{"id":"f8325bf9-8838-4145-8413-8fe49e3c2237","arxiv_id":"2504.17276","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"HeRB combines heterophily-lessening edge augmentation with homophilic knowledge transfer to improve node classification for low-degree tail nodes.","lead":"HeRB is a graph neural network method that reduces heterophily by adding and removing edges, then transfers knowledge from high-degree head nodes to low-degree tail nodes. The paper reports accuracy gains over baselines on six heterophilic and two homophilic graph benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (14)'s tail-node update is not a valid algebraic identity under the aggregation convention of Eq. (13), so HeRB's homophilic knowledge transfer is undefined as written; the theory section IV.D.2 is a literal placeholder.","rationale":"I read the reader's rejection as correct but for a slightly different primary reason. The reader identifies feature similarity as a proxy for label homophily as the weakest assumption; that is a real concern, but it is an empirical assumption that could in principle be validated. The stronger problem is that Eq. (14) is internally inconsistent: the proposed tail-node update is not a valid consequence of the preceding definitions, so the paper does not actually specify the model that produced Table II. This is not a matter of disagreement with current consensus; it is an internal soundness gap. The reader's rationale does mention the 'unexplained step' in Eq. (14), and Section IV.D.2's placeholder and missing Appendix C are independently disqualifying. The ablation and sensitivity analyses are useful evidence of effort, but they do not repair the undefined update rule. I therefore do not move the verdict: REJECT remains appropriate, and the paper should be revised to supply a correct derivation, code, or both before its central claim can be assessed.","tokens_in":15292,"tokens_out":7185,"duration_ms":72769,"concrete_test":"Take Eq. (10)'s \\tilde A, Eq. (13)'s aggregation convention, and Eq. (14)'s rightmost expression, and symbolically verify whether \\tilde A (Z_vi + Z_N*vi - Z_Nvi) equals \\tilde A Z_vi for a small graph with one tail node whose one-hop and two-hop neighborhoods differ. If the equality fails, request the authors' code and a corrected derivation, then re-run the Cornell and Wisconsin experiments using the literal leftmost update rule; if the implemented model instead matches the rightmost expression, the evaluated algorithm differs from the one stated in the paper.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim rests on the homophilic knowledge transfer mechanism, whose only concrete implementation is the tail-node update in Eq. (14). That equation is invalid as written. Eq. (13) establishes the convention that expressions like A''Z_vi mean adjacency-weighted neighborhood aggregation, i.e. (AZ)_vi = sum_j A_ij Z_j. Eq. (14) then asserts g^(l)(\\tilde A Z_vi^(l)) = phi_g(\\tilde A (Z_vi^(l) + Z_N*vi^(l) - Z_Nvi^(l)) W). No definition in Section IV.B makes this an identity: it would require \\tilde A (Z_N*vi - Z_Nvi) = 0 for every tail node, which is neither assumed nor enforced, and is false in general for the weighted adjacency matrix of Eq. (10). Since Z_N* and Z_N are pooled embeddings of different neighbor sets, and for tail nodes these sets differ by design, the rightmost expression is not the aggregation of Eq. (13). Thus the described update rule is not a well-defined GNN propagation step, and the Table II results cannot be attributed to the proposed mechanism without code or a corrected derivation. The surrounding theoretical support is also absent: Section IV.D.2 is literally '•: Balabala.', and Section IV.A.3 promises a theoretical analysis in Appendix C, which the article does not contain. The entropy argument in IV.D.1 never links the feature-similarity edge selection to a bound on inter-class edges, so even the augmenter's guarantee is unproven.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":15617,"tokens_out":2898,"duration_ms":27365,"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":[{"comment":"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.","section":"§IV.C.1, Eq. (14)"},{"comment":"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.","section":"§IV.D.2 and §IV.A.3"},{"comment":"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.","section":"§IV.D.1, Eq. (20)"},{"comment":"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.","section":"§IV.A.3"}],"minor_comments":[{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"§III.B, Eq. (1)"},{"comment":"The placeholder subsection heading '•: Balabala.' should be removed or replaced with actual content before any resubmission.","section":"§IV.D.2"},{"comment":"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.","section":"References"}],"recommendation":"reject","confidential_remarks":"The manuscript appears to be an early draft: the theory section contains a literal placeholder, Appendix C is referenced but absent, and the main tail-node equation is not algebraically valid. These are not minor presentation issues; they affect the core contribution. I would encourage the authors to provide a corrected derivation, complete the theoretical analysis, and release code, after which a resubmission could be considered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nBut 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.\n\nSection 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.\n\nThe 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.\n\nWho 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.","headline":"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.","tokens_in":16173,"tokens_out":1611,"would_cite":false,"duration_ms":18518,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["graph neural networks","structural imbalance","graph heterophily","graph augmentation","knowledge transfer","tail nodes","degree imbalance","node classification"],"falsifier":"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.","tokens_in":15043,"feed_emoji":"🕸️","tokens_out":12061,"duration_ms":98510,"temperature":0.7,"pith_summary":"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.","feed_headline":"Rewire heterophilic edges first to fix tail-node learning","feed_subtitle":"HeRB adds likely same-class edges, then transfers head-node knowledge to tail nodes, winning on six heterophilic graphs.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines neighborhood-knowledge transfer for tail nodes and supplies the localizing strategy that HeRB adapts and extends to homophilic transfer.","marker":"[5]"},{"why":"SAILOR is the prior structural-augmentation baseline targeting heterophilic tail nodes that HeRB compares against and improves upon.","marker":"[7]"},{"why":"Supplies the edge-level homophily ratio definition and the observation that MLPs can beat GNNs on some heterophilic graphs, motivating the feature encoder.","marker":"[21]"},{"why":"Documents that heterophilic nodes and homophilic tail nodes learn worst, linking heterophily with oversmoothing and motivating the rectify-first design.","marker":"[11]"},{"why":"Observes that larger degree helps GNN performance when label distributions are consistent, grounding the head-tail degree imbalance framing.","marker":"[10]"},{"why":"Provides the GCN backbone and the public data split used for the Cora and CiteSeer experiments.","marker":"[2]"},{"why":"SAug is the structural-imbalance augmentation baseline in the experiments; HeRB's augmenter is the heterophily-aware successor.","marker":"[17]"},{"why":"Shannon entropy, defined here, is the quantity the theoretical analysis uses to argue that topology modification increases message diversity and reduces oversmoothing.","marker":"[29]"}],"fun_headline_variants":["Rewire heterophilic edges before balancing GNNs","HeRB: Lessen heterophily, then transfer homophilic knowledge","Correct heterophily first to fix tail-node learning on graphs","Edge rewire plus head-to-tail transfer wins on heterophilic graphs","Heterophily-resolved balancer: add same-class edges first"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Rewire heterophilic edges before balancing GNNs","HeRB: Lessen heterophily, then transfer homophilic knowledge","Correct heterophily first to fix tail-node learning on graphs","Edge rewire plus head-to-tail transfer wins on heterophilic graphs","Heterophily-resolved balancer: add same-class edges first"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000795,"raw_usage":{"total_tokens":3497,"prompt_tokens":942,"completion_tokens":2555,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":558,"completion_tokens_details":{"reasoning_tokens":2466}},"tokens_in":558,"tokens_out":2555,"duration_ms":16910,"temperature":1.0,"reasoning_tokens":2466,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:44:06.693932+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Sailor: Structural augmentation based tail node representation learning,","cited_arxiv_id":null,"evidence_quote":"SAILOR is the prior structural-augmentation baseline targeting heterophilic tail nodes that HeRB compares against and improves upon."},{"cited_title":"Saug: Structural JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 10 imbalance aware augmentation for graph neural networks,","cited_arxiv_id":null,"evidence_quote":"SAug is the structural-imbalance augmentation baseline in the experiments; HeRB's augmenter is the heterophily-aware successor."}],"review_version":1}