shown that when a layer is ablated, later layers often compensate, making higher-order effects relatively weaker in many cases.
• Indirect effects that propagate through later layers to the output. They may still be picked up by the direct effect of these later layers. In other words, any significant indirect effect from an earlier layer could manifest as a direct effect in one or more downstream heads. Thus, our utility function can capture and address these effects by targeting the direct contributions of downstream heads.

We fully acknowledge that there can be cases where important indirect effects are not captured by our method, and these remain a limitation of our method and will be included in the Limitations section.

Thank you again for highlighting this important point and helping us clarify our claims.

[A] McGrath, T., Rahtz, M., Kramar, J., Mikulik, V., & Legg, S. The hydra effect: Emergent self-repair in language model computations. 2023. [B] Yossi Gandelsman, Alexei A. Efros, Jacob Steinhardt. Interpreting the Second-Order Effects of Neurons in CLIP. ICLR 2025

To further support our previous response regarding the limitation of considering only first‑order effects, we conducted an additional experiment comparing our method with a variant that also accounts for indirect (second‑ and higher‑order) effects of attention heads during the identification stage.

• Experimental Setups.

Instead of decomposing the image representation as a linear sum of the direct contributions of attention heads for identification and ablation, the variant measures each attention head’s influence by directly ablating its output in the forward pass, thereby capturing both direct and indirect effects. We evaluated both methods on the Waterbirds dataset, where for each method we use a single sample per edit, repeat three times to reduce randomness, and report the average accuracy and worst‑case accuracy when ablating the top‑T identified attention heads.

• Results:
  • The results (in tables below) show that the variant ("With indirect effects") performs marginally better for $T=1$. However, as $T$ increases, our method ("Direct effect only") consistently outperforms the variant in both average and worst-case accuracy. This suggests that while indirect effects may matter when ablating a single head, considering only direct effects yields better performance when more heads are removed.
  • We believe this is because indirect effects are complex and intertwined, making it harder to achieve effective ablation when considering all orders. In contrast, focusing on direct effects allows more targeted and decoupled interventions.
  • Additionally, our method is much more efficient: it requires only one forward pass, which can be reused for both training and testing, whereas the variant needs repeated forward passes for each head evaluation.
  • Therefore, omitting indirect effects is both practical and effective. It achieves strong error correction performance while keeping computational cost low.

Avg.Acc(%)	Original	T=1	T=3	T=6	T=9	T=12	T=15
Direct effects only	72.85	72.75±0.77	75.33±1.88	78.21±1.21	79.37±1.93	80.03±1.22	79.92±0.74
With indirect effects	72.85	72.78±0.06	73.05±0.80	74.53±0.87	75.88±1.43	76.08±1.10	74.73±1.08

Wst.Acc(%)	Original	T=1	T=3	T=6	T=9	T=12	T=15
Direct effects only	45.62	44.16±2.04	50.98±5.31	60.92±2.18	64.10±5.02	67.63±4.65	66.98±6.79
With indirect effects	45.62	47.55±3.50	47.15±3.62	52.9±5.62	55.72±3.64	56.77±0.55	55.26±3.56

Thank you again for bringing this important point to our attention. We hope our additional experiments and analysis have addressed your concern. If you have any further questions or would like more clarification, we are happy to provide it.