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REVIEW 5 major objections 5 minor 48 references

The Oversmoothing Fallacy: A Misguided Narrative in GNN Research

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper argues that deep GNN performance collapse is a vanishing-gradient problem, not oversmoothing.

desk verdict Provocative and useful, but its central attribution experiment runs on untrained Glorot nets and cannot yet separate zero-collapsing from oversmoothing. read the letter →

arxiv 2506.04653 v1 pith:PWVYR7NM submitted 2025-06-05 cs.LG

MoonJeong Park , Sunghyun Choi , Jaeseung Heo , Eunhyeok Park , Dongwoo Kim This is my paper
classification cs.LG
keywords oversmoothinggraphneuralnetworksvanishinggradientzero-collapsingdeepGNNsresidualconnectionsbatchnormalizationnodesimilarity
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

This paper argues that the standard narrative blaming oversmoothing for the failure of deep graph neural networks is largely a misdiagnosis. Decomposing each GNN layer into aggregation, linear transformation, and nonlinear activation, it finds that the transformation and activation steps, not the aggregation over neighbors, drive node embeddings toward the zero vector in deep networks. That zero-collapsing is the familiar vanishing-gradient problem of ordinary neural networks, and the paper shows that oversmoothing proper can be escaped by a trained GCN. If the argument holds, deep GNNs do not need graph-specific fixes: classical residual connections plus batch normalization suffice, and the paper demonstrates GCNs trained to 1,024 layers with stable accuracy.

What carries the argument

The central machinery is a stepwise ablation that splits each GNN layer into aggregation (A), linear transformation (T), and nonlinear activation ($\sigma$) and measures how three node-similarity metrics decay for each subset; this isolates which step drives the collapse. The paper also relies on the distinction between two convergence definitions, degree-scaled convergence for GCNs and uniform convergence for GATs, with the zero vector as a special case that made the two easy to confuse. The residual-connection-plus-batch-normalization recipe then serves as the practical instrument showing that the collapse is optimizable.

What would settle it

Re-run the stepwise node-similarity measurements on a deep GCN using trained weights or a ReLU-adapted initialization: if the aggregation-only variant decays as fast as the full network, or if deep trained networks without residual connections retain performance under that initialization, the paper's attribution of the collapse to transformation and activation would be refuted.

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Extended reading notes

Core claim

The paper's central claim is that prior work confused two distinct phenomena: true oversmoothing, in which embeddings converge to a node-degree-scaled or uniform limit, and zero-collapsing, in which the linear transformation and ReLU activation drive all embeddings toward the zero vector. Measured on untrained 128-layer GCNs and GATs under the default initialization, the aggregation step alone produces only mild decay of three standard node-similarity measures, while the combination of transformation and activation reproduces the full exponential decay; histograms show features collapsing to zero within a few layers. The authors conclude that the exponential oversmoothing reported in the literature is mostly a vanishing-gradient artifact, that a GCN with all node features initialized identically can still be trained to near-baseline accuracy, and that skip connections plus batch normalization, classics for vanishing gradients, allow very deep GCNs to train without degradation.

Load-bearing premise

The step-by-step verdict that aggregation is nearly harmless comes from measuring node similarity in untrained networks under one default weight-initialization scheme, and the appendix shows the decay rates change substantially under a different initialization, so the attribution may not hold for trained networks.

Editorial extensions

If this is right

  • Exponential collapse of node similarity in GCNs and GATs is mostly an artifact of transformation plus ReLU activation under the default initialization, not of message passing.
  • A GCN whose embeddings are already perfectly smoothed (all node features identical) can still be trained to near-baseline accuracy, so oversmoothing alone does not block learning.
  • Adding skip connections and batch normalization lets GCNs scale to 1,024 layers with stable accuracy, and these two classics beat dedicated oversmoothing methods such as DropEdge, PairNorm, and SkipNode.
  • Zero-collapsing appears in ordinary MLPs as well, so the depth problem of GNNs belongs to the general neural-network optimization literature rather than to graph-specific theory.
  • The optimal depth of a GNN is dataset-dependent, with heterophilic and large-scale datasets capable of benefiting from depth once zero-collapsing is handled.

Reading between the lines

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

  • The paper leaves implicit that many aggregation-targeting oversmoothing methods may owe their gains to regularization or optimization side effects, since the aggregation step itself is exonerated.
  • A natural test the authors do not run is to repeat the stepwise attribution on trained weights rather than untrained forward passes; the paper's own appendix shows the conclusion could shift with initialization choice.
  • If the central claim holds, benchmark suites for deep GNNs should include a plain GCN with skip connections and batch normalization as a control before attributing gains to graph-specific mechanisms.
  • The argument implies that widening the depth hyperparameter search beyond the usual few layers is promising for heterophilic and large-scale datasets, where the paper finds best accuracy at deeper layers.
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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 / 5 minor

Summary. This position paper challenges the dominant narrative that oversmoothing is the primary obstacle to training deep graph neural networks. The authors identify two definitions of oversmoothing in the literature (degree-scaled and uniform convergence), assert that many prior studies have conflated these with the zero-vector special case they call 'zero-collapsing,' and argue that the aggregation step has only a marginal effect on this phenomenon. To support this, they decompose GCN and GAT layers into aggregation, transformation, and activation, and measure three oversmoothing metrics on untrained Glorot-initialized forward passes for 128 layers; they find that models without activation decay much more slowly and that embeddings collapse to zero. They further show that GCNs can be trained even when all input features are identical, and that residual connections plus batch normalization allow GCNs to be trained to 1,024 layers. The paper concludes that vanishing gradients, not oversmoothing, cause deep-GNN performance collapse.

Significance. If the paper's claims were fully established, they would constitute an important correction to a widely cited narrative in GNN research and would refocus the community on architecture design and initialization rather than on graph-specific smoothing. The paper's strengths include a clear decomposition of the GNN update into its three steps, a transparent experimental setup across many datasets, and a compelling demonstration that classical residual connections and batch normalization substantially improve training of very deep GCNs. The appendices provide extensive supplementary experiments. However, the central diagnostic claim rests on an untrained, Glorot-initialized forward-pass analysis whose conclusions change with initialization, and the similarity measures used do not distinguish zero-collapsing from genuine node-wise convergence. The significance of the work is therefore conditional on the authors strengthening the causal evidence.

major comments (5)
  1. [Section 3.2, Fig. 3, Appendix C.5] The conclusion that 'aggregation alone has a minimal impact' is based on measuring similarity decay on untrained forward passes with Glorot-initialized parameters. Appendix C.5 (Figs. A6–A8) shows that with He initialization the decay rates of the same metrics change substantially and zero-collapsing is largely mitigated, which the paper itself acknowledges ('Parameter initialization has a significant impact'). As a result, the reported attribution of exponential decay to transformation and activation rather than aggregation is a property of the chosen initialization, not of the GNN architecture under training. To support the claim about what causes training failure, the authors should repeat the stepwise analysis with He initialization and with trained (or at least partially trained) weights, or alternatively restrict their conclusion to Glorot initialization and justify why that is the relevant setting for the prior oversmoothing literature.
  2. [Section 3.2, Appendix A] The three similarity measures used (µ_cai, µ_wu, µ_rusch) all have the all-zero embedding as a fixed point, so their exponential decay in Fig. 3 is consistent both with genuine node-wise convergence (Proposition 1 or 2 with nonzero c) and with global collapse of the embedding norm (c = 0). The histograms in Fig. 4 show that zero-collapsing occurs, but they do not separate the contribution of zero-collapsing from that of directional convergence in each of the four model variants. A scale-invariant measure of directional convergence (for example, the cosine similarity between node embeddings, or the Dirichlet energy normalized by the squared norm of the embedding) is necessary before the authors can attribute the decay to transformation and activation rather than to aggregation.
  3. [Section 3.2, Fig. 3] Even the aggregation-only curve in Fig. 3 decays exponentially. For a per-layer factor of 0.9–0.95, which fits the aggregation-only curves, at the paper's headline depth of 1,024 layers (Section 4.1) the similarity measure is reduced by a factor between roughly 10^-23 and 10^-47, i.e., total collapse. Calling this effect 'marginal' is therefore depth-relative and does not transfer to the very deep regime that the paper advocates; the authors should either report depth-normalized decay rates or explicitly state that the claim is limited to the 128-layer range shown.
  4. [Section 3.3, Fig. 5] The Xone experiment, which underlies the claim that 'GCNs are capable of escaping the oversmoothing regime,' is presented without error bars or a statement of repeated runs in Fig. 5. Appendix D states that 10 standard splits are used for these experiments, so the authors should report mean and standard deviation (or a distribution) for each bar. Without this information, the reader cannot assess whether the GCN advantage over GAT and MLP is significant, particularly on datasets like Chameleon where the paper claims even better accuracy with uniform features.
  5. [Abstract, Section 4.1, Fig. 6] The paper claims that residual connections and batch normalization enable 'successful stacking of deep GNN layers without performance degradation.' However, Fig. 6 shows that on Cora, PubMed, and Photo the test accuracy with SC & BN still declines substantially with depth (e.g., Cora falls from roughly 80% at shallow depths to roughly 40% at 1,024 layers). The claim should be weakened to 'without catastrophic collapse' or the authors should provide evidence that the depth degradation is removed relative to a competitive baseline; otherwise the empirical support for the abstract's phrasing is missing.
minor comments (5)
  1. [Appendix A, last paragraph] The sentence 'µcai(·) satisfies µwu(X) = 0 if and only if Proposition 2 holds' appears to have a typo; it should refer to µrusch, since Proposition 2 concerns uniform convergence and the measure being described is the Rusch Dirichlet energy.
  2. [Section 3.2, paragraph after Fig. 3] The sentence 'A+T is equal to the MLP architecture' should read 'σ+T is equal to the MLP architecture'; the text immediately before correctly identifies the σ+T variant as the MLP.
  3. [Figure 5 caption] The caption 'The cross-hatched bar uses the original features X, while others use uniform features Xone' is ambiguous; please indicate which bar in each group is cross-hatched.
  4. [Throughout] The paper alternates between 'oversmoothing' and 'over-smoothing' (e.g., in the Section 1 heading and the caption of Fig. 3); please use a consistent spelling throughout.
  5. [Section 3.2, near Fig. 3] The main text does not explicitly state that the forward passes in Fig. 3 are untrained; this is mentioned only in Appendix D. State this in the main text to avoid misleading readers about the experimental protocol.

Circularity Check

1 steps flagged · score 6.0 of 10

The central zero-collapsing/oversmoothing distinction is definitional: the paper's own convergence conditions include the zero vector, so declaring zero convergence 'not genuine oversmoothing' relabels the prior result rather than deriving a new one.

  1. self definitional [Section 3.2, paragraph following the discussion of contradictory GCN results]
    "In response to the question raised by the contradictory results discussed in Section 3.1, we believe the confusion arises because the target embedding vector c in Propositions 1 and 2 includes the zero vector as a special case. Consequently, many previous studies incorrectly interpreted convergence to the zero vector as evidence of oversmoothing. However, our experiments suggest that convergence to the zero vector is not a genuine result of oversmoothing; rather, it occurs due to a zero-collapsing phenomenon."

    By the paper's own Propositions 1 and 2, oversmoothing is defined as convergence to a vector c, and the zero vector is explicitly allowed as a special case. Moreover, all three similarity measures used in Figure 3 (mu_cai, mu_wu, mu_rusch) vanish when embeddings converge to zero, so the zero limit already satisfies the prior oversmoothing definitions the paper quotes. The paper then introduces 'zero-collapsing' as the same zero limit and asserts it is 'not a genuine result of oversmoothing.' This assertion is not derived from the experiments, which only show that the zero limit occurs; it is fixed by the new terminology.

full rationale

The paper contains no fitted-parameter-as-prediction and no load-bearing self-citation; the 1,024-layer residual+BN experiments and the uniform-feature recovery experiment are genuine external evidence. However, the central conceptual step — that prior work confused zero-collapsing with oversmoothing — is a relabeling. Propositions 1 and 2 include the zero vector as an admissible limit, and mu_cai, mu_wu, and mu_rusch all have the all-zero embedding as a fixed point, so the decay curves and histograms cannot separate 'oversmoothing' from 'zero-collapsing.' The paper simply names the zero limit 'zero-collapsing' and then asserts it is not genuine oversmoothing; that conclusion is built into the definition. The aggregation-marginality conclusion also inherits this confound because the same similarity measures are used to rank A versus sigma+T. Independent evidence keeps the paper from being entirely circular, hence 6 rather than 8 or 10.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The central claim rests on (i) the three-step factorization, (ii) the validity of prior similarity measures, (iii) the assumption that untrained Glorot-initialized forward passes reveal the cause of training failure, and (iv) the restriction to ReLU and GCN/GAT. No fitted parameters are introduced by the paper; hyperparameters are standard.

free parameters (2)
  • hidden_dim = 32 (decomposition), 64 (training)
    Standard width choice; fixed across experiments, not fitted to the central claim.
  • learning_rate = searched over {0.001, 0.005, 0.01}
    Hyperparameter search with validation selection; affects results but is a standard practice.
assumptions (4)
  • domain assumption The layer update X(ℓ+1)=σ(ÂX(ℓ)W(ℓ)) fully decomposes into aggregation, transformation, and activation steps (Eqs. 2-4).
    Adopted as the analysis framework in Section 2.1; the stepwise ablation in Section 3.2 depends on this factorization.
  • domain assumption The similarity measures µcai, µwu, and µrusch from prior work are valid proxies for oversmoothing.
    Used in Section 3.2 and Appendix A to quantify oversmoothing; the attribution of decay to transformation/activation rests on these measures.
  • ad hoc to paper Untrained forward passes with Glorot-initialized weights reveal the cause of training failure in deep GNNs.
    Section 3.2 measures similarity without training because 128-layer GNNs cannot be trained (Appendix D). Appendix C.5 shows He initialization changes the decay rates, making this assumption load-bearing and only partially justified.
  • domain assumption ReLU is the relevant activation, and the two asymptotic convergence regimes in Propositions 1 and 2 exhaust the oversmoothing phenomena.
    Section 2.2 restricts the analysis to ReLU and GCN/GAT; the zero-collapsing distinction is defined relative to these premises.
invented entities (1)
  • Zero-collapsing independent evidence
    purpose: A new label for the convergence of node embeddings to the zero vector, distinguished from oversmoothing.
    Supported by histograms (Fig. 4) showing feature values collapse to zero within a few layers; the concept is a renaming of a known MLP phenomenon (dying ReLU / mean-collapse).

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Cite this review

Pith. "Pith review of The Oversmoothing Fallacy: A Misguided Narrative in GNN Research." pith.science (2026). https://pith.science/paper/PWVYR7NM

@misc{pith2026250604653,
  author       = {Pith},
  title        = {Pith review of: The Oversmoothing Fallacy: A Misguided Narrative in GNN Research},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PWVYR7NM}},
  note         = {Machine review of arXiv:2506.04653}
}
read the original abstract

Oversmoothing has been recognized as a main obstacle to building deep Graph Neural Networks (GNNs), limiting the performance. This position paper argues that the influence of oversmoothing has been overstated and advocates for a further exploration of deep GNN architectures. Given the three core operations of GNNs, aggregation, linear transformation, and non-linear activation, we show that prior studies have mistakenly confused oversmoothing with the vanishing gradient, caused by transformation and activation rather than aggregation. Our finding challenges prior beliefs about oversmoothing being unique to GNNs. Furthermore, we demonstrate that classical solutions such as skip connections and normalization enable the successful stacking of deep GNN layers without performance degradation. Our results clarify misconceptions about oversmoothing and shed new light on the potential of deep GNNs.

Figures

Figures reproduced from arXiv: 2506.04653 by the authors.

Figure 1
Figure 1. Changes in node embeddings across GCN layers, where all node features are initialized to [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Similarity between nodes across layers, reported in Rusch et al. [32]. However, interpreting oversmoothing solely from this per￾spective can be misleading, dangerous, and inappropriate, as there are fundamentally different definitions of over￾smoothing as we have shown in Propositions 1 and 2, and the misconception only represents Proposition 2. We investigate the reasons why researchers became con￾fused about overs… view at source ↗
Figure 3
Figure 3. Oversmoothing levels measured by three metrics across 128-layer GCN and GAT models [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Histogram of node embedding values X(ℓ) from four selected layers. All features are collapsed to zero within the first few layers. decay rate is much lower than that of models including activation. We present additional results on other datasets in Appendix C.1, where …
Figure 5
Figure 5. Figure 5: Test accuracy of models with all node features initialized to the same vector across nodes. The cross-hatched bar uses the original features X, while others use uniform features Xone. To make the situation more straightforward, we conduct an experiment on node classifi…
Figure 6
Figure 6. Figure 6: Effectiveness evaluation of skip connections and batch normalization on GCN. We report [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Test accuracy of GCN with different over-smoothing mitigation methods. We evaluate the [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Test accuracy of GCNs with uniform fea￾tures Xone on two datasets, Cora and PubMed. A star indicates the best accuracy. To support our hypothesis, we provide addi￾tional interesting results in [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.