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REVIEW 4 major objections 5 minor 43 references

Graph as a feature: improving node classification with non-neural graph-aware logistic regression

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Graph-aware Logistic Regression, a non-neural model that concatenates each node's adjacency row with its feature vector, ranks first across 13 node-classification datasets and runs up to two orders of magnitude faster than the best neural…

desk verdict A simple logistic regression on concatenated adjacency and features is a strong, fast baseline, but the paper's 'outperforms GNNs' claim is a 0.15 average-rank margin that a single timeout rule can flip. read the letter →

arxiv 2411.12330 v1 pith:YKXUFMEW submitted 2024-11-19 cs.LG

Simon Delarue , Thomas Bonald , Tiphaine Viard This is my paper · ORCID
classification cs.LG
keywords nodeclassificationgraphneuralnetworkslogisticregressiongraph-awarehomophilyfeaturescalabilitynon-neuralbaselines
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

Graph-aware Logistic Regression (GLR) is a non-neural classifier that builds each node's input by concatenating its row of the adjacency matrix with its own attribute vector, then fits a single logistic regression. The paper claims this recipe beats classical graph algorithms and state-of-the-art graph neural networks on a benchmark of 13 real-world attributed graphs, ranking first overall and first or second in 9 of 13 cases, while running up to two orders of magnitude faster than the best neural model. The authors argue that message passing, the core mechanism of GNNs, can drag in uninformative neighbor signals on heterophilous graphs, whereas a linear model on concatenated topology and features can learn to weigh the two sources. If the claim is right, strong node classification does not require a neural architecture, and feature-aware linear baselines should be standard in graph benchmarks.

What carries the argument

The load-bearing object is the concatenated representation $h_u = \mathrm{CONCAT}(A_u, X_u)$: the binary adjacency row of node $u$ followed by $u$'s feature vector, classified by $\hat{y}_u = \mathrm{softmax}(\beta^T h_u + \beta_0)$. This 'graph as a feature' move converts structure into an ordinary input vector, so the model can weight topology and attributes with a single learned linear map instead of running message passing. The paper compares GLR to SGC, noting that SGC is also a logistic regression but on smoothed features $S^l X$, whereas GLR keeps raw adjacency and raw features separate and concatenated. Training time is $O(n(n+L))$ with $n+L$ parameters, contrasted with the $O(mL + nLd)$ per-layer cost of message passing. The paper's second mechanism is feature homophily, $H_f(u) = \frac{1}{d_u} \sum_{v\in \mathcal{N}(u)} \mathrm{sim}(X_u, X_v)$, a diagnostic used to explain when features, rather than labels, carry the signal.

What would settle it

Run the same 13-dataset benchmark with per-dataset hyperparameter search for each GNN (e.g., 50 random trials per dataset) and no 5-hour timeout; if the average rank of H2GCN or GCNII drops below GLR's, the paper's central claim is refuted.

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Extended reading notes

Core claim

The paper's central discovery is that substituting the graph itself for the first layer of a GNN—using the raw adjacency row plus node features as the input to a linear softmax—is sufficient to outperform both foundational and specialized GNNs on diverse graphs. Under a k-fold protocol with fixed seeds, GLR's average rank over the 13 datasets is 3.23, ahead of H2GCN's 3.38, the best neural competitor; GLR is first or second in 9 of the 13 datasets, and it wins outright on most Wikipedia-based and heterophilous networks. The exceptions are the classic citation networks Cora, Pubmed, and Citeseer, where GNNs keep the lead. To explain this split, the paper introduces feature homophily—the average similarity between the attributes of connected nodes—and shows that on graphs with informative features (medium to high feature homophily), GNNs frequently fail to exploit the features, while GLR does. The authors also report that three highly homophilous graphs where GLR wins (CS, Photo, Ogbn-arxiv) have higher feature homophily than the citation networks, so label homophily alone does not predict which model will win.

Load-bearing premise

The comparison assumes that using each GNN's author-recommended hyperparameters unchanged across all 13 datasets, plus a 5-hour training cap with timed-out models ranked last, is a fair measure of each architecture's performance.

Editorial extensions

If this is right

  • GLR becomes a baseline every node-classification benchmark should include; it is simpler, faster, and in this comparison at least as accurate as the best GNN.
  • The claim that GNNs are the best for node classification needs qualification: on heterophilous and feature-rich graphs, a linear model on concatenated adjacency and features can win.
  • Feature homophily gives practitioners a cheap pre-training check: if a graph has medium-to-high feature homophily, a linear feature-aware model may outperform a message-passing network.
  • Scalability results imply large attributed graphs can be classified accurately without GPU training or aggressive sampling; GLR finishes where GNN baselines time out under the 5-hour budget.

Reading between the lines

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

  • A direct extension the authors do not test is applying the same concatenation recipe to link prediction and graph classification; if it transfers, the 'graph as a feature' principle would hold beyond node classification.
  • Because GNN hyperparameters are fixed at author-recommended values across all datasets, the superiority claim is protocol-dependent; per-dataset tuning or relaxed time limits could narrow or reverse the gap.
  • The feature-homophily diagnostic could be used as a selection rule before training: compute $H_f$ and choose GLR when it is high, a GNN when label homophily is high and feature homophily low.
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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

4 major / 5 minor

Summary. The paper introduces Graph-aware Logistic Regression (GLR), a non-neural node classifier that concatenates each node's adjacency row with its feature vector and feeds the result into logistic regression. The authors evaluate GLR against eight GNN baselines and several non-neural baselines on 13 datasets spanning diverse sizes, densities, and homophily levels, using a unified k-fold cross-validation protocol. They report that GLR ranks first in average rank (3.23 vs. 3.38 for H2GCN), achieves competitive accuracy on homophilous and heterophilous graphs, and is up to two orders of magnitude faster. They also introduce 'feature homophily' as a complementary explanatory variable to label homophily and argue that GNNs underuse node features when those features are informative.

Significance. If the central claim is sustained, the paper is significant: it shows that a simple linear model that does not aggregate messages can match or beat specialized GNNs on a broad suite of benchmark graphs, while being far cheaper. The controlled evaluation framework, the inclusion of non-neural baselines, and the publicly available code are concrete strengths. The feature homophily analysis, though exploratory, is a useful step beyond label homophily. These strengths make the paper potentially important for the node-classification literature. The main reservation is that the headline 'ranks first' claim depends on a small average-rank margin that is sensitive to the handling of timed-out runs and to the choice of fixed GNN hyperparameters; these points need to be addressed before the stronger claims can be accepted.

major comments (4)
  1. [Section 7.2, Table 1] The claim that 'GLR ranks first across the 13 datasets' rests on an average-rank margin of only 0.15 over H2GCN (3.23 vs. 3.38). Because models that exceed the 5-hour limit are assigned the lowest rank, H2GCN's timeout on Wikivitals+ contributes a rank of 15. If H2GCN had completed that run at any rank at or below 13 (e.g., a mid-table rank of 8), its average would improve by (15-8)/13 = 0.54 and it would overtake GLR. The result is therefore sensitive to a single unobserved run of a competing method. The paper should report a sensitivity analysis (e.g., a table of average ranks under different treatments of timeouts, or a per-dataset win/loss count) and qualify the 'ranks first' statement accordingly. Without this, the headline claim is not robust.
  2. [Abstract and Section 7.2] The abstract and Section 7.2 state that GLR 'outperforms both foundational and sophisticated state-of-the-art GNN models.' Table 1 does not support an unqualified reading: H2GCN has higher accuracy on Cora, Pubmed*, Citeseer, and CS, and GLR's advantage over H2GCN on many other datasets is within one standard deviation. The accurate statement is that GLR has the best average rank under the adopted timeout rule and is competitive with or better than H2GCN on most datasets, while being much faster. The abstract and conclusions should reflect this qualified claim rather than a blanket outperformance.
  3. [Appendix C, Table 4 and Section 6.2] The GNN hyperparameters are fixed to the values proposed in the original papers for all 13 datasets, with no per-dataset tuning. In contrast, GLR's regularization strength appears to be a free parameter (though the paper does not state whether it is tuned per dataset). If GLR's regularization is tuned on each dataset while GNNs use fixed defaults, the comparison is not a fair test of accuracy under equal tunability. The paper should disclose the GLR regularization values and either tune the GNNs as well (e.g., with a small validation-based search) or explicitly justify that the fixed defaults are representative and that tuning would not change the conclusions.
  4. [Section 4.2] The complexity analysis is not rigorous enough to support the scalability claims. The paper states that GLR's training time complexity is O(n(n+L)), which is quadratic in node count and would be worse than the stated GNN cost O(mL+nLd) for large sparse graphs. If the intended meaning is that the number of parameters is n+L, that is not a training-time complexity. The empirical speedups in Figure 3 may be valid for the specific implementations and dataset sizes, but the asymptotic comparison as written is misleading and should be corrected or removed.
minor comments (5)
  1. [Section 6.1] The evaluation framework states that k-fold cross-validation is used, but the value of k is never specified. Appendix C gives a 75%-25% split, which suggests k=4, but this should be stated explicitly.
  2. [Section 1 and Section 8] There are several typos: 'In this work, propose combining' is missing 'we'; 'compared to it best neural competitor' should be 'its best'; 'computation time reduction up to two orders' should be 'reduction of up to two orders'; 'results in a total of k training and testing experiments' should be 'k training and testing experiments per fold'.
  3. [Table 4] The SGC row is labeled '1-layer GAT(K=2)' which appears to be a copy-paste error; it should say SGC.
  4. [Section 7.4] The dataset name is written as 'Ogbn-arixv' in the text; it should be 'Ogbn-arxiv'.
  5. [Section 4.2 and Appendix C] The paper does not report the regularization strength of the logistic regression used in GLR. Since this is the only free hyperparameter of the proposed method, reporting its value (or the tuning procedure) would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: GLR's predictions are genuine out-of-sample evaluations of a linear model on concatenated adjacency row and features; the post-hoc feature-homophily analysis is interpretive, not load-bearing.

full rationale

GLR's only construction is Eq. (5), h_u = CONCAT(A_u, X_u), followed by softmax logistic regression, whose parameters are trained on labeled nodes. The reported accuracies are test-set averages over k-fold cross-validation (Section 6.1), so the 'predictions' are not equal by construction to any fitted input. Feature homophily (Eq. 8) is introduced in Section 7.4 after the benchmark results and used only to interpret where GLR wins; it is not fed back into the model or into the ranking, so it creates no self-definitional loop. The closest thing to a structural concern is the Section 7.2 rule assigning time-out models the lowest rank, which affects the headline average-rank claim; however, this is a stated evaluation-protocol choice weighting scalability equally with accuracy, not a reduction of the model's output to its input, and the paper discloses it in the same sentence. No load-bearing self-citation or imported uniqueness theorem is used to justify the GLR form. Hence no circular step can be exhibited.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

GLR's only fitted quantities are its logistic weights, learned normally. The load-bearing choices are all in the evaluation protocol: default GNN hyperparameters, the time-out ranking rule, and the post-hoc feature homophily measure. These do not make the method circular, but they limit how strongly the empirical conclusions can be stated.

free parameters (1)
  • Regularization strength of GLR logistic regression = not reported
    The paper does not state whether L1/L2 regularization or its coefficient is used; on high-dimensional inputs this can change accuracy and is therefore a hidden choice.
assumptions (5)
  • domain assumption Transductive semi-supervised setting where all graph structure and node features are available at training time
    Section 3.1 defines the problem this way; it excludes inductive settings and affects how adjacency rows are used.
  • ad hoc to paper GNN hyperparameters from original papers are appropriate across all datasets
    Appendix C, Table 4 fixes hyperparameters; no per-dataset tuning is performed, which is a strong premise for a fair comparison.
  • ad hoc to paper A 5-hour training limit with time-outs assigned the lowest rank is a fair evaluation rule
    Section 7.2 states this rule; it affects average ranks and favors fast methods like GLR.
  • ad hoc to paper Cosine similarity is the appropriate measure of feature homophily
    Section 7.4 defines Hf using sim(.,.) and gives cosine as an example; the conclusions about GLR's success depend on this choice.
  • domain assumption 75/25 stratified splits with fixed seeds give representative performance estimates
    Section 6.1 and Appendix C set this protocol; the conclusions are conditional on it.

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Pith. "Pith review of Graph as a feature: improving node classification with non-neural graph-aware logistic regression." pith.science (2026). https://pith.science/paper/YKXUFMEW

@misc{pith2026241112330,
  author       = {Pith},
  title        = {Pith review of: Graph as a feature: improving node classification with non-neural graph-aware logistic regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YKXUFMEW}},
  note         = {Machine review of arXiv:2411.12330}
}
read the original abstract

Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still struggle to generalise well beyond datasets that exhibit strong homophily, where nodes of the same class tend to connect. This limitation has led to the development of complex neural architectures that pose challenges in terms of efficiency and scalability. In response to these limitations, we focus on simpler and more scalable approaches and introduce Graph-aware Logistic Regression (GLR), a non-neural model designed for node classification tasks. Unlike traditional graph algorithms that use only a fraction of the information accessible to GNNs, our proposed model simultaneously leverages both node features and the relationships between entities. However instead of relying on message passing, our approach encodes each node's relationships as an additional feature vector, which is then combined with the node's self attributes. Extensive experimental results, conducted within a rigorous evaluation framework, show that our proposed GLR approach outperforms both foundational and sophisticated state-of-the-art GNN models in node classification tasks. Going beyond the traditional limited benchmarks, our experiments indicate that GLR increases generalisation ability while reaching performance gains in computation time up to two orders of magnitude compared to it best neural competitor.

Figures

Figures reproduced from arXiv: 2411.12330 by the authors.

Figure 1
Figure 1. Overview of our Graph-aware Logistic Regression (GLR) method for node classification. We [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Test average accuracy (and standard deviation) for the best GNN and non-neural baselines. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Tradeoff between accuracy and computation time. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Node label and feature homophily distributions across graphs. Width of the violins is scaled by [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Cumulative node degree distributions. B Models B.1 GNNs In our study, we consider both foundational and specialised GNN models to benchmark our approach. These neural models include the following: Graph Convolutional Network (GCN) (Kipf & Welling, 2017), a standard and…
Figure 6
Figure 6. Figure 6: Average accuracy on the test set for Wikischools, according to the proportion of nodes in the test set. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.