Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks

We thank the reviewer for raising these insightful and technically relevant questions. We appreciate the opportunity to clarify the positioning of Stable-ChebNet with respect to recent advancements in hierarchical and attention-based GNN architectures. Below, we provide a detailed discussion on the comparative aspects regarding performance, scalability, and potential extensions of our model through integration with learnable hierarchies or dynamic clustering mechanisms.

Performance comparison: The common dataset we share with the mentioned references is the Peptides dataset of Long Range Graph Benchmark (LRGB). Below we provide a comparative analysis that we would be happy to add in a revised version, especially given that Multi-Resolution Graph Transformers and Wavelet Positional Encodings make interesting benchmarks for our case.

In terms of performance, StableChebNet has an overall comparative performance to the Multi-Resolution Graph Transformer [3], as the latter shows a better performance in the regression task of Peptides-struc, while our model’s advantage is in the classification task of Peptides-func.

Moreover, in our earlier experiments with the Peptides-func graph-level task, introducing a Virtual Node did not enhance our model’s performance, nor did the inclusion of positional encodings. We believe a potential reason for that is the fact that Stable-ChebNet and its vanilla counterpart already account well enough for the graph’s structure and cover a wide-enough receptive field that makes a global Virtual Node more redundant. We report the findings in the Table below, where we notice that a VN is more valuable for a GCN than for Stable ChebNet.

Dynamic clustering and scalability: While making an interesting direction to explore, it is worth noting that Dynamic Clustering methods come with a certain computational cost, whether using adaptive attention or pooling-based GNNs that use Gumbel-Softmax trick for sampling, which might make the choice less plausible. That being said, in terms of scalability, Stable‑ChebNet offers some advantages over the aforementioned approaches. Hierarchical attention models could incur O(nlog⁡n) complexity to compute global or multi‑scale attention maps, while Stable‑ChebNet performs only Chebyshev recurrences, yielding strictly O(K∣E∣) work per layer (with K the polynomial order). Similarly, the Multi-Resolution Graph Transformer performs costly precomputations: wavelet bases or Laplacian eigendecompositions that can scale as O(n^3) or require significant storage across scales, whereas our method needs only Chebyshev recurrence approximation the Laplacian eigendecomposition with repeated sparse multiplications. We make a similar point in our response to Reviewer E5Qi, highlighting that, unlike benchmarks such as DRew or S2GCN, our approach avoids expensive pre-processing steps for finding geodesic distances or performing full Laplacian eigendecomposition. Instead, we demonstrate the efficiency of using the Chebyshev approximation as a computationally lightweight alternative, with Stable-ChebNet offering stronger experimental results due to its non-dissipative properties.

Integrating learnable hierarchies: We believe Dynamic Clustering integrations can boost StableChebNet’s performance in task-specific scenarios. One example is graph-level tasks requiring both local AND global context where a notable amount of graph information is “lost” in pooling layers. The integration of hierarchical learning and Dynamic clustering can be especially beneficial for very large graphs. In that scenario, a suitable approach consists of partitioning a very large graph (as in OGB benchmarks) and performing an intra then inter-cluster stable propagation. This strategy benefits from both advantages StableChebNet and dynamic clustering have to offer. For smaller graphs GCN could serve as a better backbone prior to dynamically clustering and learning in hierarchy, to allow for a fair combination of local and global information. This can be seen in the Table above whereby for the smaller Peptide graphs, Virtual Nodes, being one layer of hierarchical learning, had more benefit on top of GCN as compared to Stable-ChebNet which has already accounted for the global picture.

On the other hand, many node-level tasks require very long-range propagation but do not necessarily benefit from a full global context vector. In that case, dynamic clustering might be counterproductive given the limited improvement and the higher cost of training associated with it. That being said, we believe that the benefit of hierarchical learning and the inclusion of global context vectors prior to classification highly depends on the task under disposal whereas the amount of local and global information needed should be tested. However, we believe this is indeed an interesting direction that should be explored in future extensions.

On studying temporal graphs : We thank the reviewer for the insightful suggestion. Indeed handling dynamic and evolving networks is an important challenge in graph learning, especially considering its significance in numerous applications. While Stable-ChebNet focuses on the dynamics within the spatial domain, we agree that integrating it to the temporal setting would be a fascinating direction. Given the broad literature on temporal and dynamic GNNs, and the separate considerations for long-range dependencies in the temporal setting (See [7]) , we believe this would be more suitable for future work.

Further validation on a newly released benchmark: We broaden our evaluation to include the recently released City-Networks benchmark by Liang et al. [8], which features large-scale, transductive tasks grounded in real-world urban road networks. This benchmark is specifically designed to assess GNNs' capacity to model long-range dependencies.

The benchmarking results of that paper align with our findings and show (though without detailed analysis) that ChebNet performs well on long-range interactions given that it is often the best baseline and has a consistently high influence score, even on Ogbn-arxiv which we report in our paper. To further validate our model on real-world road networks, we ran our Stable-ChebNet on the Paris City-Networks data and compared it to vanilla ChebNet in the Table below.

These results highlight Stable‑ChebNet’s effectiveness in capturing long-range dependencies across both synthetic and large-scale real-world scenarios, all while maintaining parameter efficiency.

On separating anti-symmetry: Following the reviewer’s suggestion, we carried out an additional experiment on the OGB‑Proteins benchmark to examine the isolated impact of antisymmetric weights in our model. We tested a variant that enforces antisymmetry but excludes the forward‑Euler discretization. This “antisymmetry‑only” model achieved a notably lower test accuracy (72.2%) compared to the full Stable‑ChebNet (79.5%), emphasizing the crucial role of combining antisymmetry with the discretization scheme for effective learning.

Extension to other spectral bases: Thank you for the thoughtful question. In this study, we chose to focus on ChebNet given its historical importance and its status as one of the most prominent and widely adopted spectral GNN models. While we anticipate that similar dynamics would arise with alternative bases such as graph wavelets and multiresolution spectral domains, formally extending our theoretical analysis to those settings would require a fresh examination of the spectral norm and Jacobian behavior. Providing such a comprehensive analysis is beyond the current scope but represents a promising avenue for future research.

We genuinely hope that our responses and revisions have resolved your concerns and led you to reconsider your evaluation and score. We once again thank the reviewer for their valuable time and thoughtful assessment.

[7] Marisca et al. (2025). Oversquashing in Spatiotemporal Graph Neural Networks . arXiv preprint https://arxiv.org/abs/2506.15507

[8] Liang et al. (2025). Towards Quantifying Long-Range Interactions in Graph ML. arXiv preprint https://arxiv.org/abs/2503.09008

Thank you for the thoughtful and encouraging feedback. We appreciate the recognition of our clear writing, the importance of revisiting spectral methods for long-range interactions, and our novel re-evaluation of ChebNet. We're grateful for the acknowledgment of our principled design of Stable-ChebNet—its theoretical grounding, simplicity, and strong empirical performance without positional encodings. Your insights have been valuable in refining the paper. Below, we address your comments and outline our revisions.

We thank the reviewer for their thoughtful feedback and valuable suggestions regarding the empirical evaluation section.

On node-level tasks: We would like to clarify that, although it may not have been sufficiently emphasized in the original submission, our evaluation already includes several node-level prediction tasks. Specifically, the synthetic tasks—SSSP, Eccentricity, and the Barbell task—are formulated as node-level tasks, where the goal is to predict scalar values at each node. The only graph-level benchmarks in our evaluation are LRGB and the Diameter dataset in the GraphProp tasks, which we included to complement the node-level analyses.

Tree-NeighborsMatch dataset: In response to the reviewer’s helpful suggestion, we have now included results on the Tree-NeighborsMatch, a dataset commonly used to assess long-range information propagation and over-squashing [2]. Up until a depth of 4, we can reach an accuracy of 100% with both Stable ChebNet and vanilla ChebNet. At depth 5, we reach 65% with vanilla ChebNet alone, which is already better than most baselines. Given the timeline of the rebuttal and the intense runtime at depths higher than 4, we were not able to run until depth 8 of this dataset, but we are happy to include them in the revised version. We expect that around depth 5 or 6, ChebNet will collapse while Stable ChebNet will persist as in the case of the Barbell task.

On the inclusion of heterophilic datasets: We appreciate the suggestion to explore how label heterophily connects with long‑range dependency. In this work, however, we did not include standard heterophilic benchmarks, since there is currently no established correspondence between a graph’s heterophily and the need for long‑range information propagation—the latter being our primary focus. In fact, a recent position paper [5] argues that heterophily and long‑range reasoning are not inherently linked: the authors give examples of graphs that may exhibit strong heterophily yet only demand local feature aggregation, or conversely be highly homophilic but require messages to traverse many hops.

To address your point empirically, we have now retrained both ChebNet and our Stable‑ChebNet model on the Roman‑Empire and Amazon‑Ratings datasets, using the hyperparameter settings from Platonov et al. [3]. Encouragingly, both models reach performance on par with the best updated MPNN results reported in the paper, while noting that the hyperparameter tuning was not extensive and it is possible that we could reach even higher results. An interesting observation from the tables below is the fact that even at a higher receptive field K, the degradation of Stable-ChebNet’s signal is less than that of ChebNet, as can be seen at K=6 for the Roman Empire dataset.

Dataset: Amazon-Ratings

Dataset: Roman-Empire

Further validation on a newly released benchmark: We extend our evaluation to the recently published City‑Networks benchmark by Liang et al. [4], which comprises large-scale, transductive tasks based on real-world urban road networks and is specifically designed to test GNNs’ ability to capture long-range dependencies. The benchmarking results of that paper align with our findings and show (though without detailed analysis) that ChebNet performs well on long-range interactions given that it is often the best baseline and has a consistently high influence score, even on Ogbn-arxiv which we report in our paper. To further validate our model on real-world road networks, we ran our Stable-ChebNet on the Paris City-Networks data and compared it to vanilla ChebNet in the Table below.

These results highlight Stable‑ChebNet’s effectiveness in capturing long-range dependencies across both synthetic and large-scale real-world scenarios, all while maintaining parameter efficiency.

Clarifying Figure 1: We apologize for the confusion surrounding Figure 1. This figure shows, at each layer, the "temperature" of each node—that is, the magnitude (or "heat") of its signal after being processed by the filter. In the classical ChebNet (top row), high-order Chebyshev filters behave like a dissipative diffusion process: by step T, most nodes have nearly "cooled" to zero, meaning that their signals have diminished significantly. This indicates that information dissipates over layers, leading to unbounded dynamics where small perturbations may grow uncontrollably or vanish. In contrast, our Stable ChebNet (bottom row) uses an antisymmetric, non-dissipative update rule that preserves signal magnitude even at large T. As a result, information remains stable and well-conditioned throughout the layers. We acknowledge that "temperature" was not clearly defined in the original caption and will include this explanation in the revised version.

Expanding the Related Work Discussion: We appreciate the reviewer’s suggestion and will substantially enrich our discussion of rewiring strategies and Graph Transformers in the revision. In the main text’s Background section, we will introduce a broader spectrum of rewiring techniques and transformer-based graph architectures, highlighting how each approach addresses long-range dependency challenges. In particular, we will emphasize methods such as DRew for which we already include comparative runs alongside the benchmarked baselines in our tables. Several relevant transformer-based models are also represented in our main tables, including SPEXFormer, Exphormer, TIGT, and SAN+LapPE. These models reflect a range of strategies for overcoming long-range dependency and over-squashing issues in graph learning, and we will more clearly articulate how our approach relates to them. A more comprehensive comparison will be provided in the appendix, with key insights integrated into Section 2 where space allows.

Effect of Positional Encoding (and Virtual Node): We did in fact extend our peptide‑function experiments with both Laplacian positional encodings (LapPE) and random‑walk structural encodings (RWSE), but found that neither led to gains—instead, accuracy dipped by roughly 1–2 points and per‑epoch training time increased by 20–30 percent. We suspect two main factors: first, ChebNet’s polynomial filters already capture much of the same spectral information that LapPE explicitly provides, so appending handcrafted eigenvector features can introduce redundancy or even noise, leading to slight overfitting on small peptide graphs. Second, computing LapPE via partial eigendecomposition (and RWSE via truncated walk statistics) incurs nontrivial overhead—especially on batches of variable‑size peptide graphs—so the resulting slowdown outweighs any marginal benefit. Given these findings, we opted not to include positional encodings in our main table, but we will add a brief note in Table 5’s caption summarizing that neither LapPE nor RWSE improved peptide‑function performance and that both incurred noticeable computational cost.

Furthermore, in our preliminary experiments on the Peptides-func graph-level task, incorporating a Virtual Node did not lead to improved model performance, nor did the addition of positional encodings. We attribute this to the fact that both Stable-ChebNet and its vanilla version already capture the graph structure effectively and possess a sufficiently large receptive field, rendering the global Virtual Node largely redundant. The results, presented in the table below, show that the Virtual Node offers more benefit to GCN than to Stable-ChebNet.

We sincerely hope that our clarifications and revisions have addressed your concerns and prompted a reconsideration of your evaluation and score. We thank again the reviewer for their time and consideration.

[4] Liang et al. (2025). Towards Quantifying Long-Range Interactions in Graph ML. arXiv preprint https://arxiv.org/abs/2503.09008

[5] Adrián Arnaiz‑Rodríguez and Federico Errica (2025). Oversmoothing, “Oversquashing”, Heterophily, Long‑Range, and more: Demystifying Common Beliefs in Graph Machine Learning. Position paper published on https://arxiv.org/abs/2505.15547

I thank the authors for their response.

First, I would like to clarify that my suggestion regarding experiments on node-level tasks was not motivated by an interest in probing long-range capabilities, but rather by the goal of obtaining a more complete picture of the capabilities of (Stable-)ChebNet on these tasks:

The node-level datasets are also lacking, with only ogbn-proteins and ogbn-arxiv being used in the empirical evaluation. Since Stable-ChebNet improves signal propagation, I am wondering if it could also obtain better performance on heterophilic datasets, such as the ones introduced in [Platonov et al.];

Regarding the authors’ comments on node-level datasets:

our evaluation already includes several node-level prediction tasks. Specifically, the synthetic tasks

While these are indeed node-level tasks, I believe they are not a good proxy for real-world node-level applications. As the authors note, these are synthetic datasets primarily used to evaluate long-range capabilities. I maintain my view that ogbn-proteins and ogbn-arxiv are insufficient for a thorough real-world assessment of the proposed method. Additionally, the authors do not clarify why datasets such as PCQM-Contact from the LRGB benchmark are not included.

That said, I appreciate the inclusion of the Trees, Roman-Empire, Amazon-Ratings, and City-Networks datasets. I believe the experimental evaluation section is now in better shape. Furthermore, the discussion on the use of positional encodings is interesting and adds value.

At this point, I will maintain my score while following the ongoing discussion between the authors and Reviewer E5Qi, who I believe has similar concerns, and is raising some good points. I would like to observe the rest of the exchange before making a final decision.

I thank the authors for their rebuttal and discussions. They have done a very good job addressing most of the concerns, and I now believe that the paper is in a very good shape; therefore, I will recommend acceptance.

We sincerely appreciate the reviewer’s insightful feedback on our work. Thank you for highlighting our novel analysis of ChebNet’s limitations and our proposed solution, as well as recognizing that our method delivers performance on par with other state‑of‑the‑art approaches. We’re also grateful for your kind words about the clarity and quality of our writing. Your comments and score motivate us to further strengthen and refine this research. Below, we address the reviewer’s comments in detail.

Extension to different basis functions: Thank you for the insightful question. In this work, we focused on ChebNet due to its historical significance as the most well-known and widely used spectral GNN model. That said, a formal extension of our theoretical analysis to alternative bases (such as the ones discussed in [1,2]) would require revisiting the spectral norm and Jacobian dynamics in those settings. While we expect similar dynamics to emerge, a comprehensive treatment is outside the scope of this paper and is an exciting direction for future work. In theory, the non-dissipative aspect should generalize to other basis though we leave the analysis for separate work. Only then it would be interesting to address heterophily and compare different basis' ability to tackle a long-range, heterophilic graph given their ability to both propagate information in a stable manner and tackle different frequency levels depending on their filter properties which would prompt an interesting comparison across spectral basis (e.g Bernstein vs ChebNet).

Model behavior under normalization: We appreciate the reviewer’s suggestion and agree that applying normalization techniques such as LayerNorm or InstanceNorm could help alleviate some of the instabilities observed in high-order ChebNet by implicitly bounding feature magnitudes. However, we would like to emphasize that the internal mechanisms of such normalization layers are complex, often dataset-dependent, and their stabilizing effect on model dynamics is not fully understood from a theoretical standpoint. In contrast, our proposed approach, based on Euler discretization and antisymmetric parameterization, is a principled and interpretable framework for enforcing stability, with formal guarantees on the Jacobian spectrum and resulting signal propagation properties of the model. That said, we agree that further comparison would be valuable. We will include a brief discussion of this point in the revised version of the paper, and we plan to investigate the empirical effect of normalization-based strategies as part of our camera-ready submission or future work.

Isolation antisymmetric effect: Thank you for the insightful suggestion regarding component ablations. Following your recommendation, we conducted an additional experiment on the OGB‑Proteins benchmark to isolate the effect of antisymmetric weights in our model. Specifically, we evaluated a variant that enforces antisymmetry but omits the forward‑Euler discretization. This “antisymmetry‑only” model resulted in a significantly lower performance (72.2% test accuracy) compared to the full Stable‑ChebNet (79.5%), highlighting the importance of combining both antisymmetry and the discretization scheme for effective learning.

On Stable-ChebNet’s ability function approximation ability: We appreciate the reviewer addressing this concern. However, this point is not directly applicable to our method, as Stable-ChebNet does not alter the basis functions or the parameterization of the spectral filters used by ChebNet. The modification we propose applies solely to the propagation dynamics (i.e., how information flows through layers), by introducing a stable ODE-inspired formulation. As such, the filter expressivity and approximation capacity remain unchanged. We will make this clarification more explicit in the revised manuscript to avoid confusion on this point.

We sincerely hope that our responses and revisions have addressed your concerns. We once again thank the reviewer for their valuable time and consideration.

We sincerely thank the reviewer for their encouraging feedback. We appreciate the recognition of the clarity and utility of our visualizations. We are also grateful for the acknowledgement of our theoretical and empirical contributions, as well as our effort to address a gap in GNNs. Below, we address the reviewer’s comments in detail.

Clarifying the model’s figure: We apologize for the confusion around Figure 1; To clarify, in this figure we plot at each layer the temperature of each node—by which we mean the ‘heat’ or magnitude of its signal—propagated through the filter. In the classical ChebNet (top row), high‑order Chebyshev filters act like a dissipative diffusion: by step T, most nodes have “cooled” almost to zero (very low temperature), indicating that information has effectively leaked away and that small perturbations can blow up or vanish uncontrollably—i.e. unbounded dynamics. In contrast, our Stable ChebNet (bottom row) enforces an antisymmetric, non‑dissipative update so that heat (information) is retained even at large T, yielding bounded, well‑conditioned propagation across layers. The main aim of this figure was to shed light on the importance of developing an information-preserving system by drawing an analogy to heat dissipation. We agree that “temperature” was not defined clearly in the original caption, and we’ll incorporate exactly this explanation in the corrected version.

Comparison with S2GCN and real world setting: Although DRew and S2GCN achieve high AP on Peptides‑func, they both depend on expensive graph preprocessing steps: DRew must perform costly graph rewiring (e.g. all‑pairs shortest paths plus positional encoding construction) before training, while S2GCN requires a full Laplacian eigendecomposition for its spectral filter basis. These operations impose prohibitive runtime and memory overhead on large or evolving graphs. By contrast, Stable‑ChebNet delivers competitive long‑range accuracy entirely within the standard Chebyshev‑polynomials which approximate the Laplacian eigendecomposition: each layer executes sparse, polynomial‑filter updates in O(K·|E|) time, without any rewiring, eigencomputations, or additional encodings. This keeps training times and memory costs on par with a vanilla ChebNet, preserves end‑to‑end differentiability, and requires no extra implementation complexity, making Stable‑ChebNet both practically scalable and straightforward to deploy. The cost of using ChebNet compared to DRew is highlighted in Figure 2, which further motivates the need for a performant ChebNet on long-range tasks given its simplicity.

While the community still lacks gold‑standard long‑range GNN benchmarks, we evaluated Stable‑ChebNet in complementary scenarios covering both graph and node-level tasks to demonstrate its applicability on real‑world and synthetic data. On the Peptides‑func benchmark, which highlights distant residue interactions, Stable‑ChebNet is on par with sota methods. On the OGB‑Proteins dataset where graphs can exceed 100k nodes, it achieves accuracy on par and often better than Graph Transformers, proving that stable information can compete with Transformers and other models of high complexity.

Testing on a newly released benchmark: We note that very recently, Liang et al. [4] publicly released City‑Networks, a large‑scale transductive benchmark designed explicitly to probe long‑range dependencies in GNNs, derived from real-world city road networks.

Aligned with our findings, the benchmarking results of that paper show (though without detailed analysis) that ChebNet performs well on long-range tasks; it is often the best baseline and has a consistently high influence score, even on Ogbn-arxiv which we also report in our paper. To further validate our model on real-world road networks, we ran our Stable-ChebNet on the Paris City-Networks data and compared it to vanilla ChebNet in the Table below.

These results underscore Stable‑ChebNet’s ability to capture long‑range dependencies in both synthetic and large‑scale real‑world settings using parameter‑efficient operations.

Additional benchmarks: In line with the reviewer’s suggestion, we will additionally include results for the Bundle Neural Network (BuNN) from Bamberger et al. [2] across the common benchmarks, allowing for a more comprehensive comparison. In addition, we would like to clarify that our submission already includes a set of Graph Property Prediction tasks, namely Diameter, SSSP, and Eccentricity, designed to test long‑range information propagation (see Section 4 and Table 1). We believe these tasks are important to evaluate the long‑range capabilities of GNNs.

On the inclusion of heterophilic datasets: We agree that examining the relationship between label heterophily and long‑range dependency is valuable. In this work, we do not benchmark on common heterophilic datasets as we believe there is not yet a clear connection between a graph being heterophilic and the presence of long-range dependencies — the latter being the main challenge this paper aims to address. One recent position paper sheds light on this issue [5], emphasizing that heterophily and long-range dependencies are not inherently linked as a graph can be heterophilic and require only local reasoning, or homophilic and require long-range reasoning.

To further investigate this phenomenon, we have followed your recommendation and trained ChebNet and Stable‑ChebNet on the Roman‑Empire and Amazon‑Ratings datasets using the hyperparameters from Platonov et al. [3]. We find that both vanilla ChebNet and Stable-ChebNet can indeed match the highest performances reported in the Table with updated MPNN performances. Interestingly, we find that on both Amazon-Ratings and Roman-Empire, we converge towards higher performances at relatively lower hop neighborhoods, indicating a more local aspect to these heterophilic graphs.

Dataset: Amazon-Ratings

Dataset: Roman-Empire

Emphasizing the importance of the Barbell dataset: While Barbell‐like structures might seem like a purely synthetic scenario, it actually captures a very common challenge in real‑world networks that are not well represented in the GNN community’s long-range benchmarks; One suitable example is two densely interconnected communities joined by just one or a handful of bridging connections. For instance, in infrastructure graphs we might have two urban centers whose local roads are very dense yet connected to each other by just one main highway. In protein‐interaction networks, functional modules such as signaling pathways can be highly interconnected internally, yet communicate with other modules through very few cross‐module interactions. These cases all mirror the barbell topology: high intra‐module cohesion plus a narrow inter‐module bottleneck. This creates exactly the same narrow bottleneck that standard GNNs struggle to traverse without squashing information. Hence, despite its simplicity, the barbell graph provides a useful stress test for how well GNN architectures can propagate information across real‐world “bridge” edges without oversquashing or loss of signal fidelity by just adjusting clique size.

The Role of Hyperparameter Tuning: Thank you for your thoughtful suggestion and for pointing us to [1]. We have carefully considered the findings and discussions presented in that work. In fact, we had already examined [1] and noted the improvements in performance achieved through more rigorous hyperparameter tuning and architectural modifications such as the inclusion of additional layers or normalization techniques. At the time of our experiments, we adhered to the benchmark settings commonly used in prior work to ensure a fair and consistent comparison. While we did observe that deeper GNN architectures can lead to performance gains, we consciously operated within a parameter budget to highlight the efficiency of our model. We followed a similar protocol for Peptides func where we were bound to 500k params, above which we could reach near 72 AP on Peptides-func.

Indeed, the improvements reported in [1], especially for GCN and GAT on the OGB-Proteins dataset—come with significantly increased parameter counts (on the order of ~1M and ~3M, respectively). In contrast, our ChebNet-based model uses only ~80K parameters, yet still manages to outperform even the 1M-parameter GCN variant on the same dataset. This demonstrates the effectiveness of our approach under a constrained parameter budget. That said, we acknowledge that incorporating ideas from [1] could further improve our model’s performance and plan to explore these enhancements in future work.

We sincerely hope that our revisions have effectively addressed your concerns and encouraged a reconsideration of your evaluation and score.

[4] Liang et al. (2025). Towards Quantifying Long-Range Interactions in Graph ML. arXiv preprint https://arxiv.org/abs/2503.09008

[5] Adrián Arnaiz‑Rodríguez and Federico Errica (2025). Oversmoothing, “Oversquashing”, Heterophily, Long‑Range, and more: Demystifying Common Beliefs in Graph Machine Learning. Position paper published on https://arxiv.org/abs/2505.15547