Towards a deeper GCN: Alleviate over-smoothing with iterative training and fine-tuning

Furong Peng; Jinzhen Gao; Kang Liu; Sheng Wang; Xuan Lu; Yifan Huo

REVIEW 3 major objections 5 minor 34 references

Towards a deeper GCN: Alleviate over-smoothing with iterative training and fine-tuning

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Trainable linear transformations in GCNs drive over-smoothing, and a gradual layer-wise training schedule with identity initialization and low-rank fine-tuning keeps plain GCNs accurate at 32 layers.

desk verdict LGT is a genuinely useful training recipe for deep GCNs, but the paper's causal story about linear transformations driving over-smoothing is not supported by the SGC comparison. read the letter →

arxiv 2506.17576 v2 pith:BZR3IM26 submitted 2025-06-21 cs.LG

Furong Peng , Jinzhen Gao , Xuan Lu , Kang Liu , Yifan Huo , Sheng Wang This is my paper · ORCID

classification cs.LG

keywords GraphConvolutionalNetworksover-smoothingfeaturecollapselayer-wisetraininglow-rankadaptationidentityinitializationdeepneuralsimplifiedconvolution

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

The paper tries to establish that the main engine of over-smoothing in deep GCNs is not the graph propagation itself but the trainable linear transformations inside each layer, and that a training schedule rather than a new architecture can solve it. It shows that SGC, which removes learned weights, keeps separable features up to 32 layers, while vanilla GCN collapses by 8 layers. The proposed Layer-wise Gradual Training (LGT) adds layers one at a time, initializes each new layer as the identity, and fine-tunes earlier layers with low-rank updates, allowing a vanilla GCN to reach 32 layers with accuracy near that of specialized anti-over-smoothing methods. If correct, this shifts the over-smoothing discussion from architectural design to optimization and offers a general recipe that can be combined with existing methods.

What carries the argument

The central object is Layer-wise Gradual Training (LGT), a training schedule with three components: incremental layer-wise training adds one layer at a time and freezes earlier ones; low-rank adaptation writes each frozen weight as $W_0 + AB$ with a small rank $r$ so shallow layers stay lightly trainable; identity initialization starts every new layer at the identity matrix so it passes representations through unchanged at first. Together these isolate newly added parameters from the already stabilized network, so depth grows without a sudden random perturbation that collapses features.

What would settle it

Train an SGC-style network that keeps per-layer nonlinear activations but fixes all linear weights at the identity (SGC plus ReLU). If its accuracy and feature diversity collapse by 8 layers, the collapse is not caused by trainable linear transformations.

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Extended reading notes

Core claim

The paper's central claim is that trainable linear transformations in GCN layers, rather than repeated Laplacian propagation alone, are a primary accelerant of over-smoothing: on Cora, standard GCN accuracy drops to about 40% at 32 layers while SGC, which removes learned weights, stays near 70%. To keep expressiveness while avoiding collapse, the paper proposes LGT and reports that GCN+LGT reaches around 81% on Cora at 32 layers and similarly strong results on Citeseer, Pubmed, and AmazonPhoto, outperforming vanilla GCN, SGC, and several anti-over-smoothing baselines. LGT also improves PairNorm and ContraNorm in most tested settings and cuts training time by avoiding full-model retraining.

Load-bearing premise

The diagnosis rests on the SGC comparison, which removes linear transformations together with nonlinearities and layer collapse, so the stability of SGC at 32 layers does not isolate the effect of the learned weights.

Editorial extensions

If this is right

A vanilla GCN can be trained to 32 layers with accuracy comparable to specialized anti-over-smoothing architectures, so depth itself need not force an architecture change.
Normalization-based methods such as PairNorm and ContraNorm inherit the training-efficiency and accuracy gains, so LGT can be stacked on top of existing fixes.
Because LGT only changes the training schedule, it applies to any GCN-like model without modifying the forward pass or the graph structure.
Deep GCN training becomes cheaper: since only the newest layer is fully trained and older layers are lightly adapted, reported training time drops substantially at 8, 16, and 32 layers.

Reading between the lines

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

Inference: if the diagnosis is right, the same staged schedule should transfer to attention-based or message-passing architectures with learned per-layer maps, such as GAT, without architectural changes.
Inference: the paper's account predicts a new test: monitoring feature diversity (for example Dirichlet energy) across LGT stages would show diversity preserved during the schedule, not just at the final layer; this is not reported.
Inference: a cheaper variant might drop LoRA and rely on identity initialization alone for some datasets; the paper's ablations show LoRA helps at depth, but the interaction is data-dependent.
Inference: the role of the learned weight matrices could be probed by freezing all layers at identity after their initial stage, which would separate the benefit of the schedule from the benefit of continued light adaptation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague—

The thing to know about this paper: the LGT training recipe is real and worth trying. Incremental layer-wise training plus LoRA fine-tuning plus identity initialization makes 16–32 layer vanilla GCNs get accuracy in the high 70s to low 80s on these benchmarks, which is a big jump over standard GCN. The ablation shows all three pieces contribute, and the method is architecture-agnostic and plays well with PairNorm/ContraNorm. That is a genuine engineering contribution.

What is not solid is the paper's explanation of why it works. The central claim that trainable linear transformations are a primary driver of over-smoothing rests on Figure 1, which compares GCN with SGC. SGC differs from GCN in three ways at once: no nonlinearities, no per-layer weights, and the propagation collapsed into a single matrix power. The comparison cannot attribute the observed collapse to linear transformations. The stress-test note gets this exactly right. The paper's own conclusion admits the lack of theory, so the confounded figure is the only support for the mechanism.

Other soft spots: the 'state-of-the-art' claim is overstated. There are no GCNII, JK-Net, or DropEdge comparisons, and only four small datasets with five splits. Experimental details like stage schedules and LoRA rank per stage are missing. And Table 3 contradicts the 'reduces training time' claim: on AmazonPhoto at 16 layers, GCN+LGT takes 1452 seconds versus 228 for GCN. That is an anomaly the authors should explain.

To be fair, the method is clearly described, the code link is provided, and the empirical gains over vanilla GCN are consistent across all four datasets. The training recipe is plausible even if the mechanism is not established. The paper would benefit from a proper diagnostic experiment—e.g., ablating nonlinearities separately from per-layer weights—and a stronger baseline set.

I would not cite this in my own work right now, but I would bring it to a reading group as an example of a training-centric approach to over-smoothing. If this crossed my desk, I would send it to peer review: the recipe deserves scrutiny and the baseline comparison can be fixed in revision. I would not desk-reject it, but I would expect major revision before acceptance.

Referee Report

3 major / 5 minor

Summary. The paper argues that over-smoothing in deep GCNs is driven not only by repeated Laplacian propagation but also by trainable linear transformations, and it proposes Layer-wise Gradual Training (LGT), which combines incremental layer-wise training, LoRA-based fine-tuning of frozen layers, and identity initialization of newly added layers. LGT is evaluated on Cora, Citeseer, Pubmed, and AmazonPhoto for depths 4, 8, 16, and 32, and is also combined with PairNorm and ContraNorm. The authors report large accuracy gains over plain GCNs, improved training efficiency, and state-of-the-art performance for deep vanilla GCNs.

Significance. If the causal claim were established, the paper would make a useful contribution by reframing over-smoothing as partly an optimization problem and by offering a training-side remedy that is compatible with normalization-based methods. The LGT recipe is simple, the code is public, and the ablation in Figure 4 gives some support for the contribution of each component. However, the central diagnostic claim rests on a confounded comparison, the state-of-the-art claim is not supported by the included baselines, and one reported training-time result contradicts the efficiency claim. The empirical improvement of deep GCNs with LGT is plausible and interesting, but the paper's scientific and comparative claims need substantial revision.

major comments (3)

[Section 1, Figure 1, Section 4] The central diagnostic claim—that trainable linear transformations, rather than the graph Laplacian, are a primary driver of over-smoothing—is not established by the evidence presented. Figure 1 compares GCN with SGC, but SGC differs from GCN in three simultaneous ways: it removes per-layer nonlinearities, collapses the stacked propagation into a single matrix power, and reduces trainable weights to a final classifier. Any of these differences could explain SGC's stability at 32 layers, so the comparison cannot isolate the effect of trainable linear transformations. Section 4 repeats this attribution when motivating LGT, and the paper's own conclusion concedes that no theoretical analysis is provided. To support the claim, the authors should add controlled experiments that vary only the trainability of the linear weights at fixed depth and nonlinearity (e.g., a deep GCN with frozen or identity-initialized weights versus trained weights), and report a quantitative feature-collapse measure such as Dirichlet energy rather than relying on accuracy and t-SNE plots alone.
[Section 5.1, Table 2] The claim that LGT achieves 'state-of-the-art performance on vanilla GCN' is substantially overstated. Table 2 compares LGT only against SGC, IresGCN, PSNR, PairNorm, ContraNorm, and vanilla GCN; standard deep-GCN baselines such as GCNII, JK-Net, and DropEdge—which are discussed in Section 2.1—are missing. Moreover, GCN+LGT does not consistently outperform the included baselines: on AmazonPhoto at 32 layers, IresGCN reaches 91.68% versus 91.34% for GCN+LGT, and on several settings PairNorm+LGT is worse than PairNorm itself (e.g., Citeseer at 16 layers: 65.12% versus 66.66%). The 'state-of-the-art' wording should be replaced by a more precise claim, and the missing baselines should be added or the comparison scope stated explicitly.
[Section 5.4, Table 3] Table 3 contradicts the efficiency claim that LGT 'significantly reduces training time.' On AmazonPhoto at 16 layers, GCN+LGT requires 1452 seconds versus 228 seconds for vanilla GCN, an increase of more than sixfold, and at 8 layers GCN+LGT (41s) is only marginally faster than GCN (72s) despite the qualitative claim in Figure 5. The authors should either correct the table, explain the anomaly (e.g., different hardware or LoRA rank settings), or restrict the efficiency claim to the settings where it actually holds; as written, Section 5.4's central assertion is not supported by its own data.

minor comments (5)

[Section 5.5] In the rank analysis paragraph, 'shadow networks' should read 'shallow networks.'
[References] Reference [10] contains a typo: 'International onference' should be 'International Conference.'
[Section 5.1] The experimental setup does not report key hyperparameters such as the number of stages, epochs per stage, early stopping patience, learning rate, or LoRA rank per dataset; the code link alone is insufficient for reproducibility.
[Figure 1 and Section 5.2] The caption and text describe SGC as maintaining 'stable performance,' but SGC accuracy on Cora drops from 79.88% at 4 layers to 69.62% at 32 layers, so 'stable' should be qualified.
[Abstract, Table 2] The abstract's statement that LGT 'further enhances' PairNorm and ContraNorm is too broad; Table 2 shows several settings where PairNorm+LGT or ContraNorm+LGT is worse than the base method, so the compatibility claim should be stated as improving performance in most but not all settings.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the method is evaluated on held-out accuracy against external baselines, and the SGC comparison, while confounded, is an experimental-validity concern rather than a circular derivation.

full rationale

The paper's central empirical claim is supported by an independent comparison against an external baseline (SGC, Wu et al. 2019), and its method (LGT) is evaluated on held-out test accuracy across four datasets against external baselines. No parameter is fitted to the target quantity and then renamed as a prediction: the only validation-based selection is the LoRA rank (Section 5.5), which is a hyperparameter choice and not presented as a test of the over-smoothing mechanism. The single self-citation, [21] in Section 3, is used only to reference evaluation methodology and is not load-bearing. The SGC-vs-GCN contrast in Figure 1 is confounded (SGC removes nonlinearities and collapses depth as well as per-layer linear transforms), but that is an experimental-validity concern, not circularity: the contrast is not defined in terms of the paper's own claims, and LGT's reported gains do not reduce to the SGC comparison by construction. No equation in the paper defines a predicted quantity in terms of its own input or imports a uniqueness theorem from the authors' prior work. Accordingly, no circular step is present.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The method introduces no new physical or mathematical entities. It relies on standard GCN machinery and adds a training schedule. The only tuned quantity is the LoRA rank (plus unspecified stage details); the diagnosis claim depends on the SGC comparison assuming no confounding from nonlinearity or layer collapsing.

free parameters (2)

LoRA rank r = 10 (recommended, searched over {2, 10, 20, 32})
Rank controls the capacity of the low-rank update; the paper tunes it per dataset and depth based on validation performance and recommends 10 (Section 5.5, Figure 6).
Stage schedule and per-stage epochs = not reported
The number of layers added per stage and the training epochs per stage are not specified; these hand-chosen choices affect the reported accuracy and runtime across all experiments.

assumptions (3)

domain assumption The normalized graph Laplacian propagation (Eq. 1) is the correct model for GCN message passing.
Standard in the literature; the paper adopts it without proof in Section 3.
domain assumption The over-smoothing limit (Eq. 3), convergence to a constant matrix, is the operational definition of the problem.
Introduced in Section 3; used to motivate the need for deep GCN training.
ad hoc to paper The comparison of GCN vs SGC in Figure 1 isolates the effect of removing trainable linear transformations.
SGC also removes nonlinearities and collapses layers, so this isolation is asserted, not established.

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Cite this review

Pith. "Pith review of Towards a deeper GCN: Alleviate over-smoothing with iterative training and fine-tuning." pith.science (2026). https://pith.science/paper/BZR3IM26

@misc{pith2026250617576,
  author       = {Pith},
  title        = {Pith review of: Towards a deeper GCN: Alleviate over-smoothing with iterative training and fine-tuning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BZR3IM26}},
  note         = {Machine review of arXiv:2506.17576}
}

read the original abstract

Graph Convolutional Networks (GCNs) suffer from severe performance degradation in deep architectures due to over-smoothing. While existing studies primarily attribute the over-smoothing to repeated applications of graph Laplacian operators, our empirical analysis reveals a critical yet overlooked factor: trainable linear transformations in GCNs significantly exacerbate feature collapse, even at moderate depths (e.g., 8 layers). In contrast, Simplified Graph Convolution (SGC), which removes these transformations, maintains stable feature diversity up to 32 layers, highlighting linear transformations' dual role in facilitating expressive power and inducing over-smoothing. However, completely removing linear transformations weakens the model's expressive capacity. To address this trade-off, we propose Layer-wise Gradual Training (LGT), a novel training strategy that progressively builds deep GCNs while preserving their expressiveness. LGT integrates three complementary components: (1) layer-wise training to stabilize optimization from shallow to deep layers, (2) low-rank adaptation to fine-tune shallow layers and accelerate training, and (3) identity initialization to ensure smooth integration of new layers and accelerate convergence. Extensive experiments on benchmark datasets demonstrate that LGT achieves state-of-the-art performance on vanilla GCN, significantly improving accuracy even in 32-layer settings. Moreover, as a training method, LGT can be seamlessly combined with existing methods such as PairNorm and ContraNorm, further enhancing their performance in deeper networks. LGT offers a general, architecture-agnostic training framework for scalable deep GCNs. The code is available at [https://github.com/jfklasdfj/LGT_GCN].

Figures

Figures reproduced from arXiv: 2506.17576 by the authors.

**Figure 1.** Comparison of over-smoothing in GCN and SGC on Cora. (a) Accuracy trend with increasing depth, where GCN suffers severe degradation beyond 8 layers, while SGC maintains stable performance. (b-e) Node embedding visualization (via t-SNE [16]) at different depths: GCN’s features collapse as depth increases, whereas SGC preserves clear class separability even at 32 layers [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Illustration of Layer-wise Gradual Training (LGT). At each stage, only the newly added layer is fully trained, while shallow layers are fine-tuned via LoRA. Once stabilized, a new layer is added and initialized with an identity matrix to ensure smooth integration. 4.1 Incremental Layer-wise Training To address over-smoothing caused by rapid parameter growth, LGT decomposes GCN training into multiple stages. At each … view at source ↗

**Figure 3.** Effect of initialization methods. Identity initialization stabilizes the training of newly added layers compared to random initialization. prior methods that modify GCN architectures or impose explicit constraints on node representations, LGT addresses over-smoothing through an optimizationcentric training paradigm, offering a scalable and compatible solution for training deep GCNs. The effectiveness of LGT is vali… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Results of ablation study (Cora). Compatibility with Existing Anti-over-smoothing Methods. When applied to ContraNorm, LGT enhances its performance on Cora, Citeseer, and AmazonPhoto. On Pubmed, where standard ContraNorm suffers from out-ofmemory (OOM) issues at 8 lay…

**Figure 5.** Figure 5: Training efficiency and accuracy comparison. Line plots show classification accuracy across different network depths, and circle sizes indicate relative training time. LGT significantly improves GCN’s accuracy while reducing training time. For PairNorm, LGT enhances …

**Figure 6.** Figure 6: Results of rank changing over layers (AmazonPhoto). unnecessary computational overhead. Thus, rank=10 is recommended for practical use, offering robust performance across depths with controlled complexity. 5.6 Node Embedding Visualization We visualize the 32-layer nod…

**Figure 7.** Figure 7: The node embedding visualization of GCN, ContraNorm, and their re [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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