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REVIEW 5 major objections 6 minor 33 references

Towards Scalable and Deep Graph Neural Networks via Noise Masking

T0 review · 5 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that over-smoothing in simplified graph neural networks is driven not by propagation depth itself but by redundant low-hop information accumulating inside each deeper hop, and that a plug-and-play noise-masking…

desk verdict A genuinely plausible noise-masking idea for scalable GNNs, but the central algorithm is unspecified and, read literally, infeasible at the claimed scale. read the letter →

arxiv 2412.14602 v2 pith:MU47T4XC submitted 2024-12-19 cs.LG cs.AI

Yuxuan Liang , Wentao Zhang , Zeang Sheng , Ling Yang , Quanqing Xu , Jiawei Jiang , Yunhai Tong , Bin Cui This is my paper · ORCID
classification cs.LGcs.AI
keywords graphneuralnetworksover-smoothingmodelsimplificationnoisemaskingrandomwalkPersonalizedPageRanknodeclassificationscalability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Model-simplification graph neural networks precompute propagated features once, but their accuracy collapses as the number of propagation hops grows. This paper argues that the collapse is caused by noise: each higher hop re-delivers information already captured by lower hops, and this redundancy accumulates and smooths node representations together. To fix it, the authors propose RMask, a module that identifies noise through shortest-path distances and masks it away, then uses biased random walks to sample only the pure information of each hop. Plugged into existing methods such as SIGN, S2GC, GBP, and GAMLP, RMask keeps accuracy stable well past 20 hops and reports consistent gains on six datasets, while making pre-processing sparse and parallel enough to cut end-to-end time.

What carries the argument

The machinery is the de-noise matrix $M^h$, whose entry is 1 when the shortest-path distance from the target node is exactly $h$ and 0 when it is smaller, combined with a random walk $\mathrm{RW}(G, M^h, T, S)$ that samples only unmasked nodes using Personalized PageRank scores $S = \alpha (I - (1-\alpha)\hat{A})^{-1}$ as edge weights. The matrix identifies which nodes at each hop are redundant, the importance scores steer the walk toward informative neighbors, and the random-walk formulation decouples hops so they can be processed in parallel and sparsely, replacing the dense serial matrix propagation that dominates pre-processing.

What would settle it

Run RMask on ogbn-papers100M while timing only the construction of the de-noise matrix; if building it requires an all-pairs shortest-path computation whose wall-clock cost matches or exceeds the original serial propagation, the claimed sub-linear pre-processing is not achieved.

Watch

Extended reading notes

Core claim

The central claim is that continuous P operations, the repeated propagation steps shared by all model-simplification GNNs, inject noise into every hop, and this noise, not depth per se, is what triggers over-smoothing. RMask replaces the P operation with a de-noise random walk: a de-noise matrix $M^h$ marks a neighbor as noise unless the shortest-path distance from the target is exactly $h$, and a biased random walk guided by Personalized PageRank importance scores samples the remaining nodes. The authors report on Cora, Citeseer, Pubmed, ogbn-arxiv, ogbn-products, and ogbn-papers100M that SIGN, S2GC, GBP, and GAMLP each improve when their propagation stage is swapped for RMask, that accuracy no longer falls as hops increase to 30, and that pre-processing drops to a smaller fraction of end-to-end time, with S2GC+RMask reported 2.9-4.9x faster than S2GC alone.

Load-bearing premise

For the method to work as advertised, identifying which nodes are noise at each hop must be far cheaper than the dense propagation it replaces; the paper assumes this can be done on graphs with over a hundred million nodes without computing all distances between all pairs.

Editorial extensions

If this is right

  • Existing model-simplification GNNs can be extended to 20-30 propagation hops on ogbn-arxiv without the accuracy collapse normally seen beyond a dozen hops.
  • Pre-processing becomes a smaller share of end-to-end time; the paper reports 2.9-4.9x end-to-end speedups for S2GC+RMask across six datasets.
  • The benefits are larger on sparse graphs: with heavily dropped features, edges, or labels, RMask-equipped models degrade more slowly than their original versions.
  • The noise-masking view is orthogonal to other over-smoothing remedies, so RMask can be combined with methods like DAGNN and still improve accuracy.
  • Because RMask is plug-and-play, any future model-simplification GNN with a different combination rule can adopt the same masked propagation without changing its training model.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same distance-based mask could be applied to message passing during training, not just pre-processing; if the noise diagnosis is right, masking inside full GNN layers should also slow over-smoothing. This is an extension the paper does not test.
  • On graphs where exact shortest-path distances are too expensive, the de-noise matrix could be approximated with random-walk hitting times or landmark distances; whether accuracy survives the approximation is an open question.
  • The redundancy ratio between consecutive hop neighborhoods could serve as a dataset-level predictor of how much depth a model can tolerate before over-smoothing.
  • Comparing RMask to a plain exclusive-hop random walk with the same sampling budget would isolate whether the benefit comes from the masking step or from the random-walk reformulation itself.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper proposes RMask, a plug-and-play module for model-simplification GNNs such as SGC, SIGN, S2GC, GBP, and GAMLP. The central claim is that over-smoothing in deep propagation is caused by 'noise information'—redundant lower-hop information contained in each propagation step—and that this noise can be removed by a de-noise matrix M^h built from shortest-path distances, combined with biased random walks guided by Personalized PageRank. The authors report consistent accuracy improvements over the original baselines on six datasets (Cora, Citeseer, Pubmed, ogbn-arxiv, ogbn-products, ogbn-papers100M) and claim large speedups in pre-processing. The method is presented as a scalable replacement for the Propagation operation, with complexity analysis in Table 1 and ablations in Table 3.

Significance. If the method worked as described, RMask would be a practically useful plug-in: it addresses a real limitation of model-simplification GNNs, is evaluated on standard public benchmarks, and the idea of treating redundant low-hop information as noise is interesting and orthogonal to existing over-smoothing remedies. The consistent gains in Table 2 and the orthogonal combination with DAGNN in Table 3 are credible strengths. However, the central mechanism is underspecified to the point of being unverifiable: the de-noise matrix in Eq. (2), the random walk function in Eq. (3)/(5), and the Personalized PageRank inverse in Eq. (4) are not given feasible algorithmic constructions, and the complexity analysis omits the dominant costs. Because the claimed scalability and the reported results rest on these primitives, the significance cannot be assessed as the paper stands.

major comments (5)
  1. [Noise Information Identification, Eq. (2)] The de-noise matrix M^h is defined via exact shortest-path distances: m_ij = 1 when distance(v_i, v_j) = h and 0 when distance(v_i, v_j) < h. For ogbn-papers100M, which has 111,059,956 nodes and 1,615,685,872 edges (Table 4), no feasible algorithm is given for computing these distances. A literal reading requires BFS from every node or all-pairs shortest paths, i.e., O(NM) in the worst case, which is intractable at this scale. Algorithm 1 line 1 simply states 'M = union M^h with Eq. (2)' without specifying any approximation, sampling, or data structure. The complexity in Table 1 omits the cost of constructing M^h entirely, so the scalability thesis is unsupported by the stated method.
  2. [Neighbor Nodes Importance Assignment, Eq. (4)] Eq. (4) defines S = alpha(I - (1-alpha) Ahat)^-1, which is a dense N x N matrix inverse. On graphs with millions or hundreds of millions of nodes, materializing S as a dense matrix is impossible. The citation to approximate Personalized PageRank does not bridge this gap, because Algorithm 1 line 2 invokes Eq. (4) without specifying how the inverse is approximated, truncated, or stored. Table 1 again omits the preprocessing cost of Eq. (4), so the reported speedups in Figure 5(c) cannot be reconciled with the stated complexity.
  3. [RMask Pipeline, Eqs. (3) and (5)] The random walk function RW is never formally defined. The paper does not specify the transition probabilities, the number of steps, the restart behavior, how the de-noise matrix M^h is combined with the importance matrix S, or how the T walks are aggregated. Algorithm 1's line 'W^h = union_t W_t^h / T' is not a well-defined operation on matrices. This makes the core mechanism of the method irreproducible and prevents verification of the 'de-noise random walk' claim.
  4. [Motivation, Figure 2] The causal claim that noise inside P is the cause of over-smoothing is not established. Eq. (2) defines noise operationally as any node within distance strictly less than h, but the evidence in Figure 2(b) is only a correlation between the proportion of redundant information and the Graph Smoothness Level as the hop count grows. There is no controlled experiment isolating whether masking those nodes, rather than changing the effective propagation kernel or the total number of reachable nodes, is responsible for the accuracy improvements. A formal definition of over-smoothing and a derivation of how the hard mask in Eq. (2) reduces it are needed.
  5. [Experiments, Table 2 and Figure 5] The empirical comparison is only against each baseline model's own original version; there is no comparison to other recent scalable GNNs or to state-of-the-art results on the OGB datasets. More importantly, the claimed speedups in Figure 5(c) (2.9x to 4.9x) are not accompanied by end-to-end timings that include the construction of M^h and S. Without a reproducible implementation or a careful accounting of these costs, the trade-off claim in Figure 5(a) is not convincing.
minor comments (6)
  1. [Introduction] There is a typo in 'Contirbutions' in the Contributions paragraph.
  2. [Throughout] The word 'propagation' is misspelled as 'propogation' in several places, including the abstract and the introduction.
  3. [Table 2] The values for SIGN+RMask on Cora are printed as '84.3 ± 0.684.3 ± 0.684.3 ± 0.6'—a formatting error that also appears in other rows; the table should be regenerated with clean alignment.
  4. [Figure 5(a)] The horizontal axis label reads 'Ramdom walk numbers' instead of 'Random walk numbers', and the legend uses 'SSGC' while the text refers to S2GC.
  5. [Algorithm 1] Line 9 has a bracket mismatch: 'concatenate([Wh1||[Wh2||...])' is missing a closing bracket and the intended concatenation syntax is unclear.
  6. [Appendix, Hyperparameters] The hyperparameter search ranges are described only for small datasets and large datasets together, but it is not stated which propagation steps and random walk counts were selected for each dataset and each baseline; this is needed for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: RMask is evaluated against external benchmarks and its de-noise matrix is defined independently of the prediction target.

full rationale

RMask's derivation does not reduce to its own inputs. The de-noise matrix M^h (Eq. 2) is defined by shortest-path distances, and the random-walk matrices W^h are built from it before any accuracy measurement; the accuracy comparison is then run on held-out splits of six external datasets against external model-simplification baselines (SIGN, S2GC, GBP, GAMLP). Hyperparameters and propagation depths are selected by grid search on validation performance, not fitted to the reported test outcomes, so no prediction is forced by construction. The only same-author citations (GAMLP and NAFS) are used as a baseline and for the standard stationary-state fact about normalized adjacency powers, respectively; the central claim does not depend on either being true. The scalability objection raised by a literal reading of M^h on ogbn-papers100M is a feasibility/correctness concern about an omitted algorithm and omitted complexity terms, not a circularity: if the primitive is intractable the method is unsupported, but the method would not thereby be equivalent to its inputs. No equation in the paper is both premise and conclusion, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 3 assumptions · 2 invented entities

The central claim rests on a small set of tuning parameters (T, alpha, H) and on three unproven assumptions: that lower-hop overlaps are harmful noise, that randomized walks approximate the mask well, and that PPR can be computed at scale. The invented 'noise information' and 'de-noise matrix' are paper-defined constructs without independent empirical handles.

free parameters (3)
  • number of random walks T = grid search over {5, 10, 15, 20, 25, 30}
    Controls the accuracy-efficiency trade-off; results improve with T, so the reported accuracy depends on selecting a favorable T.
  • restart probability alpha = not stated in the paper
    Used in Personalized PageRank (Eq. 4) for neighbor importance; its value is chosen by hand, not derived.
  • propagation hops H = grid search over {6-15}; depth experiments up to 30
    The paper tunes the number of hops per dataset via grid search; deeper exploration is the central scenario.
assumptions (3)
  • domain assumption Adjacency-matrix powers overlap lower-hop supports, and these lower-distance entries are 'noise' that should be removed.
    Motivation section and Figure 2 present this as a new finding, but it is an unstated assumption that masking these entries improves learning.
  • ad hoc to paper Random walks with T samples and the de-noise matrix approximate the exact masked propagation well enough to preserve accuracy.
    Eqs. (3)-(5) provide no convergence analysis or error bound for the RW function.
  • standard math Personalized PageRank S can be computed approximately at scale (citing Bojchevski et al. 2020) and can guide random walks effectively.
    Eq. (4) relies on existing approximation techniques, but the integration with the de-noise mask is not analyzed.
invented entities (2)
  • noise information
    purpose: Postulated redundant low-hop content within each propagation hop that causes over-smoothing.
    Defined via the paper's own de-noise matrix; no external falsifiable measurement is provided, and the noise proportion in Figure 2 is never defined.
  • de-noise matrix M^h
    purpose: Binary mask marking nodes at exact distance h as pure and shorter-distance nodes as noise.
    Introduced in Eq. (2); its efficient computation for large graphs is not specified, and it has no outside validation.

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Cite this review

Pith. "Pith review of Towards Scalable and Deep Graph Neural Networks via Noise Masking." pith.science (2026). https://pith.science/paper/MU47T4XC

@misc{pith2026241214602,
  author       = {Pith},
  title        = {Pith review of: Towards Scalable and Deep Graph Neural Networks via Noise Masking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MU47T4XC}},
  note         = {Machine review of arXiv:2412.14602}
}
read the original abstract

In recent years, Graph Neural Networks (GNNs) have achieved remarkable success in many graph mining tasks. However, scaling them to large graphs is challenging due to the high computational and storage costs of repeated feature propagation and non-linear transformation during training. One commonly employed approach to address this challenge is model-simplification, which only executes the Propagation (P) once in the pre-processing, and Combine (C) these receptive fields in different ways and then feed them into a simple model for better performance. Despite their high predictive performance and scalability, these methods still face two limitations. First, existing approaches mainly focus on exploring different C methods from the model perspective, neglecting the crucial problem of performance degradation with increasing P depth from the data-centric perspective, known as the over-smoothing problem. Second, pre-processing overhead takes up most of the end-to-end processing time, especially for large-scale graphs. To address these limitations, we present random walk with noise masking (RMask), a plug-and-play module compatible with the existing model-simplification works. This module enables the exploration of deeper GNNs while preserving their scalability. Unlike the previous model-simplification works, we focus on continuous P and found that the noise existing inside each P is the cause of the over-smoothing issue, and use the efficient masking mechanism to eliminate them. Experimental results on six real-world datasets demonstrate that model-simplification works equipped with RMask yield superior performance compared to their original version and can make a good trade-off between accuracy and efficiency.

Figures

Figures reproduced from arXiv: 2412.14602 by the authors.

Figure 1
Figure 1. Example of two limitations in model-simplification GNNs. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Observation and our insight. Related Work Sampling Graph Neural Networks. Over the past few years, the graph convolution operation introduced by GCN has increasingly become the standard form in most GNN ar￾chitectures (Kipf and Welling 2017). GCN adopts a layer￾wise propagation rule and a multi-layer non-linear fea￾ture transformation network to form the new representation. However, this approach has expensive messa… view at source ↗
Figure 3
Figure 3. The architecture of proposed RMask. Motivatoin In this section, we make a deep analysis of the two limita￾tions that exist in model-simplification GNNs and then pro￾vide our insight to help us design the architecture of RMask. Study on Noise Information. Model-simplification GNNs implement P operations by continuously performing matrix product operations on the initial normalized matrix Aˆ using Eq. (1) to increase … view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Test accuracy on ogbn-arxiv along the propagation [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: (a) Trade-off between efficiency and accuracy on ogbn-products. (b) Time cost breakdown. (c) Speedup analysis. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Test accuracy on the Pubmed dataset under different levels of feature, edge and label sparsity. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

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Reviewed August 11, 2026 · model on record in the stance chip above.