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Locality-Aware Multiresolution Graph Spectral Filtering to Mitigate Oversmoothing and Oversquashing. |
Soundness: 2: fair
Presentation: 2: fair
Contribution: 2: fair
Rating: 2: reject
Confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. |
This paper presents a hierarchical, multiresolution framework called Hierarchical Spectral Learning (HSL) for mitigating oversmoothing and oversquashing in graph neural networks. The key idea is to construct a locality-aware, degree-weighted Haar basis from a multi-view Laplacian that jointly captures topology and feature affinity. The model introduces a diffusion barrier to separate incompatible nodes and learns hierarchical spectral filters that adaptively combine low- and high-pass information at multiple resolutions.
1. The introduction of a diffusion barrier and degree-aware local Haar basis provides a principled approach to enforce locality in spectral filtering.
2. In the experiments, HSL achieves consistent improvements over strong baselines on both heterophilous and homophilous datasets for node and graph classification.
1. The motivation for exploring multiresolution graph learning as a way to prevent oversmoothing and oversquashing is not clearly explained.
2. The readability of the manuscript is poor; it is difficult to follow. The notations and symbols are complex and sometimes inconsistent.
3. The overview of the HSL framework is unclear, and the overall procedure for implementing HSL is not well described.
4. The experimental results are not reproducible. The authors need to provide more implementation details or direct examples to clarify how the results in the tables and figures can be reproduced.
5. The computational complexity analysis is unclear. In addition, the experimental studies do not clearly demonstrate how efficient HSL is compared with other baseline methods.
1. Can the authors provide an intuitive interpretation or visualization of the learned multiresolution spectral filters (e.g., frequency response plots or spatial localization examples) to help understand what each resolution captures?
2. How does HSL relate to or differ from other multiresolution or hierarchical graph frameworks, such as graph wavelet networks, framelet-based methods, or hierarchical message passing networks? |
Fully AI-generated |
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Locality-Aware Multiresolution Graph Spectral Filtering to Mitigate Oversmoothing and Oversquashing. |
Soundness: 3: good
Presentation: 1: poor
Contribution: 2: fair
Rating: 4: marginally below the acceptance threshold
Confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. |
This paper proposes a Locality-Aware Multiresolution Graph Filtering framework called **Hierarchical Spectral Learning (HSL)** to address oversmoothing, oversquashing, and hub domination in spectral Graph Neural Networks (GNNs). HSL leverages a multi-view Laplacian (fusing topology and feature affinity) to construct diffusion barriers, recursively builds a hierarchical tree via balanced spectral coarsening, and designs strictly local, degree-aware orthonormal Haar bases for diagonal spectral filtering. It achieves linear computational complexity and demonstrates state-of-the-art (SOTA) performance on node classification (up to 3% gain on heterophilous graphs) and graph classification (up to 7% gain on MUTAG) across standard benchmarks.
1. HSL introduces a novel "locality-first" multiresolution paradigm that combines multi-view geometric information (topology + feature affinity) with local Haar basis filtering—filling gaps in existing spectral GNNs that rely on global, dense eigenbases. The integration of diffusion barriers to prevent spurious co-clustering and balanced spectral relaxation for coarsening is a creative combination of spectral learning and hierarchical graph pooling.
2. The paper provides rigorous theoretical guarantees (5 theorems) to formalize the mitigation of hub domination, oversmoothing, and oversquashing. Empirically, it validates HSL on diverse benchmarks (homophilous/heterophilous node graphs, biomolecular/chemical/social graph classification datasets) and conducts ablation studies to confirm the necessity of key components (e.g., diffusion barriers, degree-aware Haar bases).
3. HSL addresses critical scalability limitations of prior spectral methods (e.g., EigenPool’s \(O(n^3)\) complexity) by achieving linear per-layer complexity (\(O(md + nd)\)), making it applicable to large graphs. Its ability to adapt filtering (low-pass for homogeneous regions, high-pass for semantic boundaries) also enhances robustness to region-specific heterophily in real-world graphs.
1. The paper uses "conductance" and "local homophily ratio" as inputs to the lightweight network $g_\theta$ for learning Laplacian mixing weights $\alpha_C$, but fails to specify their exact computational definitions: - Conductance is not tied to a standard metric (e.g., the ratio of cut edges to total edges in a cluster). - "Local homophily" is not clarified (e.g., whether it uses label-based $H_{lab}$ or feature-based cosine similarity). Additionally, the architecture of $g_\theta$ (e.g., number of layers, activation functions) is unmentioned, risking inconsistent reproducibility across different implementations.
2. The mixing weights $\alpha_C$ are claimed to balance topology and feature contributions, but no analysis is provided on their distribution across heterogeneous scenarios (e.g., high-heterophily Chameleon vs. high-homophily Cora). It remains unproven whether $\alpha_C$ adaptively adjusts (e.g., reducing $\alpha_C^{(2)}$ for feature-noisy graphs) to align with data characteristics.
3. Theorem 2 requires $\lambda \geq \Delta_{mix}/\Psi_{min}$ (where $\Delta_{mix}$ is the mixed-geometry gap and $\Psi_{min}$ is the minimal incompatibility mass) to avoid spurious co-clustering. However, $\Delta_{mix}$ and $\Psi_{min}$ depend on **ground-truth clusters $S^*$**, which are unknown in real-world tasks (e.g., molecular graphs, social networks). The paper uses $\lambda=0.1$ in experiments but does not explain if this value is empirically tuned or estimated via unsupervised methods, nor does it include a sensitivity analysis (e.g., how performance changes with $\lambda=0.01, 0.5$).
4. While HSL claims linear complexity, it only tests scalability on REDDIT-12K (average 233 nodes per graph). There is no comparison of training time/memory overhead with baselines (e.g., EigenPool $O(n^3)$, DiffPool $O(n^2)$) on **extra-large graphs** (e.g., Amazon Reviews with $10^5+$ nodes). Additionally, the coarsening threshold $h$ (stopping condition for hierarchical tree construction, i.e., $|V^{(L)}| \leq h$) is not analyzed—no experiments explore how $h=10, 50$, or other values trade off performance and computational efficiency.
see weaknesses |
Fully AI-generated |
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Locality-Aware Multiresolution Graph Spectral Filtering to Mitigate Oversmoothing and Oversquashing. |
Soundness: 2: fair
Presentation: 2: fair
Contribution: 2: fair
Rating: 2: reject
Confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked. |
The paper proposes a locality-aware hierarchical spectral framework that constructs local orthonormal Haar bases and uses multi-view Laplacians to mitigate “hub domination”, oversmoothing and oversquashing.
The paper tackles an important problem -- the limited expressive power of GNNs when dealing with heterophilous graphs.
(1) The paper claims that existing GNNs suffer from a “non-orthogonal bias,” yet most spectral GNNs (including those designed for heterophilous graphs) are grounded in Laplacian eigendecomposition, where eigenvectors are orthogonal by definition.
(2) The paper attributes scalability issues of prior works to explicit eigendecomposition, overlooking that many spectral GNNs employ polynomial approximations that avoid such explicit computations and scale linearly with graph size.
(3) The central motivation -- that existing models suffer from a “hub domination” problem -- is not rigorously demonstrated. In Figure 1 and the accompanying explanation, the observed behavior could also reflect high-frequency interactions rather than domination. The authors should more carefully define this phenomenon.
(4) The paper overlooks several closely related node-adaptive GNNs that also perform local filtering [1,2,3]. Moreover, the evaluation is limited to small or biased benchmarks, while larger and more balanced datasets should be included [4].
[1] Node-wise diffusion for scalable graph learning
[2] Graph neural networks with diverse spectral filtering
[3] Rethinking node-wise propagation for large-scale graph learning
[4] A critical look at the evaluation of gnns under heterophily: are we really making progress?
See weaknesses. |
Lightly AI-edited |
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Locality-Aware Multiresolution Graph Spectral Filtering to Mitigate Oversmoothing and Oversquashing. |
Soundness: 1: poor
Presentation: 2: fair
Contribution: 2: fair
Rating: 2: reject
Confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked. |
This paper improves existing spectral GNNs that filter graph signals from a global perspective. In these models, the diversity of filters required in different local spatial regions cannot be easily specified. To address this issue, the paper proposes a hierarchical spectral learning approach that distinguishes local clusters which do not share the same filter pattern as their neighbors and forms a multi-resolution hierarchy tree. This structure allows smaller regions to be distinctive while, at a coarser level, sharing the same filter.
1. The hub domination fact, as demonstrated in Figure 1, serves as a good motivation for the work, and the proposal aligns closely with it.
2. The presentation of the methodology, with rigorous justifications, seems solid.
1. The examples on real world datasets for demonstrating the hub domination problem are missing, which makes the rather small improvements on graph and node classification tasks less convincing.
2. From my understanding, the graph classification task is not ideal for evaluating the proposal of this paper, as it is more about identifying local details of a large graph, while the pooling function used for graph level tasks might reduce the usefulness of such adjustments. In addition, for node classification tasks, the numbers reported in Table 2 miss important strong baselines such as GCNII.
3. I also did not see the evaluations on oversmoothing and oversquashing mentioned in the title. Therefore, I think the overall empirical evaluation is weak and not very closely tied to the motivation. Please first justify the existence of these issues in real world scenarios.
Please see the weaknesses above. |
Fully human-written |
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Locality-Aware Multiresolution Graph Spectral Filtering to Mitigate Oversmoothing and Oversquashing. |
Soundness: 2: fair
Presentation: 3: good
Contribution: 2: fair
Rating: 6: marginally above the acceptance threshold
Confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. |
This paper introduces Hierarchical Spectral Learning (HSL) to prevent oversmoothing and over-quashing in graph neural networks. The HSL estimates diffusion neighborhoods and coarsens the graph into a hierarchy for multi-scale representation. The local degree-aware block-sparse Haar basis is designed to provide an orthonormal decomposition that separates global averages, inter-cluster contrasts, and intra-cluster variations without leakage. This paper provides a formal analysis of hub domination and offers theoretical guarantees. The proposed HSL achieves SOTA results on several challenging node and graph classification benchmarks, demonstrating a particularly strong performance on heterophilous graphs.
1) This paper is easy to follow.
2) The concept of a diffusion barrier as an explicit penalty in the spectral clustering objective is a creative and well-motivated way to enforce locality.
3) This paper goes beyond simply applying the predefined wavelets by constructing an adaptive Haar basis that respects the learned multiscale structure of graph.
4) HSL is shown to achieve SOTA results on several challenging node and graph classification benchmarks, with a particularly strong performance on heterophilous graphs.
1) The Haar wavelet introduced in the paper depends on the node indices and therefore does not satisfy the permutation invariance on graphs.
2) The hierarchical GNNs and spectral methods are not new.
3) There are several typos, and some variables are not explicitly defined in the paper. In addition, the ranges of some subscripts are not specified, which increases the difficulty to read. For example, in Line 252, it should be $L^{mix,C}$ rather than $ L_{mix,C}$. In Eq. 4, $L^{(k)}$ is not defined. In Line 464, $d$ is defined as the feature dimension, while the $d_l$ is not explained in Line 270 and $d_i^{(l)}$ in Line 308 denotes the degree mass.
4) Lack of citations for the methods compared in Table 1 and Table 2.
5) Lack of comparison of latest works. For example, the comparison methods were all published before 2022 in the graph classification.
1) What are the advantages of the diffusion barrier combined with the Haar wavelet method as compared to directly using the heat kernel wavelet method?
2) Graph wavelets are generally required to satisfy the permutation invariance. Can the authors explain the rationale behind the design of the Haar wavelet proposed in the paper.
3) Please explain in detail the dimensions and meanings of each variable in Eq. 4, for example, whether $\phi_C$ is a scalar and $g_\theta(\phi_C)$ is a two-dimensional vector. |
Fully human-written |