Thank you for taking the time to write a detailed and broad review. We are pleased with your broader perspective, mentioning additional references (going beyond circuit discovery literature) and suggestions to clarify and better articulate what this work is trying to do, and what it is not.

At its core, the goal of this paper is not to rediscover existing circuits, nor to benchmark a new variant of an existing circuit discovery pipeline. Instead, we’re trying to take a step back and ask, What if the atomic units we analyze, like neurons or heads, are too coarse to fully describe the computations these models perform? Singular vector directions in weight matrices provide a finer-grained, orthogonal basis that isn't constrained by component boundaries. This paper tries to make a case for interpreting behavior in that subspace.

We address the clarifications/suggestions below.

• Suggested Related Works We agree with your suggestions; we should have cited the works you mentioned. We thank you for providing a broader scope to this work by including works in vision, feature reconstruction, and visualization. We hope you understand that the omission of these works was an oversight, not an attempt to overstate novelty. The novelty lies in shifting how SVD directions are used, i.e., not just for reconstruction or feature visualization, but as functional units optimized to preserve model behavior. The novelty lies in shifting how SVD directions are used, not just for reconstruction or feature visualization, but as functional units optimized to preserve model behavior, which was missing from the prior art. We will be including all of them in the updated version of the paper.

• We agree that Sparse Attention Decomposition (Franco & Crovella, 2024) is somewhat related to our work, and in hindsight, we should have framed the relationship more clearly. That said, the goal in [2] is to identify a sparse subset of singular directions that reconstruct the attention scores themselves. Our objective is quite different; we’re optimizing for preservation of end-to-end model behavior (as done in circuit discovery methods), not intermediate reconstruction (done in SAE-type methods). This distinction matters. The directions they find reconstruct attention scores well, but aren’t necessarily predictive in the downstream sense. In contrast, the directions we find preserve the full output distribution (measured via KL divergence) and often correlate with interpretable, task-relevant roles. It is important to note that this work's primary goal is to look at things differently and see if abstract circuits exist, rather than using components as atomic units; we use these directions that were found to play specific roles in the tasks.

• We would like to emphasize that Section 5 is intentionally qualitative. Rather than recovering known causal circuits (that can be obtained via any faithfulness-preserving optimization objective), we explored whether individual singular directions encode interpretable roles, suggesting that attention heads are not monolithic but contain overlapping subroutines. The examples were chosen to support this hypothesis through detailed case studies, not an exhaustive search (so we may have missed a few roles). We agree that a more systematic faithfulness is needed, but that is still an open research problem in the interpretability domain, which remains future work. In our analysis, we included the patterns that were explainable; we explored the other directions as well, but could not generalize the findings. Also, it takes much more time to analyze each direction separately. Overall, what we’ve consistently found is that directions tend to be overlapping and distributed, multiple directions in the same head contribute to distinct, sometimes competing subfunctions. This is precisely the reason we moved away from component-level analysis; the head as a whole doesn’t do “one thing”; it houses several subroutines. The SVD basis lets us isolate these roles. The key idea we want to put here is to understand not just "which head is active?", but "what kinds of structure live inside a single head?", formulating a different level of abstraction/atomic units of role-playing components. Sections 2 and 3 set up the decomposition for all major matrices (QK, OV, MLP), but we focused our case studies (that required some sort of manual inspection, which is time-consuming) and visualizations on QK matrices, since the QK matrices showed the highest sparsity in learned masks, making them easier to interpret direction-wise in manual case study/inspection. Moreover, the semantics of QK directions (via dot products) lend themselves to clearer qualitative interpretation as reported in the paper. On the other hand, OV and MLP components tend to exhibit denser, more distributed masks, complicating direction-wise analysis. This could be another direction to explore in future work. Regarding the faithfulness, the masks learned over these matrices are still predictive and preserve model behavior (as confirmed via KLD), but are less sparse and harder to dissect cleanly. This observation aligns with the idea that different components in transformers express different forms of computation, some more modular and interpretable than others.

• Thank you for pointing this out; it’s an oversight that we didn’t report this clearly in the main paper, since the objective that we minimize in the algorithm is expected to learn a mask that preserves model behaviour. Hence, the main focus was to check if these directions that came out are actually interpretable, and whether this could be a new direction/atomic units to be used in the circuit discovery literature. We’ve now added these results, including KL divergence between masked and unmasked model outputs typically falls within 0.07-0.12 of the original, depending on the component, along with 96% of exact prediction match and 82% accuracy (full model has 84% accuracy) on the IOI task. Also, the learned masks outperform both top-k singular direction and random masks, which degrade performance more significantly. All of these metrics validate that the learned subspaces not only align with interpretable roles but also retain the functional essence of the model. We'll report these results more prominently in the revised version.

• On RoPE Models and Generalization We agree that applying this framework to RoPE-based models presents challenges. Unlike fixed positional embeddings, RoPE introduces position-dependent rotations, meaning the dot product between Q and K is not directly interpretable as a simple inner product on a static SVD basis. This introduces two issues: 1) Each token pair effectively uses a different QK interaction subspace, making a single SVD-based decomposition less meaningful. 2) Interpreting SVD directions in this dynamic context requires either reversing or compensating for the positional rotation or projecting into a unified subspace post-attention. That said, this challenge is also an opportunity. The fact that multiple position-dependent QK subspaces exist could enable richer decompositions, and perhaps even multiple, composable attention circuits within the same head. We believe adapting SVD decomposition to the RoPE regime is a natural next step, and could be explored in future work. At this point, we chose to focus on models without RoPE to first test the viability of the idea that singular directions themselves can act as interpretable subroutines. We’ll now add this limitation explicitly and outline how the method might extend to RoPE-based models.

Response to the Questions:

• When we refer to mean activation, we mean the average activation of a given singular direction over the entire dataset. This averaging helps identify directions that are consistently active and not just responding to spurious examples or rare token contexts. Regarding the formulation, you're absolutely right in how you wrote the formulation.

• The learned masks are continuous values between 0 and 1, not binary. We use a sparsity-inducing regularization (via an L1 penalty), which encourages many values to go to zero, but doesn’t hard-threshold them. We intentionally chose this softer form of masking to 1 avoid hard zeroing that may disrupt gradients during learning. 2) Allow finer control over relative importance between directions.

• Yes, we use the full-rank decomposition for all components, including QK, OV, and MLP layers. For QK matrices, the effective rank is often 64, so r = 64 is both natural and complete. For OV and MLP matrices, the rank can differ (observed to be 65 for OV after the augmentation matrix formulation), and we retain all non-zero singular directions based on the decomposition (i.e., no truncation). So even though we say “top-r”, in practice we don’t discard any singular directions unless we explicitly test lower-rank baselines (e.g., top-k SVD vs. learned mask). We thank you for noticing this, as it may come out in the other way to the readers, we will make it clearer in the updated version of the paper.

First, thank you for the very detailed and careful response.

• I would like to explain my reasoning for suggesting [2] and [3] as more than just citations, but as important points of comparison. I agree with you regarding [1]. It would likely be difficult to adapt its experimental setup to your work, so a citation and discussion are sufficient. For [2] and [3], I believe an experimental comparison would significantly strengthen your claims. Here is my thinking:

  • On comparing with [2]: You define your novelty as optimizing SVD directions to preserve model behavior. However, the method in [2] aims to reconstruct the attention scores. Since the attention scores determine a layer's output, reconstructing them is also a way to preserve the model's behavior. Because both your method and [2] aim to preserve behavior through different objectives (downstream performance vs. attention score reconstruction), a direct comparison would help readers understand the trade-offs. This is especially relevant to your goal of finding a sparse subspace. In Figure 1 of your paper, some important heads (like (9, 9) and (10, 7)) do not seem to result in very sparse masks. This leads to a natural question: Is your method finding a small set of important directions, or is it learning to rescale the full set of SVD directions? Comparing your results to a method like [2], which is designed to find a sparse set of vectors, would provide a clear, quantitative answer and better demonstrate the advantages of your approach.
  • On comparing with [3]: This paper offers a direct method for interpreting the SVD of the OV and MLP parts of the model. Since you also analyze these components in Section 2, the analysis from [3] could serve as a great baseline. Showing that the directions your method learns are meaningful, when viewed through the lens of [3], would provide strong evidence for your claims about finding "functional units."

  In summary, adding these experimental comparisons would make your paper's contributions much clearer and more convincing. It would provide strong evidence that your method for preserving model behavior is more effective in practice than these other approaches.

• See my previous answer.

• The core hypothesis that attention heads contain overlapping "subfunctions" which can be isolated by SVD direction is compelling, and the case studies provide an interesting proof of concept. However, I believe the claims could be significantly strengthened. While I understand that a full, systematic analysis is future work, the current evidence, drawn from a manual inspection of a few directions in a single task, feels preliminary. To address the scalability issue of manual inspection that you mentioned, and to make the evidence for these subfunctions more robust, I suggest considering a more systematic analysis. For example, performing targeted causal interventions on the key SVD directions you identify, similarly to [4], or using tools like Autointerp could provide quantitative support for their interpretable roles without requiring an exhaustive manual search. Regarding the focus on QK matrices, your reasoning is clear. I am not suggesting you perform the same time-consuming manual inspection for the OV and MLP components. Instead, I recommend adding the results you already have to an appendix to make the paper more complete. This would include:

  1. Visualizations of the learned masks for OV and MLP matrices (similar to what you show for QK in Figure 1).
  2. The discussion you provided in your comment, explaining that these masks are denser but still preserve model behavior, as confirmed by the KL divergence.

• Thank you for reporting these results. Another suggestion is to have a metric to show the sparsity of the masks, such as the number of singular directions used (or the L0 norm of the mask).

• I completely agree with all the points about RoPE, and as you mentioned, they should be added as limitations/future work in the paper.

• Regarding the questions, thank you for all the clarifications.

Thank you for your thoughtful and constructive feedback. We're glad that the core contribution, bringing interpretability to the level of singular vector directions within weight matrices, stood out clearly. Your comment that this work extends circuit discovery to a finer granularity without using SAEs captured exactly what we hoped to demonstrate. The primary focus is to think in a different direction (level of granularity) for finding/abstracting out functional components playing a specific role in a specific task.

We are particularly pleased that you resonated with the main idea of reframing interpretability from a component-level view to one grounded in singular vector directions. Our motivation was not to simply replicate known circuits through another lens, but to challenge how we define atomic units of function inside LLMs. Rather than focusing exclusively on causal faithfulness or reconstructing known pathways, we explored towards understanding what abstract predictive directions exist in model weights, even if not strictly necessary in a minimal circuit sense.

We are happy for your careful reading and your detailed points. We respond to the major points/clarifications below.

• Comparison with Other Circuit Discovery Algorithms We agree that the paper could more clearly position/fit itself in relation to prior circuit discovery methods. However, we would like to emphasize that [also discussed in Section 5.1 (“Comparison with Existing Circuit Discovery Methods”)], our work proposes a fundamentally different level of abstraction, i.e., instead of treating entire components (e.g., heads, MLPs) as atomic units, we decompose these into granular orthogonal directions via SVD. This perspective does not completely align with previous work, such as ACDC or SAE-based methods, which focus on edge-level causal paths between predefined components. The proposed method instead focuses on uncovering predictive structure within components, revealing overlapping and distributed subfunctions that standard tracing cannot detect. We also agree that neuron-level mask-based approaches (e.g., subnetwork probing) may share similar optimization objectives. However, those typically treat neurons as the smallest unit, while we show that singular directions inside each weight matrix provide a finer and often more meaningful granularity (as reported roleplaying directions in Section 5 of the paper). We thank you for this insight, and we will revise the Related Work section to better reflect this distinction and reference relevant efforts (e.g., sparse subnetworks and Merullo et al. [2024b]). If you have any other works, we would be happy to include those as well.

• Faithfulness of Masked Directions Thank you for highlighting this. We agree that explicitly reporting performance retention after masking would be essential to support our claim about preserving model behavior. In our experiments, we did learn the masks with early stopping based on KL divergence convergence to the unmasked model (on held-out validation set as done in prior arts like ACDC, EP, and EAP), so functional preservation was expected. However, to make this more straightforward in the updated version, we will report the KL divergence and task performance (e.g., top-1 accuracy) after applying the learned masks. These results show that learned masks consistently outperform top-k and random SVD baselines in preserving behavior, supporting the idea that our method selects functionally meaningful subspaces. Section 5 is intentionally qualitative. Rather than recovering known causal circuits (that can be obtained via any faithfulness-preserving optimization objective), we explored whether individual singular directions encode interpretable roles, suggesting that attention heads are not monolithic but contain overlapping subroutines. The examples were chosen to support this hypothesis through detailed case studies, not an exhaustive search (so we may have missed a few roles). We agree that a more systematic faithfulness is needed, but that is still an open research problem in the interpretability domain, which remains future work.

• High Mask Scores in Non-Wang Heads We thank you for this insightful observation, and we agree it deserves more discussion. In general, we found that some heads not part of the Wang et al. circuit still receive high mask scores, and our current interpretation/speculation is that these heads may encode redundant or auxiliary predictive routines not captured by causal tracing (since Wang et al do not specifically use KLD). They could reflect task-agnostic computations (e.g., syntax, position handling) or serve as fallbacks that are predictively useful but not causally necessary. We plan to include resample ablation experiments in the revision to understand their role better. Preliminary results suggest that masking these directions does lead to measurable degradation (better if we can show that using some experiments), supporting their functional relevance, even if they were not selected by prior tracing work.

• Effect of Choosing "r" for Top-r Singular Values We selected r = 64 for QK and r = 65 for OV based on the effective rank after augmentation (i.e., number of non-zero singular values). This was a pragmatic/natural choice to balance computational efficiency and expressiveness. While it worked well in our experiments, we agree that sweeping r or optimizing over the full orthogonal basis (specifically for MLP layers) could yield richer insights, possibly uncovering weak but interpretable directions. We will clarify this design decision and suggest full-rank optimization as an avenue for future work.

• Early Stopping Details Our early stopping strategy was based on KL divergence convergence on a held-out validation set (like done in works like ACDC, EAP, and EP, we specifically use EP's held-out validation set), the training was stopped when L1 norm of the mask and kl divergence were saturated (KL value was in range 0.07-0.12 at the point of saturation, depending on the penalty on L1). We agree that a hybrid strategy combining KLD and sparsity metrics could be more principled and propose it as future work. This also balances out the reward hacking (extra amount of pruning to preserve task-specific behaviour), and keeps the optimization joint.

• KL Divergence vs. Logit Difference We chose KL divergence as our loss function because it compares entire output distributions, forcing the masked model to match the original model’s behavior globally, not just on the answer token. In general, we observed that the KLD is compromised when logit difference is used as a loss objective; hence, to maintain the model behavior intact/close as possible, we prefer using KLD as a loss function. We thank you for pointing this out. We will add a small discussion with some preliminary results (if possible) to add an extra layer of transparency for future work.

• Additional Related Works We thank you for pointing these out. We agree that the mentioned previous works are significantly relevant to be included in the literature review.

Response to the Questions:

• Reporting the performance before and after applying the learned mask on a test set. We agree that this is essential for evaluating the effectiveness of the learned mask. We have now added results (showing the KL divergence and task accuracy on the test set, i.e., KL divergence was 0.07-0.12 (IOI) (masked vs. unmasked model),and the learned masks recover 96%(exact prediction match for IOI) of the original behavior (better than top-k or random masks). Also, for the Task accuracy, the performance drops are minimal (masked model has 82% accuracy, full model has 84% accuracy on IOI task), supporting the faithfulness of the learned subspace. These results confirm that the selected singular directions preserve core model behavior and are not only interpretable but also functional.

• Early stopping criteria and number of epochs We used early stopping based on KL divergence saturation on a held-out validation set (similar to the one used in EP), i.e., the mask optimization terminated when KLD stopped decreasing and plateaued near the baseline model.

• Sensitivity to hyperparameters, especially the value of "r", we selected r = 64 for QK and r = 65 for OV, based on the effective rank after augmentation. Although we did not perform a wide hyperparameter sweep (specifically for MLP). We will include a discussion on this and propose full-rank optimization as promising future work.

• We would like to higlight that the L1 values that we obtain is around 700, which is around 2k for the wang et al circuit components, that would be one way of comparison. We believe that the current perspective is quite different from what is done in the past, the recent work with MIB benchmark [Mueller et al 2025], also lays down a generic measure of sparcity going to the dimension level (also referred as neuron level measure, refer to section 3.1 "Measuring circuit size." subsection)

• Regarding the universally useful directions, we agree that some of the roles that we discover play a similar role in different tasks when investigated manually, some of the ones that are reported in the paper/appendix include Figures 6 and 7 [also see description for these roles].

• We agree that it would be interesting, looking at the counterfactual importance of singular values, especially the ones labelled as "other head types,". We are currently running these experiments and will report some of the initial findings in the paper if possible.

• We would be happy to add the requested related work and reframing the novelty of the paper to be along the lines of extending SVD-based interp to task-specific settings/circuits.

• The random masks were initialized using a normal distribution, and multiple experiments with different seeds led to similar mask distributions learned during the optimization process.

Thank you for your thoughtful and encouraging review. We’re very happy that the primary ideas of the paper came through clearly, especially the integration of input augmentation, SVD-based decomposition, and sparse mask learning to isolate functional subspaces inside transformer models.

We are also pleased with your recognition of the simplicity and coherence of this approach, i.e., freezing weights and learning diagonal masks to identify task-relevant directions. This line of thinking grew out of an inclination to shift the conversation in mechanistic interpretability away from fixed components (like heads and layers) and toward functional directions embedded across the model.

• On Scaling to Larger Models (e.g., LLaMA): We agree this is a natural and exciting next step. The framework was intentionally designed to be scalable, learning masks over SVD directions in frozen models is memory-efficient and parallelizable. We used the GPT2 architecture following the current literature in mechanistic interpretability. Moreover, GPT2 is been widely studied and help make the experimentation faster, with an added advantage of ground truth components already discovered by studies like Wang et al. that help validate the working of the presented approach, in the future, it would be interesting to see a combination of such directions playing role in bigger/larger models, making them more interpretable and alignable/steerable for a specific behaviour. More specifically, we chose GPT-2 for this study to keep our focus on interpretability and avoid confounding factors introduced by very large-scale models. Our aim was to first establish the methodological foundation, validate it with the existing literature, and later go towards scaling it for bigger models.

• On Additional Circuits (e.g., arithmetic tasks), this is a great suggestion. We agree that the arithmetic tasks present unique opportunities/ways for discovering compositional or algorithmic circuits; however, they also require careful setup to ensure alignment between directionality and symbolic function. We believe this would be an interesting direction to explore in future works.

We are happy for your support of the work and for identifying its originality and potential impact. The positive signals from the current results, clear task-relevant directions, behavior preservation under masking, and alignment with known heads are encouraging and strong signs that this direction-based lens could become a useful method in interpretability, presenting a new direction to look at model behaviour.

Thank you for engaging with our work and understanding the key aspects of this work. We are pleased that your summary captures the spirit of what we aim to present, i.e., shift the focus in mechanistic interpretability from components like attention heads to the directions within them, represented by singular vectors, as the real atomic units of function.

We believe this perspective opens up a different way of seeing what’s happening inside transformers. Rather than assuming that heads or layers are monolithic, our work shows that they are better understood as overlapping bundles of functional subroutines/subfunctions, each of which can be observed as embedded in a low-rank direction. This reframing is the core contribution, and we’re encouraged that you found this idea both clear and interesting.

We respond to your suggestions and questions point by point as below:

• We agree with your insights regarding providing an ablation study to provide more empirical justification, for understanding the behaviour of the learned masks, that include the behaviour preservation, inversion (i.e., removing these directions that lead to performance that is near random), and comparison that includes observing the learned directions outperforming, both top-magnitude and random SVD baselines [also see table below]. We will try to include these comparisons in the updated version of the paper. However, we would also like to highlight that in the current version, we followed the prior art and took the circuits/components by Wang et al. as ground truth for model components playing a role, and it was interesting to see that similar components show a high mask value when compared to the rest of the model. We believe that since the mask optimization is done using the model behavior preserving metric, it is easier to get the learned directions that retain 96% of exact prediction match and 0.07-0.12 KLD with the full model and 82% accuracy on the IOI task, confirming they’re sufficient for behavior (due to the optimization objective of the task). In this work, the primary goal was to see if the independent directions also play a role in this behaviour preservation, i.e., the directions with high singular values are not the only ones that are important, and there are some task-specific directions that make the subroutine/behaviour possible for a task.

• Figures 1 and 2 demonstrate that previously identified functional heads are generally associated with higher mask values, we agree that the stastical distribution may be matching with some of the other heads (non role playing heads), as also shown in the figure 2, however the primary focus is that there are independent directions (not always with a highest singular values), that play a curtial role in this model behaviour, to validate it in more detail, we provide the entire section 5 and the additional investigations in the appendix about different component's different directions playing a specific role for a specific task. In this work, the primary goal was to look at circuit discovery from a different lens that goes away from taking a module/component as an atomic unit and discover the abstract spaces learned/used by the model to perform a task.

• We are happy for your detailed suggestion regarding comparing the distributions of activations for "functionally-relevant" vs irrelevant tokens, and adding statistical tests to demonstrate differences. We believe this would add an additional set of verifications regarding the independent directions. In the current version of the paper, we considered investigating the behaviour of the found directions in a qualitative sense, as done in the prior arts on the mechanistic interpretability literature. We believe a lack of suitable metrics to make this comparison between activations is the primary bottleneck that limits the ability to consider/take a statistical comparison as a strong source of verification. Activation comparison in general is a vast field that is filled with some limitations of comparing the model comparison, and the behaviour preservation, like the faithfulness score (comparison with the original model), is the only metric widely used in the community. We believe the qualitative investigation was more necessary, and it took too much time to help us frame a justification for the current approach of finding abstract components and studying patterns that came with some of the directions. This was helpful for suitable validation that some of the directions are more important than others, and a new way to think about model components is to take these directions as atomic units instead. If you have any other specific metric for the activation comparison that is used in the literature and would make this study more general, we would be happy to try out the same.

Response to Questions/Clarifications:

• Q: Is this like model pruning? Yes, we are glad that you noticed this in detail, the current way of masking can indeed be seen as a task-specific, low-rank pruning strategy, but one that operates in the directional basis of parameter matrices rather than weights or neurons or any other component. The primary difference is that we’re not just simplifying, we’re studying/exploring the functional geometry (with discovered directions) of how models think/make decisions.

• Q: What is the effect of lambda (L1 sparsity)? The lambda controls the trade-off between sparsity and performance. It is a hyperparameter that can be tuned to control the sparsity. In the current setup, we used annealing lambda with linear increase [0,5e-4] to lead to interpretable masks with minimal task degradation. Intuitively, we can say that too high a lambda can lead to losing coverage; on the other hand, too low values will make the masks lose meaning.

• Q: Is optimization done jointly or separately? We optimize all the masks jointly to get a more coordinated structure.

• Q: “Can Fig. 1 be made more concise?” Yes, we agree with the suggestion to make Figure 1 more concise. We specifically used Figure 1 (with ordering of singular values, rather than that of mask values), to highlight that the peak mask are different from the singular values, in the SVD decomposition it is natural to assume that the more singular values will play a more important role in matrix reconstruction, however we believe the peaks coming in the middle highlight that some of the directions are more task relevant than the ones with more singular values, showcasing the non monolithic nature of these modules with more detail. As per the suggestion, we can keep another image with sorting heads and singular directions by activation strength. Thanks for this practical and helpful suggestion.

We started this work from a simple question, i.e., what if we’re looking for functional units in the wrong place? Rather than treating entire components as atomic, we asked whether a function lives/occurs in directions, and whether those directions can be disentangled, isolated, and understood. In our initial study, we found that the early evidence suggests yes, and that a lot of what we consider “component function” may be an emergent property of overlapping directional subroutines, which we aim to disentangle in this work. We believe there is a lot to explore when taking/studying model components, and this work may lead to one such foundational way of thinking about model behaviour.

1. IOI Task accuracy: Thank you for the clarification. I was requesting for the full model performance, which you mentioned in 84% in your response. I did not find this information in your responses earlier (I checked the paper and your responses to my review). Did you mention it somewhere before and I missed this? My sincere apologies if that's indeed the case. As you mentioned, the full model performance is very close to the model performance when the learned mask is applied. This result addresses my concern.

2. Quantitative results: I respectfully disagree with the authors that the table provided by them is quantitative evidence in support of their claim that the learned singular value masks have higher values for previously-identified functional heads (Figs 1 & 2). I would have liked to see a statistical comparison between the distribution of mask values for functional vs non-functional heads. To this end, I think the authors could have done statistical tests to estimate how different their hypothesis (mask values for previously identified functional heads) is from the null distribution (mask values for previously identified non-functional heads). I liked the idea of using t-tests and KS test for this purpose, which the authors proposed in one of their responses.

Overall, I think the proposal presented by authors is interesting and warrants more attention from the community. The more recent task results have convinced me of the validity of this method for the IOI task. I hope this result allows the community to evaluate this proposal on larger networks and more complex tasks. Given this result, I will increase my rating to 5 (accept) and would like to congratulate the authors again on this very interesting work.