{"id":"bfefcb75-a7a7-4bfa-889d-bc472cad8e02","arxiv_id":"2412.08310","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"ES-MLP extends Graph-MLP with an edge-splitting mechanism from ES-GNN so that a pure MLP can match graph neural networks on homophilic and heterophilic node classification without using edges at inference.","lead":"This paper introduces ES-MLP, a model that classifies nodes using only node features at inference time and avoids message passing. It combines Graph-MLP's contrastive training with ES-GNN's edge-splitting to handle both homophilic and heterophilic graphs, reporting competitive accuracy and two to five times faster inference than message-passing rivals.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Abstract overclaims 'on par ... on all datasets': ES-MLP fails on Minesweeper, where labels depend on neighbor features; the paper's own Limitations section admits this boundary.","rationale":"The stress-test pass confirms the reader's weakest assumption: the model's validity is bounded by the requirement that labels be recoverable from the node's own features at inference time. The paper itself states this limitation in Section 6 and in the Limitations paragraph, yet the abstract still claims performance 'on par with homophilic and heterophilic models on all datasets.' The Minesweeper result (50.87 vs. 88.90 for GraphSAGE) makes the overclaim concrete. This is load-bearing because it qualifies the central claim and the paper's title. The reader's CONDITIONAL verdict already requires addressing this overclaim, so my read does not change the verdict. I did not identify a separate internal inconsistency in the method; the edge-splitting mechanism and the losses are coherently defined. A secondary concern about the lack of an ablation of the splitting mechanism itself (e.g., fixing alpha=0) could be raised, but it does not change the primary verdict, and the paper's adjacency visualizations provide some evidence that the splitting is active. Therefore the verdict remains CONDITIONAL with the same requested revision.","tokens_in":22865,"tokens_out":8465,"duration_ms":87877,"concrete_test":"Re-run the Minesweeper benchmark under the paper's protocol and verify ES-MLP's AUROC is approximately 50% while GraphSAGE is approximately 89%. If confirmed, the abstract's 'on par with ... all datasets' is false and must be revised to explicitly exclude tasks where class labels are not recoverable from node features alone.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim in the abstract is that 'ES-MLP is on par with homophilic and heterophilic models on all datasets without using edges during inference.' This is directly contradicted by Table 2 on Minesweeper: ES-MLP reaches only 50.87 AUROC, essentially chance, while GraphSAGE reaches 88.90. The paper's Discussion (Section 6) contains the decisive admission: 'the node features are independent of the class of a node... Since MLP-based models do not have access to these features during inference time, they are unable to classify these nodes correctly.' This is not a minor benchmark miss; it is a hard boundary on the model class. The architecture's 'no message passing' property, which is the paper's headline advantage, is exactly what prevents access to neighbor features at inference. Therefore the claim 'node classification on homophilic and heterophilic graphs without message passing' is only valid for graphs where the node's own feature vector is sufficiently informative about its label. Tasks where class labels depend on neighbor features or on neighborhood distribution are outside the model's validity. The abstract and title should be scoped accordingly, e.g., 'when node features are informative' or 'except when labels depend on neighbor features.' This concern matches the reader's weakest_assumption and is already reflected in the reader's CONDITIONAL verdict.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes ES-MLP, a node-classification model that combines the edge-splitting mechanism of ES-GNN with the neighborhood-contrastive training of Graph-MLP. During training, node features are projected into task-relevant and task-irrelevant subspaces, the adjacency matrix is split into two exclusive weighted matrices, and the model is trained with a combined cross-entropy, neighborhood-contrastive, and irrelevant-consistency loss. At inference only the MLP on the task-relevant representation is used, so no adjacency matrix is required. The authors evaluate ES-MLP on seven real-world datasets and CSBM synthetic graphs, compare with six baselines, and report competitive accuracy on the homophilic citation graphs, best results on Actor, Roman, and Amazon, robustness to edge noise, and faster inference than MPNNs.","tokens_in":23174,"tokens_out":6780,"duration_ms":68752,"significance":"ES-MLP is a sensible combination of two existing ideas, and the empirical study includes useful elements: ablations of the two auxiliary losses, hyperparameter sensitivity analysis, robustness experiments, and an inference-time comparison on full-graph versus test-only inputs. If the claims are properly scoped, the paper gives evidence that an MLP trained with edge-splitting can match or exceed message-passing baselines on several heterophilic benchmarks while keeping the inference-time advantages of a pure MLP. The release of source code is a further strength. The main weaknesses are that the headline 'all datasets' claim is false as stated and one baseline appears to be configured in a way that weakens the comparison; both are fixable.","major_comments":[{"comment":"The abstract's statement that ES-MLP 'is on par with homophilic and heterophilic models on all datasets' is contradicted by Table 2 on Minesweeper: ES-MLP obtains 50.87 ± 2.03 AUROC, essentially chance, while GraphSAGE obtains 88.90 ± 2.37. Section 6 itself explains that this is because 'the node features are independent of the class of a node' and MLP-based models have no access to neighbor features at inference. This is a hard boundary of the model class, not a minor benchmark miss, and it should be stated explicitly in the title and abstract, e.g., by scoping the claim to settings where node features carry label information.","section":"Abstract, Table 2, Section 6"},{"comment":"For Actor and Amazon, the reported Graph-MLP configuration sets α_NC = 0, i.e., the neighborhood-contrastive term, which is the component that distinguishes Graph-MLP from an MLP, is disabled on exactly the heterophilic datasets used to argue that Graph-MLP underperforms. The discussion in Section 6 that Graph-MLP 'cannot compete on the heterophilic dataset, since the original neighborhood contrastive loss is based on the homophily assumption' is therefore not supported by the Actor/Amazon experiments. The authors should either report Graph-MLP with a nonzero α_NC on these datasets or explain why α_NC = 0 was chosen and how the Amazon result (Graph-MLP 37.07 vs MLP 44.05) arises under the stated reuse of MLP hyperparameters.","section":"Appendix A Table 10 vs Table 2 and Section 6"},{"comment":"Section A.2 states that the adjacency power r is searched over {1, 2, 3}, but Table 9 reports r = 4 for Cora and Minesweeper. Table 11 also contains a malformed entry ('0.5.7') in the Amazon row. Because the reported results depend on these hyperparameters, the tables must be corrected and the search range reconciled; otherwise the experiments cannot be reproduced from the description.","section":"Section A.2 and Tables 9, 11"}],"minor_comments":[{"comment":"References [21] and [23] are the same paper (Lim et al., 'Large scale learning on non-homophilous graphs'), which should be merged or cited consistently.","section":"References"},{"comment":"The word 'seperately' should be 'separately' in the paragraph describing the per-channel forward pass.","section":"Section 3"},{"comment":"The text says 'reporter in Table 12' and 'best results are marked in bolt'; these should read 'reported' and 'bold'.","section":"Appendix C"},{"comment":"The sentence 'The difference to the best-performing models GCN and Graph-MLP is between 0.31 and 2.07 points' understates the CiteSeer gap: Graph-MLP achieves 77.79 and ES-MLP 75.67, a difference of 2.12 points.","section":"Section 6"},{"comment":"The x-axis labels give homophily values but not the corresponding amount of edge noise; please add the noise levels or describe the mapping in the caption.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable empirical contribution and the code release helps. The main issues are the overbroad 'all datasets' claim, the apparently degenerate Graph-MLP baseline on two heterophilic datasets, and the hyperparameter-table inconsistencies. None of these appears to require a fundamentally new approach, but the authors need to rerun or clarify the Graph-MLP baseline and rescope the claims before the paper can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: ES-MLP is exactly what it says—Graph-MLP's neighborhood contrastive loss with ES-GNN's edge splitting, plus a renormalized R/IR channel split. It gives a practical MLP-style model that is competitive on several heterophilic benchmarks and needs no adjacency matrix at inference. The main experimental claim is broadly supported, but the abstract overstates it: on Minesweeper the model is at chance (50.87 vs. GraphSAGE's 88.90), and the paper's own Limitations section admits why. That boundary is real and should be in the title or abstract, not just in Section 6.\n\nWhat's actually new and good: the combination is new relative to the cited literature. The two-channel splitting with renormalization to keep gamma_R + gamma_IR = 1 is a sensible fix to the small-coefficient problem. The evaluation is thorough: seven real datasets plus a CSBM grid, ablations, hyperparameter sensitivity, timing, and robustness experiments. Code is released. The ablation is useful—it shows both loss terms matter, and the sensitivity analysis indicates the method is not brittle to its hyperparameters. That is solid empirical practice.\n\nSoft spots, in proportion. First, the abstract/title overclaim. The authors know the Minesweeper limitation; they state it clearly in the Discussion. The fix is simple: scope the claim to settings where node features are informative of the label. Second, the robustness result is almost tautological: if you don't use edges at inference, test-time edge noise cannot affect you. That is the point of the model, not a flaw, but it shouldn't be framed as an empirical discovery. Third, the timing numbers have no variance or significance test; with 10 runs, a standard deviation is cheap to report. Fourth, the inference-time comparison lets MLP-based models be evaluated on test nodes only while MPNNs are forced to use the full graph; that is a legitimate operational advantage, but the framing should acknowledge that MPNNs could also be run on the full graph in a real deployment.\n\nWho this is for: researchers working on graph-MLP alternatives, especially for heterophilic graphs, and anyone who wants a simple, fast, no-message-passing baseline that still uses graph structure during training. It is not a field-reorganizing paper, but it is a useful within-subfield contribution. The paper deserves a serious referee: the experiments are reproducible, the method is easy to implement, and the limitations are honestly discussed. I would send it to review with a request to fix the overclaim and add variance for the timing results.","headline":"A solid, honestly-limited MLP alternative for heterophilic graphs; the abstract overclaims on Minesweeper but the core empirical work and ablations stand up.","tokens_in":23663,"tokens_out":2281,"would_cite":true,"duration_ms":24509,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"ES-MLP replaces message passing with an edge-splitting neighborhood loss, letting a pure MLP match or beat GNNs on homophilic and heterophilic graphs without ever using the adjacency matrix at inference.","keywords":["node classification","heterophilic graphs","homophily","MLP without message passing","edge splitting","neighborhood contrastive loss","inference-time robustness","graph neural networks"],"falsifier":"Run ES-MLP on a heterophilic graph whose node features carry no class information while neighbor features do (the Minesweeper setting); its accuracy will remain at chance because edges are absent at inference—and indeed the paper reports roughly 50% AUROC for ES-MLP on Minesweeper versus 88.9% for GraphSAGE.","tokens_in":22687,"feed_emoji":"⚡","tokens_out":12301,"duration_ms":107843,"temperature":0.7,"pith_summary":"The paper proposes ES-MLP, a node-classification model that never touches the graph's edges at inference time. It combines Graph-MLP's neighborhood contrastive loss with ES-GNN's edge-splitting mechanism: node features are projected into task-relevant and task-irrelevant subspaces, and each edge receives a learned weight deciding how much of it belongs to each channel. The authors claim that this two-channel loss lets a plain MLP outperform all six baselines on the heterophilic datasets Actor, Roman, and Amazon, while staying within about two accuracy points of the best message-passing models on the homophilic citation graphs Cora, CiteSeer, and PubMed. If true, message passing can be dropped entirely whenever a node's class is readable from its own features, which brings robustness to edge noise and two-to-five times faster inference.","feed_headline":"MLPs can match or beat GNNs on heterophilic graphs","feed_subtitle":"Edge-splitting loss removes the adjacency matrix at inference; stays stable under edge noise and runs 2–5x faster.","key_machinery":"The load-bearing object is the pair of splitting adjacency matrices A_R(i,j)=(1+alpha(i,j))/2 and A_IR(i,j)=(1-alpha(i,j))/2, where alpha(i,j) is a scalar in (-1,1) produced by a tanh-activated linear layer over the concatenated relevant and irrelevant embeddings of nodes i and j. Because A_R+A_IR equals the original adjacency matrix, every edge is partitioned into a task-relevant and a task-irrelevant channel. The r-th powers of these matrices feed a neighborhood contrastive loss computed separately on the Z_R and Z_IR embedding spaces, which is how the model learns from r-hop neighborhoods without message passing; an irrelevant consistency regularization term then minimizes the Z_IR distance of adjacent nodes whose predicted labels differ. At inference only the MLP on Z_R remains, so the adjacency matrix is never needed.","core_discovery":"ES-MLP's central claim is that the neighborhood structure of a graph can be digested during training, through a loss, and then discarded at inference. The model learns two exclusive splitting matrices A_R and A_IR, with A_R(i,j)+A_IR(i,j)=1 for every edge, by feeding the concatenated task-relevant and task-irrelevant embeddings of both endpoints into a tanh-activated linear layer. The neighborhood contrastive loss of Graph-MLP is then applied separately to the two embedding spaces, using powers of A_R and A_IR, so that task-relevant edges pull relevant representations together while irrelevant edges are handled in the other channel; an irrelevant consistency regularization further suppresses the irrelevant channel on edges whose endpoints are predicted to have different labels. Predictions are made solely from the task-relevant embedding Z_R. The paper demonstrates on seven real-world datasets and one CSBM synthetic family that this scheme yields accuracy on par with or better than GCN, GraphSAGE, ES-GNN, LINKX, and the two MLP baselines, and that the learned matrices separate homophilic from heterophilic edges as intended.","pith_inferences":["The Minesweeper result marks a hard boundary for all edge-free models, not just ES-MLP: whenever labels are determined by neighbor features rather than the node's own features, dropping edges at inference caps accuracy at chance; homophily level is irrelevant to this boundary.","Because the splitting coefficients are computed from the endpoints' embeddings, they could serve as a reusable edge-relevance score, for example to prune graphs or to flag distribution shift between training and deployment graphs—uses the paper does not explore.","The robustness to test-time edge noise follows directly from discarding edges at inference, so a fair comparison against other edge-free models such as LINKX on noisy graphs would be needed to isolate how much of that robustness is due to the edge-splitting loss rather than the absence of edges.","Extending the splitting to directed edges, which the paper lists as future work, could give the model a way to encode asymmetric neighborhood patterns; directed splitting coefficients would be a natural next experiment on heterophilic benchmarks."],"forward_implications":["On the heterophilic datasets Actor, Roman, and Amazon, ES-MLP outperforms all six baselines, including ES-GNN and GraphSAGE.","On the homophilic citation graphs Cora, CiteSeer, and PubMed, ES-MLP remains within about two accuracy points of the best MPNN, and it beats Graph-MLP on Cora and PubMed.","Injecting uniform or categorical edge noise into the test graph leaves ES-MLP's accuracy unchanged, while GCN, GraphSAGE, and ES-GNN drop by up to 12.7 points on Cora and 2–3 points on Amazon.","ES-MLP runs two to five times faster than the fastest MPNN baseline at inference and can be fed the test nodes alone without losing accuracy, because edges are absent by design.","The learned adjacency matrices separate homophilic from heterophilic edges, with the relevant channel carrying a higher share of same-class edges on Cora and most edges pushed into the irrelevant channel on Actor."],"supporting_citations":[{"why":"Supplies Graph-MLP, whose neighborhood contrastive loss is the training mechanism ES-MLP reuses on separate relevant and irrelevant channels.","marker":"[6]"},{"why":"Supplies ES-GNN's edge-splitting layer and irrelevant consistency regularization, which ES-MLP adapts into a message-passing-free loss.","marker":"[3]"},{"why":"Argues that MPNNs rely on consistent neighborhood label distributions rather than homophily alone; also provides the edge-noise addition algorithm used in the robustness experiments.","marker":"[5]"},{"why":"Defines the Contextual Stochastic Block Model and the parameter settings used to generate the synthetic graphs with controlled homophily.","marker":"[7]"},{"why":"GCN is the baseline message-passing model whose accuracy, inference time, and complexity ES-MLP is compared against.","marker":"[8]"},{"why":"Supplies the Actor dataset and its 48/32/20 train/validation/test split used for the heterophilic benchmark.","marker":"[22]"},{"why":"Defines the adjusted homophily ratio used to characterize the datasets and to compare homophily across different numbers of classes.","marker":"[24]"},{"why":"Provides the Amazon, Roman, and Minesweeper datasets and the evaluation protocol, including AUROC for the binary Minesweeper task.","marker":"[26]"}],"fun_headline_variants":["MLPs with edge-splitting loss match GNNs, no edges at inference","ES-MLP: train with edges, infer without, rivals GNNs","Splitting edges in loss lets MLP compete with GNNs on heterophily","No adjacency at test: MLP matches GNNs, 2-5x faster","Edge-splitting MLP: fast inference, robust to noise, GNN-level accuracy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"At inference time the node's class must be recoverable from its own feature vector, because edges are used only during training; on any task where labels are determined by neighbor features, as in Minesweeper, the model cannot classify correctly.","fun_headline_variants_meta":{"raw":{"variants":["MLPs with edge-splitting loss match GNNs, no edges at inference","ES-MLP: train with edges, infer without, rivals GNNs","Splitting edges in loss lets MLP compete with GNNs on heterophily","No adjacency at test: MLP matches GNNs, 2-5x faster","Edge-splitting MLP: fast inference, robust to noise, GNN-level accuracy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000303,"raw_usage":{"total_tokens":1801,"prompt_tokens":1059,"completion_tokens":742,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":675,"completion_tokens_details":{"reasoning_tokens":630}},"tokens_in":675,"tokens_out":742,"duration_ms":7309,"temperature":1.0,"reasoning_tokens":630,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T17:57:11.740369+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run ES-MLP on a heterophilic graph whose node features carry no class information while neighbor features do (the Minesweeper setting); its accuracy will remain at chance because edges are absent at inference—and indeed the paper reports roughly 50% AUROC for ES-MLP on Minesweeper versus 88.9% for GraphSAGE.","supporting_citations":[{"cited_title":"Es-gnn: Generalizing graph neural networks beyond homophily with edge splitting","cited_arxiv_id":null,"evidence_quote":"Supplies ES-GNN's edge-splitting layer and irrelevant consistency regularization, which ES-MLP adapts into a message-passing-free loss."},{"cited_title":"Is homophily a necessity for graph neural networks? In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022","cited_arxiv_id":null,"evidence_quote":"Argues that MPNNs rely on consistent neighborhood label distributions rather than homophily alone; also provides the edge-noise addition algorithm used in the robustness experiments."},{"cited_title":"Graph attention retrospective","cited_arxiv_id":null,"evidence_quote":"Defines the Contextual Stochastic Block Model and the parameter settings used to generate the synthetic graphs with controlled homophily."},{"cited_title":"Kipf and Max Welling","cited_arxiv_id":null,"evidence_quote":"GCN is the baseline message-passing model whose accuracy, inference time, and complexity ES-MLP is compared against."},{"cited_title":"Geom-GCN: Geometric graph convolutional networks","cited_arxiv_id":null,"evidence_quote":"Supplies the Actor dataset and its 48/32/20 train/validation/test split used for the heterophilic benchmark."},{"cited_title":"Characteriz- ing graph datasets for node classification: Homophily-heterophily dichotomy and beyond","cited_arxiv_id":null,"evidence_quote":"Defines the adjusted homophily ratio used to characterize the datasets and to compare homophily across different numbers of classes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Amazon, Roman, and Minesweeper datasets and the evaluation protocol, including AUROC for the binary Minesweeper task."}],"review_version":1}