HeRB: Heterophily-Resolved Structure Balancer for Graph Neural Networks

Ke-Jia Chen; Wenhui Mu; Zheng Liu

REVIEW 4 major objections 4 minor 32 references

HeRB: Heterophily-Resolved Structure Balancer for Graph Neural Networks

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Structural-imbalance GNNs fail on heterophilic graphs because they ignore heterophily; HeRB first rewires edges by feature similarity, then transfers homophilic head-node knowledge to tail nodes, and reports superior results on eight…

desk verdict A sensible two-module idea that is not yet a paper: the central update equation is undefined, one theory subsection is a literal placeholder, and no code or appendix backs the empirical claims. read the letter →

arxiv 2504.17276 v1 pith:RWFHKD3C submitted 2025-04-24 cs.LG

Ke-Jia Chen , Wenhui Mu , Zheng Liu This is my paper · ORCID

classification cs.LG

keywords graphneuralnetworksstructuralimbalanceheterophilyaugmentationknowledgetransfertailnodesdegreenodeclassification

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 graph structural imbalance, understood as degree imbalance with a power-law distribution, is best addressed after first repairing heterophily, because prior augmentation and knowledge-transfer methods for tail nodes fail when connected nodes have different labels or features. It proposes HeRB, a two-module method that rewires the graph to add likely intra-class edges and remove likely inter-class edges, then transfers a learnable translation relationship from homophilic head nodes to tail nodes during message passing. The paper reports that this rectify-first pipeline outperforms both structural-imbalance-aware and heterophily-focused baselines on six heterophilic and two homophilic benchmark datasets, and the ablations attribute the gains to both modules.

What carries the argument

The central machinery is the 'rectify first, then transfer' pipeline carried by two interacting objects. The heterophily-lessening augmenter computes normalized structure and feature similarity matrices $S_{\mathrm{str}}$ and $S_{\mathrm{fea}}$, adds edges satisfying $S_{\mathrm{fea}}(v_i,v_j) \geq \theta_{\mathrm{ete}}$, removes edges satisfying $S_{\mathrm{fea}}(v_i,v_j) \leq \theta_{\mathrm{homo}}$, and forms the intermediary adjacency $A'' = (A + A')/2$. The homophilic knowledge-transfer module then expands each tail node's neighborhood to second-order and homophilic head nodes via $\tilde{A} = \beta A'' + (1-\beta) A_{\mathrm{sim}}$, and learns a translation vector $r_{v_i}$ such that $z_{v_i} + r_{v_i} \approx z_{N^*_{v_i}}$, which is injected into message passing for tail nodes. Together they turn a heterophilic, degree-imbalanced graph into an approximately homophilic graph in which tail nodes receive knowledge borrowed from well-connected head nodes.

What would settle it

On any heterophilic benchmark with ground-truth labels, compute the edge homophily ratio $h(G)$ before and after the augmentation module using the paper's thresholds; if the augmented adjacency matrix $A'$ does not satisfy $h(A') > h(G)$, the module is not actually lessening heterophily and any accuracy gain must come from another mechanism. A sharper version rewires with true labels instead of feature similarity: if the oracle-rewired model clearly outperforms HeRB, the feature-similarity proxy is the limiting assumption.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the poor performance of structural-imbalance remedies on heterophilic graphs is caused by transferring or aggregating heterophilic neighborhood information, and that correcting heterophily before balancing degrees fixes tail-node learning. Concretely, HeRB uses pretrained structure and feature encoders to compute similarity scores, adds edges between structurally close and feature-similar nodes, removes edges between structurally distant and feature-dissimilar nodes, and averages the result with the original adjacency to form an intermediary graph. For tail nodes, the model expands the neighborhood to second-order and homophilic head nodes and learns a translation vector $r_{v_i}$ with $z_{v_i} + r_{v_i} \approx z_{N^*_{v_i}}$, which is applied in message passing. The paper reports an average improvement of 4.1% in Macro-F1 and 3.0% in Micro-F1 over the best baselines on eight datasets, with the largest relative gains on strongly heterophilic graphs such as Cornell.

Load-bearing premise

The load-bearing premise is that feature similarity is a trustworthy proxy for label homophily: the augmenter adds edges only between feature-similar nodes and removes edges only between feature-dissimilar nodes, and the transfer step selects head nodes by the same similarity; on heterophilic graphs, same-class nodes can have dissimilar features, so the rewired graph can still contain inter-class edges and lose useful intra-class ones.

Editorial extensions

If this is right

Structure-imbalance methods for heterophilic graphs should adopt a heterophily-rectification step before augmentation or knowledge transfer, rather than treating the observed topology as reliable.
Tail nodes can be improved without additional labels by reusing homophilic neighborhood structure from head nodes through a learnable translation residual.
Feature-similarity-gated edge rewiring is a viable way to raise the homophily ratio of a graph before standard message passing.
The reported complexity of $\mathcal{O}(Nfd)$ for sparse graphs means the two-module pipeline can be applied as a preprocessing layer on large graphs, not only on small benchmarks.
The ablation pattern implies that naive augmentation can hurt even homophilic graphs by injecting heterophilic noise, so edge rewiring should be similarity-conditioned.

Reading between the lines

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

A direct test of the proxy assumption: replace the feature-similarity thresholds with true-label-based rewiring on the same benchmarks; the performance gap would quantify how much of HeRB's gain depends on $S_{\mathrm{fea}}$ being a faithful homophily signal.
The translation-relationship formulation (node embedding plus a residual approximates the neighborhood embedding) is not specific to degree imbalance; the same mechanism could be applied to cold-start nodes, missing-neighbor graphs, or the inductive settings the paper names as future work.
The manuscript leaves Section IV.D.2 as a placeholder reading 'Balabala.', so the formal theoretical support for the augmenter currently rests only on the Shannon-entropy sketch in IV.D.1; a complete derivation would be needed to fully ground the over-smoothing story.
Because optimal thresholds $\theta_{\mathrm{ete}}$ and $\theta_{\mathrm{homo}}$ vary by dataset, one practical extension is to estimate them automatically from the graph's observed homophily ratio rather than tuning them per dataset.

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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

The idea is easy to like: fix heterophily before doing degree-imbalance augmentation, then transfer only homophilic neighborhood knowledge from head to tail nodes. The combination is genuinely new relative to Tail-GNN, SAILOR, and the authors' own SAug, and the ablation table does show that each module contributes. The reported gains on heterophilic datasets like Cornell are large enough to be interesting.

But the paper as written is not in a publishable state. The stress test is right about Eq. (14). The text sets up the convention that expressions like A''Z_v mean adjacency-weighted aggregation, and then Eq. (14) rewrites the tail-node update as \tilde A(Z_v + Z_{N*_v} - Z_{N_v}). That is not an algebraic consequence of the definition, and it is not explained as a new operation. Since this equation is the entire concrete specification of the homophilic knowledge transfer mechanism, the main mechanism is undefined as written. If it is a typo, the corrected version still needs to be stated precisely.

Section IV.D.2 is literally '•: Balabala.' There is an Appendix C referenced but no appendix exists. The entropy argument in IV.D.1 never connects feature-similarity edge filtering to a bound on inter-class edges, so even the augmenter lacks a real theoretical guarantee. This matters because the whole method leans on the assumption that feature similarity is a good proxy for label homophily in heterophilic graphs, a point the authors never justify.

The empirical tables are plausible, but they cannot carry the load. No code is released, the hyperparameters are tuned per dataset (theta, alpha, beta, k, mu), and the standard-deviation overlap with baselines on several datasets makes some gains look fragile. The strongest individual result, on Cornell, is within the paper's own variance range on some baselines and needs a proper significance test. The claim of being 'first to address structural imbalance in the context of graph heterophily' is also overstated: SAILOR targets completely heterophilic tail nodes, and the authors cite it in the same paragraph.

Who is this for? Someone working on degree-imbalanced heterophilic GNNs might find the high-level recipe worth trying. But as a research artifact, the missing theory and invalid update rule make it impossible to verify what the method actually does. A serious editor should not send this to referees as-is; the right move is to reject and invite a resubmission with a corrected derivation, an actual theory section, and code. The paper in its current form is not ready for peer review.

Referee Report

4 major / 4 minor

Summary. The paper proposes HeRB, a framework for node classification on graphs with degree imbalance and heterophily. It consists of two modules: a heterophily-lessening augmentation module that adds intra-class edges and removes inter-class edges based on structural and feature similarity, and a homophilic knowledge transfer mechanism that transfers neighborhood information from head nodes to tail nodes during message passing. The authors evaluate HeRB on two homophilic and six heterophilic benchmark datasets using GCN as a backbone, reporting improvements over several baselines, and provide ablation studies and sensitivity analyses.

Significance. If the proposed mechanism were correctly specified and theoretically supported, the paper would address a relevant and timely problem: the interaction between structural imbalance and heterophily in GNNs. The experimental results, if reproducible, suggest that the approach can yield substantial gains on heterophilic datasets. However, the paper has significant gaps in the formal presentation: the key tail-node update equation is not a valid algebraic identity, the theoretical analysis section contains a literal placeholder, and an appendix referenced for the augmenter's analysis is absent. These issues undermine the central claim because the homophilic knowledge transfer mechanism is not well-defined as written. The paper also ships no code or proofs, so the empirical results cannot be independently verified against the described method.

major comments (4)

[§IV.C.1, Eq. (14)] The tail-node update rule is not a valid algebraic identity under the aggregation convention established in Eq. (13). Eq. (13) defines g(l)(A''Z_vi^(l)) = phi_g(A''Z_vi^(l)W), interpreting A''Z_vi as adjacency-weighted neighborhood aggregation. Eq. (14) claims that g(l)(\tilde A Z_vi^(l)) equals phi_g(\tilde A (Z_vi^(l) + Z_N*vi^(l) - Z_Nvi^(l)) W). This equality only holds if \tilde A (Z_N*vi^(l) - Z_Nvi^(l)) = 0 for every tail node, which is neither assumed nor enforced, and is generally false because Z_N* and Z_N are pooled embeddings of different neighbor sets. Consequently, the described propagation step for tail nodes is not a well-defined GNN update, and the results in Table II cannot be attributed to the proposed transfer mechanism as written.
[§IV.D.2 and §IV.A.3] The theoretical analysis of the knowledge transfer mechanism is missing: Section IV.D.2 is literally the placeholder '•: Balabala.' In addition, Section IV.A.3 states that 'We provide a theoretical analysis of how the augmenter addresses the heterophily problem in Appendix C,' but the manuscript contains no Appendix C. These are not presentation issues; they are missing portions of the paper's central support and must be supplied before the claims can be evaluated.
[§IV.D.1, Eq. (20)] The entropy argument for the augmenter is not rigorous. The quantities pi, ti, and ni are not properly defined, and the claimed expression E(H(\tilde G)) = -δ log δ + (1-δ) Σ_i -pi log((1-δ)pi) is not derived from the edge-perturbation process described in Section IV.A.3. Even if the entropy inequality were correct, the argument does not connect the feature-similarity-based edge selection to any bound on the number or proportion of inter-class edges. Thus, the augmenter's guarantee that heterophily is lessened is unproven.
[§IV.A.3] The augmenter relies on the assumption that feature similarity S_fea is a trustworthy proxy for label homophily, adding edges only when S_fea(vi,vj) ≥ Thete and removing edges when S_fea(vi,vj) ≤ Thomo. In heterophilic graphs, nodes of the same class can have dissimilar features, and nodes of different classes can have similar features, so the rewiring may not achieve the intended reduction of inter-class edges. The paper provides no empirical or theoretical analysis of the label-homophily rate of the augmented graph, leaving a key premise of the method unvalidated.

minor comments (4)

[Throughout] There are several typos: 'neighobors' in the Introduction, 'heteroohilic' in the caption of Table II, 'Cornrll' in the axis labels of Figure 5, and inconsistent spellings such as 'Mirco-F1' in figures versus 'Micro-F1' in tables.
[§III.B, Eq. (1)] The notation in Eq. (1)-(3) is confusing: Thead is introduced as 'degree80%', but is then used as a threshold in Eq. (2) and (3). It would be clearer to define a scalar threshold T_head separately from the head-node set.
[§IV.D.2] The placeholder subsection heading '•: Balabala.' should be removed or replaced with actual content before any resubmission.
[References] The paper cites GRACE [15] as a structural-imbalance method, but the reference appears to be a graph contrastive learning method; please verify the citation and clarify the relationship.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: HeRB's contributions are architectural and empirically validated, not derived by construction from fitted inputs or author self-citations.

full rationale

The paper's central claims are architectural and empirical: HeRB augments the adjacency matrix using structural and feature similarities, then transfers neighborhood translation knowledge from head nodes to tail nodes. No step in the derivation reduces a predicted quantity to a fitted input. The augmentation module uses thresholds on feature similarity, but these are hyperparameters, and the reported gains are measured against external baselines on standard datasets, not asserted from the thresholds themselves. The homophilic knowledge transfer is a concrete update rule (Eqs. 13 and 14) plus a head-node regularization loss (Eq. 15); it is not obtained by fitting tail-node labels and then reporting them as predictions. The self-citations to SiGAug [16] and SAug [17] appear only in related work or as baselines and are not load-bearing; the localizing strategy used in Eq. 12 is attributed to external work Tail-GNN [5], and no uniqueness theorem is imported from the authors' prior papers. The placeholder 'Balabala' in Section IV.D.2 and the missing Appendix C are completeness and correctness defects, not circular reductions; the entropy argument, even if unconvincing, does not make a claim equal to its input. Hyperparameter tuning via random search is standard model selection and is not disguised as a prediction. Overall, no step of the derivation is equivalent by construction to its inputs, so the circularity score is 0.

Assumptions & free parameters 10 free parameters · 4 assumptions · 0 invented entities

The central gain claim rests on several domain assumptions about feature similarity as a homophily proxy and the validity of the translation relationship. No new physical entities are introduced; r_v is a learnable parameter, not a new natural kind.

free parameters (10)

degree_percentile_threshold = 80th percentile
Head/tail partition threshold chosen by hand in Section III.B (Eq. 1).
Thete = tuned per dataset, not fixed
Feature similarity threshold for adding edges (Section IV.A.3); sensitivity shown in Figure 3.
Thomo = tuned per dataset, not fixed
Feature similarity threshold for removing edges (Section IV.A.3); sensitivity shown in Figure 3.
add% = not reported
Number of nodes considered for adding edges; no concrete value given in the paper.
remove% = not reported
Number of nodes considered for removing edges; no concrete value given in the paper.
alpha = tuned per dataset
Weight between direct and two-hop neighborhoods in Eq. (9).
beta = tuned per dataset
Weight of homophilic head-node neighborhood in Eq. (10).
k = tuned per dataset
Number of top homophilic head nodes selected for each tail node (Section IV.B.1).
mu = tuned per dataset
Loss weight for head-node constraint in Eq. (17); sensitivity in Figure 5.
lambda = 0.005
Regularization weight in Eq. (16), fixed by hand.

assumptions (4)

domain assumption Nodes with similar feature vectors are likely to have the same label.
Used to select edges to add and remove in Section IV.A.3; not validated on heterophilic graphs where same-class nodes may have dissimilar features.
domain assumption Head nodes have sufficient and homophilic neighborhoods after augmentation.
Used in Eq. (13) and in L_head (Eq. 15) to enforce consistency of expanded and observed neighborhoods.
domain assumption The approximate translation relation z_v + r_v is approximately z_N_v holds after augmentation.
This is the basis of the knowledge transfer mechanism in Eq. (7) and the tail-node update in Eq. (14).
ad hoc to paper The augmented-graph entropy formula in Eq. (20) correctly measures message diversity.
The theoretical analysis in Section IV.D uses this formula to claim reduced over-smoothing, but the probabilistic model for p_i is unspecified and the inequality is asserted.

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Cite this review

Pith. "Pith review of HeRB: Heterophily-Resolved Structure Balancer for Graph Neural Networks." pith.science (2026). https://pith.science/paper/RWFHKD3C

@misc{pith2026250417276,
  author       = {Pith},
  title        = {Pith review of: HeRB: Heterophily-Resolved Structure Balancer for Graph Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RWFHKD3C}},
  note         = {Machine review of arXiv:2504.17276}
}

read the original abstract

Recent research has witnessed the remarkable progress of Graph Neural Networks (GNNs) in the realm of graph data representation. However, GNNs still encounter the challenge of structural imbalance. Prior solutions to this problem did not take graph heterophily into account, namely that connected nodes process distinct labels or features, thus resulting in a deficiency in effectiveness. Upon verifying the impact of heterophily on solving the structural imbalance problem, we propose to rectify the heterophily first and then transfer homophilic knowledge. To the end, we devise a method named HeRB (Heterophily-Resolved Structure Balancer) for GNNs. HeRB consists of two innovative components: 1) A heterophily-lessening augmentation module which serves to reduce inter-class edges and increase intra-class edges; 2) A homophilic knowledge transfer mechanism to convey homophilic information from head nodes to tail nodes. Experimental results demonstrate that HeRB achieves superior performance on two homophilic and six heterophilic benchmark datasets, and the ablation studies further validate the efficacy of two proposed components.

Figures

Figures reproduced from arXiv: 2504.17276 by the authors.

**Figure 1.** The left figure illustrates the imbalanced distributions of node degrees in the CiteSeer and Chameleon datasets. The right figure presents the MicroF1 results of GCN on the node classification task, where both head nodes and tail nodes suffer from their heterophily, leading to poorer classification performance. or sampling methods, some [4], [5] suggest transferring information from head nodes to tail nodes, while … view at source ↗

**Figure 2.** The overall framework of HeRB. The framework contains two modules: heterophily-lessening augmentation and homophilic knowledge transfer. The [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Performance variation when changing hyper-parameters [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Performance variation when changing hyper-parameters [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Performance variation when changing hyper-parameters [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

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Tail-gnn: Tail-node graph neural networks,

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Blade: Biased neighborhood sampling based graph neural network for directed graphs,

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Sailor: Structural augmentation based tail node representation learning,

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Representation learning for scale-free networks,

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