Pith. sign in

REVIEW 4 major objections 4 minor 26 references

Fixed Aggregation Features Can Rival GNNs

T0 review · 4 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read Fixed neighborhood statistics plus a tuned MLP rival trained GNNs on 12 of 14 node-classification benchmarks.

desk verdict Useful, carefully-done baseline paper whose headline overclaims: Table 1 gives 10/14, not 12/14, and the transformer comparison is inherited, not run. read the letter →

arxiv 2601.19449 v2 pith:X75KBF4J submitted 2026-01-27 cs.LG

Celia Rubio-Madrigal , Rebekka Burkholz This is my paper
classification cs.LG
keywords fixedaggregationfeaturesnodeclassificationgraphneuralnetworksKolmogorov-Arnoldrepresentationtabularlearningmessagepassingbenchmarkingexpressivity
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

This paper sets out to show that learned neighborhood aggregation—the defining component of graph neural networks—is not necessary for strong node classification on current benchmarks. The authors construct Fixed Aggregation Features (FAFs): for each node they concatenate its own features with fixed statistics (mean, sum, max, min, std) of neighbor features at several hops, and train only a plain multilayer perceptron on the resulting tabular matrix. They report that this training-free aggregation pipeline matches or beats classic GNNs on 12 of 14 standard node-classification tasks, often with mean aggregation alone. They also prove that lossless fixed aggregation is theoretically possible via Kolmogorov-Arnold representations, but argue that the reliable practical signal comes from simple, non-injective distribution summaries rather than from the lossless encoding. The stakes: if correct, many benchmark gains attributed to learned message passing actually come from tuning and readout capacity, and tabular models should be standard baselines.

What carries the argument

Fixed Aggregation Features (FAFs): a node's representation is built by applying non-learned permutation-invariant reducers (mean, sum, max, min, std) to feature multisets of neighbors at each hop k=1..K, concatenating all hops with the node's original features, and training an MLP on the resulting table. The theoretical backstop is a sum-aggregation injectivity theorem for orthogonal features at hop 1 and a Kolmogorov-Arnold-based discontinuous encoding Φ that is lossless but ill-conditioned; the practical work is done by hop-concatenation and a well-tuned nonlinear readout.

What would settle it

A concrete falsification would be a node-classification benchmark—real or synthetic—where labels depend on neighborhood structure that is not recoverable from these reducers at any hop, yet a trained GNN succeeds while FAFs fail. For example, a task where the label depends on the exact multiset of neighbor labels at hop 3 with non-orthogonal features, or on whether two specific neighbors share a common neighbor; if a tuned GNN solves it and FAF+MLP cannot, the paper's generalization claim would fail.

Watch

Extended reading notes

Core claim

The central claim is that a fixed, parameter-free aggregation of node features over neighborhoods—followed by a well-tuned MLP—can match or exceed state-of-the-art GNNs and graph transformers on 12 of 14 node-classification benchmarks. The exceptions are two heterophilous tasks (Roman-Empire and Minesweeper) that appear to need longer-range, hop-specific signal that simple reducers fail to capture. The paper further proves that 1-hop sum aggregation is injective on orthogonal features, and that a discontinuous Kolmogorov-Arnold encoding is lossless in principle yet numerically brittle in practice. The conclusion is that on most current benchmarks, learned aggregation is not the source of GNN

Load-bearing premise

The central practical claim rests on the assumption that concatenating simple distribution-only reducers (mean, sum, max, min) over a few hops preserves the task-relevant neighborhood information on these benchmarks; the paper proves this only for sum on orthogonal features at one hop, and its lossless Kolmogorov-Arnold encoding is too numerically brittle to use.

Editorial extensions

If this is right

  • A tuned FAF baseline should be included in any node-classification benchmark to calibrate what fixed aggregation alone achieves.
  • Datasets where FAFs reach state-of-the-art should be re-evaluated or retired as tests of learned message passing.
  • The ablations show that concatenating all hops and using an MLP rather than a linear readout are key to matching GNNs.
  • On most benchmarks, two hops suffice, implying that long-range aggregation is not driving current results.
  • Benchmark design should shift toward tasks where relevant signal genuinely lies at distant hops and requires learnable aggregation.

Reading between the lines

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

  • If FAFs match GNNs on these benchmarks, then reported accuracy gains of new graph architectures on the same datasets are more plausibly attributed to hyperparameter tuning, optimization, or classifier architecture than to learned aggregation; this is a testable re-evaluation, not the paper's own claim.
  • A natural extension is to swap the MLP for gradient-boosted trees or other tabular learners on FAF features; the paper hints at this but does not test it, and gains could be dataset-dependent.
  • The SHAP-based feature attribution offered by FAFs could be used prospectively to pre-screen datasets: if early-hop mean features separate classes well, a dataset is unlikely to reward GNN-specific inductive biases.
  • The two failing datasets suggest a concrete research target: characterize the precise long-range or inter-hop statistics that simple reducers miss, and design a fixed reducer that captures them.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes Fixed Aggregation Features (FAFs): for each node, the original feature vector is concatenated with fixed, untrained multi-hop aggregations of neighbor features (mean, sum, max, min, std, optionally combined), and the resulting table is fed into a tuned MLP for node classification. The authors argue that learned neighborhood aggregation is not necessary on most standard benchmarks, support this with a theory section (injectivity of sum on orthogonal features, and a Kolmogorov–Arnold lossless encoding), and report experiments on 14 datasets comparing FAF+MLP with classic GNNs (GCN, GAT, GraphSAGE) and, via numbers inherited from Luo et al. (2024), with graph transformers and heterophily-aware models. The headline claim is that FAFs rival or outperform these models on 12/14 tasks, with Roman-Empire and Minesweeper as the only exceptions. The manuscript also provides ablations over hops, reducers, classifier depth, and running time, plus a comparison with GESN and preliminary results on GraphLand.

Significance. If the empirical claim were fully supported, this would be a useful contribution: a strong, interpretable, fixed-feature baseline for node classification, with practical implications for benchmark design and for what aspects of GNNs are actually load-bearing. The paper has real strengths: the code is public, the per-variant and per-hop tables are detailed, validation/test splits are reported, and the ablations (Tables 6–10) are informative. However, the central '12/14' claim is contradicted by the paper's own Table 1, and the comparison to graph transformers is inherited rather than run in this manuscript. After correcting these issues, the core idea still has value as a strong tabular baseline, but the paper's current framing substantially overstates the evidence.

major comments (4)
  1. [Abstract, Section 5, Table 1] The abstract and introduction state that FAFs rival or outperform GNNs and graph transformers on 12/14 tasks, with only Roman-Empire and Minesweeper as exceptions. This is not supported by Table 1. Section 5 itself says FAFs 'improve on 5 datasets, match within error or 1% on another 5, and trail on 4.' The four trailing datasets are Citeseer (FAFbestval 70.48±1.24 vs GCN 72.72±0.45), Cora (82.84±0.63 vs GCN 84.38±0.81), Minesweeper (90.00±0.39 vs SAGE 97.72±0.70), and Roman-Empire (78.11±0.38 vs GCN 91.05±0.15). The Citeseer and Cora gaps exceed 1.5 points and do not overlap within standard errors, so they cannot be called 'close to parity' under the paper's own 1% criterion. The data support at most 10–11/14 for classic GNNs, not 12/14. This is a load-bearing inconsistency in the headline contribution and must be corrected by revising the counts and the list of exceptions.
  2. [Section 5, Table 1, Abstract] The abstract claims FAFs rival or outperform 'state-of-the-art GNNs and graph transformers,' but Table 1 and Section 5 only report experiments against GCN, GAT, and GraphSAGE. No graph transformer is run in this paper; the comparison to graph transformers and heterophily-aware models is inherited from Luo et al. (2024). No table reproduces those numbers or shows how FAFs compare with them. If the authors wish to retain the graph-transformer claim, they need to either run those models under the same protocol or explicitly restrict the claim to classic GNNs and cite the inherited results only as context. As written, the abstract's scope is not substantiated by the experiments.
  3. [Section 4, Theorem 4.1, Introduction] The theoretical justification for why simple reducers suffice is limited. Theorem 4.1 proves injectivity of sum aggregation only under the assumption that node features are orthogonal (and finite in number). The paper's introduction states that 'on hops 0–1, sum and mean preserve information' without this qualification, and the benchmark datasets have dense or bag-of-words features that are not orthogonal. The paper acknowledges information loss for k≥2 but still uses this theory as the main explanation for FAFs' empirical success. The claims in the introduction and Section 4 should be explicitly conditioned on the orthogonality assumption, and the text should clarify that the theorem is a proof of possibility under idealized features, not an explanation for the observed performance on non-orthogonal real-world features.
  4. [Appendix D, Table 11] The Kolmogorov–Arnold (KA) reducer is described as theoretically lossless, but the implementation for multisets is not permutation-invariant: 'we make it act on multisets by sorting, which we fix by the given data order' (Appendix D). Node ordering is arbitrary, so this is not a well-defined function on multisets; two isomorphic neighborhoods with different orderings would produce different features. The poor results in Table 11 (e.g., Cora training accuracy 14.29±0.00, which is exactly chance for 7 classes) may reflect this implementation choice rather than the intrinsic brittleness of Φ. Please either provide a canonical permutation-invariant construction or clearly state that the KA experiment is a non-invariant heuristic and not a test of Theorem 4.2.
minor comments (4)
  1. [Abstract, Section 3] 'Training-free approach' is potentially misleading because the aggregation is training-free but the downstream MLP is trained. Consider rewording to 'training-free aggregation' or 'fixed aggregation'.
  2. [Section 5, Table 5/6] The paper selects 'FAFbestval' from validation across several variants. Please state explicitly how many variants were considered for each dataset and whether the same validation split was used for all variants, so readers can assess potential selection bias.
  3. [Figure 3, Appendix A.1] The panels in Figure 3 are dense and the axes in panels (a.iii), (b.i), and (c.ii) are not all labeled. Adding labels and a short walk-through would make the visualization of Φ and its inverse much easier to follow.
  4. [Table 4, Appendix B] The table caption does not define the columns 'hop' and 'mlp layers' for FAF; adding a sentence clarifying that 'hops' is the aggregation depth K and 'mlp layers' is the number of hidden layers would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FAFs are independently defined fixed aggregations, the theory imports external theorems, and the empirical comparisons are standard train/validation/test evaluations.

full rationale

The central construction (Eqs. 1–2) defines FAFs as concatenations of fixed reducers (mean, sum, max, min, std) over hops; no target quantity is used to define the features. The MLP classifier is trained on training labels and the best FAF variant is chosen by validation (Table 5) and then reported on test (Table 6), which is standard model selection, not a fitted parameter being renamed as a prediction. The theoretical claims are imported from external work: Theorem 4.1 generalizes Lemma 5 of Xu et al. (2019) and is proved in Appendix A.2 via explicit extraction of counts from orthogonal-feature sums; Theorem 4.2 is Theorem 2 of Schmidt-Hieber (2021). These are external, citable mathematical results, not self-citations, and the paper does not rely on them to fit the empirical numbers. The Kolmogorov–Arnold encoder Φ is explicitly tested and found empirically brittle (Table 11), so the main FAF results do not secretly depend on the lossless construction. Self-citations (Rubio-Madrigal et al. 2025, Mustafa & Burkholz 2024a/b, Jamadandi et al. 2024, Reddy et al. 2026a) appear in related-work context or as optional feature augmentations (Table 12), not as load-bearing support for the paper's central claim. The abstract's '12 tasks' count is internally inconsistent with Section 5's 'trail on 4' and Table 1, but that is a correctness/consistency problem, not a circularity of derivation: no equation reduces a predicted result to its own input. The paper also explicitly labels the two-hop behavior as information-losing and frames the low-hop sufficiency as an experimentally motivated hypothesis rather than as a derived consequence. Therefore no circular step can be exhibited with the required specificity, and the appropriate circularity score is 0.

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

The practical claim rests on two free selection mechanisms (reducer set and MLP hyperparameters chosen per dataset by validation), plus a theorem that only covers orthogonal features and a KA construction that is theoretically lossless but empirically brittle. No new physical entities are introduced.

free parameters (4)
  • FAF variant selection (reducer set) = per-dataset: e.g., FAFmean on Computer, FAF4 on Pubmed
    The headline FAFbestval is the best of up to seven reducer combinations selected by validation (Table 5), so the reported test accuracy is a maximum over configurations, not a single a-priori model.
  • MLP hyperparameters = per-dataset dropout, lr, normalization, hidden channels, weight decay, MLP layers (Table 4)
    Tuned on the same validation splits used for GNN baselines; these choices materially affect the 12/14 result (e.g., FAF on Citeseer uses no dropout and lr 0.005).
  • Hop depth K = taken from best GNN depth per dataset, e.g., 2 for Computer, 15 for Minesweeper, restricted when OOM
    Depth is not learned; it is copied from Luo et al. baselines or manually restricted, which affects how much neighborhood information is available to the MLP.
  • Weight decay range = 0, 1e-2, 1e-3, 5e-4, 5e-5
    Luo et al. does not specify ranges, so the authors chose values from best runs, an ad hoc tuning choice.
assumptions (4)
  • domain assumption Sum aggregation is injective on multisets of orthogonal features of bounded size (Theorem 4.1).
    Real node features (bag-of-words, 300-d continuous embeddings) are not orthogonal; the theorem is used to motivate 1-hop preservation but does not apply to actual features or k≥2.
  • standard math Kolmogorov-Arnold representation variant (Theorem 2 of Schmidt-Hieber, 2021): existence of monotone φ and injective Φ on [0,1]^d (Theorem 4.2).
    External theorem used without proof; the paper relies on it to claim existence of a lossless fixed aggregation function.
  • standard math No continuous, permutation-invariant aggregation can be injective on all multisets of real vectors (Corso et al., 2020; Netto dimension obstruction).
    Used to justify that the lossless aggregator must be discontinuous.
  • ad hoc to paper An MLP trained on concatenated fixed features generalizes comparably to GNNs under the same splits and tuning budget.
    The empirical program assumes that tabularization does not lose task-relevant signal; this is validated only post hoc on the fourteen benchmarks, not derived.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Fixed Aggregation Features Can Rival GNNs." pith.science (2026). https://pith.science/paper/X75KBF4J

@misc{pith2026260119449,
  author       = {Pith},
  title        = {Pith review of: Fixed Aggregation Features Can Rival GNNs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X75KBF4J}},
  note         = {Machine review of arXiv:2601.19449}
}
read the original abstract

Graph neural networks (GNNs) are widely believed to excel at node representation learning through trainable neighborhood aggregations. We challenge this view by introducing Fixed Aggregation Features (FAFs), a training-free approach that transforms graph learning tasks into tabular problems. This simple shift enables the use of well-established tabular methods, offering strong interpretability and the flexibility to deploy diverse classifiers. Across 14 benchmarks, well-tuned multilayer perceptrons trained on FAFs rival or outperform state-of-the-art GNNs and graph transformers on 12 tasks -- often using only mean aggregation. The only exceptions are the Roman Empire and Minesweeper datasets, which typically require unusually deep GNNs. To explain the theoretical possibility of non-trainable aggregations, we connect our findings to Kolmogorov-Arnold representations and discuss when mean aggregation can be sufficient. In conclusion, our results call for (i) richer benchmarks benefiting from learning diverse neighborhood aggregations, (ii) strong tabular baselines as standard, and (iii) employing and advancing tabular models for graph data to gain new insights into related tasks.

Figures

Figures reproduced from arXiv: 2601.19449 by the authors.

Figure 1
Figure 1. Fixed Aggregation Features (FAFs) are calculated as a pre-processing step, concatenated to the input (⊕), and fed to an MLP. If Φ is injective, the neighborhood information is preserved. The Kolmogorov-Arnold theorem ensures the existence of such a function. toolbox of tabular learning (designed to handle noise, class imbalance, feature selection, etc.), architectural flexibility, and reduced training compute. Empir… view at source ↗
Figure 2
Figure 2. SHAP feature importance for Minesweeper, stacked by hop. Numbers show features’ rankings per hop. features carry signal independent of model choice. Fol￾lowing Donnelly et al. (2023), noisy tabular datasets often admit a “Rashomon set” of comparably well-performing models. Accordingly, feature importance is better assessed over this set—preferably constrained to simpler or sparser models—than from a single fit. This… view at source ↗
Figure 3
Figure 3. Functions Φ (Thm 4.2)—and its inverse—, mean and std. Circles and square-like panels (a.i, a.ii, b.ii, b.iii, c.i) live in the 2D space, while segments and Cantor sets (a.iii, b.i, c.ii, c.iii) live in 1D. Colors in (a) and (c) are based on angles on 2D, while colors in (b) are based on position. Here we showcase the behavior of Φ from the Kolmogorov-Arnold representation from Theorem 4.2. In Fig. 3a, we see the Φ i… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: 1 2 4 5 3 6 7 8 Feature encodings: □ = [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Train, validation, and test accuracy of FAF+MLP versus GCN. (i) 21 [PITH_FULL_IMAGE:figures/full_fig_p021_5.png]
Figure 5
Figure 5. Figure 5: Train, validation, and test accuracy of FAF+MLP versus GCN. (ii) 22 [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]
Figure 5
Figure 5. Figure 5: Train, validation, and test accuracy of FAF+MLP versus GCN. (iii) 23 [PITH_FULL_IMAGE:figures/full_fig_p023_5.png]
Figure 5
Figure 5. Figure 5: Train, validation, and test accuracy of FAF+MLP versus GCN. (iv) D. Additional Experiments and Ablations Number of hops. In Tables 7 and 8 we include the test and validation for different number of hops concatenated as features for FAF4. One hop already gives much of t…
Figure 6
Figure 6. Figure 6: SHAP feature importance for Pubmed and Amazon-Ratings. The base features are ranked according to the sum of their importance values across hops. Numbers on the stacked bars indicate the ranking of that particular feature on that particular hop. E. Comparison to Graph E…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

26 extracted references · 1 canonical work pages

  1. [1]

    DROPOUT∈(0.0 0.2 0.3 0.5 0.7)

  2. [2]

    Chen, J., Gao, K., Li, G., and He, K

    URL https://openreview.net/forum? id=udfjje2xXb. Chen, J., Gao, K., Li, G., and He, K. NAGphormer: A tokenized graph transformer for node classification in large graphs. InThe Eleventh International Conference on Learning Representations, 2023. URL https:// openreview.net/forum?id=8KYeilT3Ow. Chen, T. and Guestrin, C. Xgboost: A scalable tree boosting sys...

    2023

  3. [3]

    NORMALIZATION∈(ln bn none)

  4. [4]

    (2024) includes weight decay as a hyperparameter, there are no concrete ranges specified for it

    HIDDEN CHANNELS∈(64 256 512) While Luo et al. (2024) includes weight decay as a hyperparameter, there are no concrete ranges specified for it. Therefore, we tune all the different values from the best runs of the given datasets:

    2024

  5. [5]

    16 Fixed Aggregation Features Can Rival GNNs Moreover, Luo et al

    WEIGHT DECAY∈(0.0 1e-2 1e-3 5e-4 5e-5). 16 Fixed Aggregation Features Can Rival GNNs Moreover, Luo et al. (2024) tunes the local layers from 1 to 10 or 15. We instead take for each dataset the same value that they have found best for the GNNs, and use it to construct our fixed aggregation features up to that depth. In some cases where there are too many f...

    2024

  6. [6]

    reservoir

    MLP LAYERS∈(2 3 5). On the other hand, we do not include linear residual connections, as these are used to bypass the convolutional layers in the classical GNNs. This creates a direct difference on the two datasets that most benefit from this component, Minesweeper and Roman-Empire. In Table 4 we include the best hyperparameter choices for the four models...

    2024

  7. [8]

    Lundberg, S

    URL https://openreview.net/forum? id=Ozo7qJ5vZi. Lundberg, S. M. and Lee, S.-I. A unified approach to inter- preting model predictions. InProceedings of the 31st In- ternational Conference on Neural Information Processing Systems, NIPS’17, pp. 4768–4777, Red Hook, NY , USA,

  8. [9]

    ISBN 9781510860964

    Curran Associates Inc. ISBN 9781510860964. Luo, Y ., Shi, L., and Wu, X.-M. Classic GNNs are strong baselines: Reassessing GNNs for node classification. InThe Thirty-eight Conference on Neural Information Processing Systems Datasets and Benchmarks Track,

Show all 26 references
  1. [10]

    10 Fixed Aggregation Features Can Rival GNNs Luo, Y ., Shi, L., and Wu, X.-M

    URL https://openreview.net/forum? id=xkljKdGe4E. 10 Fixed Aggregation Features Can Rival GNNs Luo, Y ., Shi, L., and Wu, X.-M. Can classic GNNs be strong baselines for graph-level tasks? simple architec- tures meet excellence. InForty-second International Conference on Machine...

    2022

  2. [14]

    Mustafa, N

    URL https://proceedings.mlr.press/ v202/mohtashami23a.html. Mustafa, N. and Burkholz, R. Dynamic rescaling for train- ing GNNs. InThirty-eighth Annual Conference on Neural Information Processing Systems, 2024a. URL https: //openreview.net/forum?id=IfZwSRpqHl. Mustafa, N. and B...

    2023

  3. [16]

    Topping, J., Giovanni, F

    URL https://proceedings.mlr.press/ v202/shirzad23a.html. Topping, J., Giovanni, F. D., Chamberlain, B. P., Dong, X., and Bronstein, M. M. Understanding over-squashing and bottlenecks on graphs via curvature. InIn- ternational Conference on Learning Representations,

  4. [19]

    Zhou, D., Kharlamov, E., and Kostylev, E

    URL https://openreview.net/forum? id=I9omfcWfMp. Zhou, D., Kharlamov, E., and Kostylev, E. V . GLora: A benchmark to evaluate the ability to learn long- range dependencies in graphs. InThe Thirteenth In- ternational Conference on Learning Representations,

  5. [20]

    Zhu, J., Yan, Y ., Zhao, L., Heimann, M., Akoglu, L., and Koutra, D

    URL https://openreview.net/forum? id=2jf5x5XoYk. Zhu, J., Yan, Y ., Zhao, L., Heimann, M., Akoglu, L., and Koutra, D. Beyond homophily in graph neural networks: Current limitations and effective designs.Advances in Neural Information Processing Systems, 33, 2020. Zhu, J., Ross...

    2020 doi

  6. [21]

    Mohtashami, A., Jaggi, M., and Stich, S

    URL https://www.sciencedirect.com/ science/article/pii/S0167865525002168. Mohtashami, A., Jaggi, M., and Stich, S. U. Spe- cial properties of gradient descent with large learn- ing rates. In Krause, A., Brunskill, E., Cho, K., En- gelhardt, B., Sabato, S., and Scarlett, J. (ed...

  7. [22]

    LR∈(0.01 0.005 0.001 0.0001)

  8. [565]

    URL https: //doi.org/10.1007/s10994-025-06865-3

    doi: 10.1007/s10994-025-06865-3. URL https: //doi.org/10.1007/s10994-025-06865-3. Kipf, T. N. and Welling, M. Semi-supervised classi- fication with graph convolutional networks. InIn- ternational Conference on Learning Representations,

    doi

  9. [2000]

    URL https: //doi.org/10.1023/A:1009953814988

    doi: 10.1023/A:1009953814988. URL https: //doi.org/10.1023/A:1009953814988. Mernyei, P. and Cangea, C. Wiki-cs: A wikipedia-based benchmark for graph neural networks. InICML Work- shop: Graph Representation Learning and Beyond, 2020. URLhttps://arxiv.org/abs/2007.02901. Michel...

    2020 arXiv

  10. [2017]

    Kolmogorov, A

    URL https://openreview.net/forum? id=SJU4ayYgl. Kolmogorov, A. N. On the representation of continuous functions of many variables by superposition of continu- ous functions of one variable and addition. InDoklady Akademii Nauk, volume 114(5), pp. 953–956. Russian Academy of Sc...

    1957

  11. [2018]

    accepted as poster

    URL https://openreview.net/forum? id=rJXMpikCZ. accepted as poster. Wu, F., Souza, A., Zhang, T., Fifty, C., Yu, T., and Wein- berger, K. Simplifying graph convolutional networks. In Chaudhuri, K. and Salakhutdinov, R. (eds.),Proceed- ings of the 36th International Conference ...

    2019

  12. [2021]

    Corso, G., Cavalleri, L., Beaini, D., Li`o, P., and Velickovic, P

    URL https://openreview.net/forum? id=n6jl7fLxrP. Corso, G., Cavalleri, L., Beaini, D., Li`o, P., and Velickovic, P. Principal neighbourhood aggregation for graph nets. InProceedings of the 34th International Conference on Neural Information Processing Systems, NIPS ’20, Red Ho...

    2020

  13. [2022]

    Veliˇckovi´c, P., Cucurull, G., Casanova, A., Romero, A., Li`o, P., and Bengio, Y

    URL https://openreview.net/forum? id=7UmjRGzp-A. Veliˇckovi´c, P., Cucurull, G., Casanova, A., Romero, A., Li`o, P., and Bengio, Y . Graph Attention Networks. International Conference on Learning Representations,

  14. [2023]

    Li, X., Zhu, R., Cheng, Y ., Shan, C., Luo, S., Li, D., and Qian, W

    URL https://proceedings.mlr.press/ v202/kong23a.html. Li, X., Zhu, R., Cheng, Y ., Shan, C., Luo, S., Li, D., and Qian, W. Finding global homophily in graph neural networks when meeting heterophily. In Chaudhuri, K., Jegelka, S., Song, L., Szepesvari, C., Niu, G., and Sabato, ...

    2022

  15. [2024]

    Kelesis, D., Fotakis, D., and Paliouras, G

    URL https://openreview.net/forum? id=EMkrwJY2de. Kelesis, D., Fotakis, D., and Paliouras, G. Partially trained graph convolutional networks resist oversmoothing.Ma- chine Learning, 114(10):211, Aug 2025. ISSN 1573-

    2025

  16. [2025]

    Bl¨ocker, C., Rosvall, M., Scholtes, I., and West, J

    URL https://openreview.net/forum? id=nDFpl2lhoH. Bl¨ocker, C., Rosvall, M., Scholtes, I., and West, J. D. In- sights from network science can advance deep graph learning, 2025. URL https://arxiv.org/abs/ 2502.01177. Bongini, P., Pancino, N., Scarselli, F., and Bianchini, M. Bi...

    2025

  17. [2157]

    php/aimagazine/article/view/2157

    URL https://ojs.aaai.org/index. php/aimagazine/article/view/2157. Sharma, K., Lee, Y .-C., Nambi, S., Salian, A., Shah, S., Kim, S.-W., and Kumar, S. A survey of graph neural net- works for social recommender systems.ACM Computing Surveys, 56(10):1–34, June 2024. ISSN 1557-734...

    2024 doi

  18. [7503]

    URL https://www.sciencedirect.com/ science/article/pii/S1877750322000990

    doi: https://doi.org/10.1016/j.jocs.2022.101695. URL https://www.sciencedirect.com/ science/article/pii/S1877750322000990. McCallum, A. K., Nigam, K., Rennie, J., and Seymore, K. Automating the construction of internet portals with machine learning.Information Retrieval, 3(2):127–163,

    2022

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.