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REVIEW 5 major objections 7 minor 31 references

KAN KAN Buff Signed Graph Neural Networks?

T0 review · 5 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read KAN layers can replace the linear transformations in Signed Graph Convolutional Networks with no systematic loss in link-sign prediction or community-detection quality.

desk verdict An honest, incremental empirical study showing KAN layers can substitute for the linear map in SGCN with roughly comparable results; the main weakness is that the headline comparison is statistically underpowered. read the letter →

arxiv 2501.00709 v3 pith:E7GYYWGX submitted 2025-01-01 cs.LG

Muhieddine Shebaro , Jelena Tešić This is my paper · ORCID
classification cs.LG
keywords Kolmogorov-ArnoldNetworkssignedgraphneuralcommunitydetectionlinksignpredictionrepresentationlearningbalancetheoryKASGCN
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

Signed graphs encode trust and distrust, support and opposition, and Signed Graph Convolutional Networks (SGCNs) learn node embeddings by aggregating neighbors through two separate channels that reflect structural balance. The paper asks whether replacing the linear weight matrices in SGCN with Kolmogorov-Arnold Network (KAN) layers, which use learnable univariate spline functions instead of fixed activations, yields better or even comparable embeddings. It introduces KASGCN and tests it on community detection and link sign prediction across seven signed graphs. The central finding is parity: KASGCN mostly matches SGCN, with small AUC gains on most graphs and graph-dependent F1 results, while some KAN variants (Fourier, Wavelet) frequently lead and LaplaceKASGCN consistently underperforms. This matters because KANs promise greater expressivity with fewer parameters, so a drop-in replacement would offer a practical upgrade if the parity holds.

What carries the argument

The carrying object is the KAN layer $\varphi$, a learnable univariate function built from B-splines, with a grid size and spline order controlling the approximation. In KASGCN it replaces the linear transformation $W$ in the SGCN recurrence for both the positive ($h^B$) and negative ($h^U$) node representations, with variants using Fourier, Laplace, and Wavelet bases instead of B-splines. The architecture keeps SGCN's balance-theory message passing, so the KAN layer is the only change from the baseline, which lets the experiments isolate the effect of the spline-based transformation.

What would settle it

Run the same comparisons with per-dataset hyperparameter search and paired statistical tests on the 10 runs: if the Congress 12.29% AUC loss is reproduced and most of the reported gains fall within one standard deviation of run-to-run variation, the claim of competitive parity would no longer hold.

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Extended reading notes

Core claim

The paper claims that a KAN layer can take over the role of the weight matrix in the SGCN update equations without breaking the balance-theoretic structure that gives SGCN its meaning. In KASGCN, the linear transforms $W^{(l)}$ for updating positive and negative representations are replaced by KAN layers $\varphi^{(l)}$, while the two-channel aggregation over positive and negative neighbors is preserved. In experiments on seven signed graphs, KASGCN achieves competitive or comparable performance to SGCN across signed community detection and link sign prediction: it improves AUC on six of seven datasets for link sign prediction, with gains up to 3.46% on WikiElec, but F1 improvements are mixed and one graph, Congress, shows a 12.29% AUC drop. The authors interpret the results as context-dependent effectiveness rather than general superiority of KAN-based signed GNNs.

Load-bearing premise

The paper's conclusion rests on the assumption that a single fixed hyperparameter configuration (layers [32,32], grid size 5, spline order 3, learning rate 0.001, seed 42) and 10-run averages without significance tests are enough to judge which model is better.

Editorial extensions

If this is right

  • KAN layers can act as a drop-in substitute for the linear map in SGCN: for AUC, KASGCN is not systematically worse than SGCN on the seven tested signed graphs.
  • The choice of KAN variant matters more than the choice between SGCN and KASGCN: FourierKASGCN and WaveletKASGCN often finish first in community detection or link-sign prediction, while LaplaceKASGCN is consistently last.
  • Near-zero average cosine similarity (between $-0.02$ and $0.07$) between SGCN and KASGCN embeddings shows the two models produce geometrically different embeddings, yet those different geometries lead to similar downstream performance.
  • Training time grows with the number of aggregator layers for KASGCN but not for SGCN, so parity comes at a computational cost that increases with depth.

Reading between the lines

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

  • Because the embeddings are near-orthogonal yet downstream scores are similar, KASGCN may be capturing different node features than SGCN; a natural test is whether KASGCN embeddings preserve balance-theoretic cycle structure as faithfully as SGCN's.
  • The hyperparameters were fixed once for all graphs, so tuning grid size, spline order, or layer width per dataset could change both absolute performance and the variant ranking; the observed parity is therefore a lower bound on what KAN-based signed GNNs could achieve.
  • A paired significance test across the 10 runs, rather than averaged metrics alone, would tell whether gains like 2-3% AUC are real or within run-to-run noise; the paper reports no such test.
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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

5 major / 7 minor

Summary. The paper proposes KASGCN, an extension of the Signed Graph Convolutional Network (SGCN) in which the linear transformation in each layer is replaced by a Kolmogorov-Arnold Network (KAN) layer. The authors evaluate KASGCN against standard SGCN on seven signed graphs for two downstream tasks: community detection via K-means++ on node embeddings and link sign prediction via multinomial logistic regression. They also compare several KAN variants (Fourier, Laplace, Wavelet) and examine training efficiency and embedding similarity. The central empirical claim is that KASGCN achieves competitive or comparable performance to SGCN, with context-dependent variability.

Significance. If the claims are substantiated, the paper provides an early empirical datapoint on whether KAN layers can serve as drop-in replacements for linear transformations in signed GNNs. The work is honest in reporting means and standard deviations over 10 runs and in hedging its conclusions as context-dependent. However, the strength of the evidence is limited by the absence of significance or equivalence testing, the use of a clustering quality metric that conflates two components with different scales, and fixed hyperparameters without sensitivity analysis. The reported differences are often within run-to-run noise, so the 'comparable' conclusion is currently underdetermined.

major comments (5)
  1. [Section 3.2, Table 5] The observation that KASGCN shows 'consistent improvement in AUC across most datasets' is not supported by the data: the Congress dataset shows a 12.29% AUC drop (0.570 ± 0.055 vs 0.499 ± 0.046), and the gains on other datasets are small relative to the reported standard deviations. Without paired significance tests (e.g., Wilcoxon signed-rank or paired t-test over the same seeds) or confidence intervals for the differences, the aggregate pattern could be consistent with random noise. Please report paired tests and effect sizes, and explicitly discuss the Congress outlier.
  2. [Section 3.1, Eq. (5)] The clustering quality metric Q = posin + negout assigns equal weight to two components that have different scales and variances across datasets. For example, in Table 3 (K = 10), PPI shows KASGCN increasing negout from 0.784 ± 0.011 to 0.936 ± 0.009 while decreasing posin from 0.422 ± 0.037 to 0.364 ± 0.037; the reported +7.79% gain is driven primarily by the negout term. The authors should justify why equal weighting is appropriate or report the components separately with a clear interpretation of trade-offs.
  3. [Section 2.2, Tables 2-5] All hyperparameters (layers = [32,32], grid size = 5, spline order = 3, learning rate = 0.001, etc.) are fixed across datasets and models, and no sensitivity analysis is provided. Since the paper's central claim is that KASGCN is 'comparable' and 'context-dependent,' the observed differences could be an artifact of suboptimal KAN hyperparameters rather than an intrinsic property of the architecture. A sensitivity analysis over at least grid size and hidden layer size on one or two datasets is needed to support the robustness of the conclusions.
  4. [Section 3.1, Tables 2-5] The gain percentages in Tables 2-5 are computed as ratios of noisy quantities, but no uncertainty is propagated into the gains. For instance, the Congress AUC gain of -12.29% in Table 5 is derived from means with standard deviations of 0.055 and 0.046, and the confidence interval for the gain would likely include zero or even positive values. Please report absolute differences with confidence intervals, or apply a bootstrap/delta method to the gains, so that the reader can judge the stability of each reported gain.
  5. [Section 3.3, Figure 2] The efficiency claim that 'KAGCN takes significantly longer' (the text appears to mean KASGCN) is supported only by a visual inspection of Figure 2, with no quantitative runtime values in the text or a table. Please provide numerical results, such as mean training time and standard deviation for each aggregator layer, to make the efficiency comparison concrete and reproducible.
minor comments (7)
  1. [Sections 3.3 and 3.5] The text refers to 'KAGCN' in several places (e.g., 'KAGCN takes a significantly longer time' in Section 3.3 and the heading 'KAGCN Robustness' in Section 3.5); these should be corrected to 'KASGCN'.
  2. [Title] The title appears as 'KAN KAN B UFF SIGNED GRAPH NEURAL NETWORKS?' which is likely a formatting artifact; it should be corrected to a readable phrase (e.g., 'KAN-Buff Signed Graph Neural Networks?').
  3. [Tables 4-5] In Table 4, the PPI gain is reported as '8.74' without a percent sign; in Table 5, the WikiRFA F1 gain is reported as '-0.434' which should likely be '-0.43%'. Please ensure consistent formatting of percentages.
  4. [References] The reference [Anonymous, 2024] is an anonymous citation; a journal submission should cite the actual authors and venue for this work on GraphKAN.
  5. [Abstract and Section 1.1] The abstract states that KANs offer 'improved accuracy and interpretability with fewer parameters,' but the paper does not evaluate interpretability or parameter efficiency in any experiment; please soften this claim or add supporting evidence.
  6. [Section 3.4] The near-zero cosine similarity between SGCN and KASGCN embeddings is an interesting finding, but the paper does not explain why such different embeddings can still yield comparable downstream performance. A brief discussion would be useful.
  7. [Overall] No code availability statement is provided. Given that the KAN implementations rely on external repositories, a link to the experimental code would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the KASGCN-vs-SGCN comparison is empirical and does not reduce to a fit or a self-citation chain.

full rationale

The paper is an empirical architecture comparison, not a derivation. KASGCN is defined by replacing the SGCN weight matrix W with a KAN layer, with the replacement justified by external prior work (Bresson et al., Liu et al.), not by the authors' own prior results. The evaluation metrics (pos_in, neg_out, Q, AUC, F1) are defined independently of the model outputs, and the KAN hyperparameters (layers, grid size, spline order, learning rate, etc.) are fixed before the experiments and are not fitted to the reported target metrics. No quantity is fitted to a subset of the data and then renamed a prediction; no uniqueness theorem is imported from the authors' own work; no ansatz is smuggled in via self-citation. The paper's central claim is that KASGCN shows competitive or comparable performance to SGCN, which is a direct reading of the tables rather than a conclusion forced by the construction of the method. Concerns about statistical significance, the Congress AUC drop, and the absence of equivalence tests are correctness or evidence-quality issues, not circularity. The circularity burden is therefore effectively zero.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the standard math of KAN (Kolmogorov-Arnold theorem), the domain assumption that balance theory is the right way to build signed message passing, and several evaluation choices (Kmeans++ and logistic regression as probes). The free parameters are all hyperparameters chosen by hand rather than fitted to the data; none of them are loaded with the target result.

free parameters (8)
  • KAN grid size = 5
    Number of spline intervals for the KAN activation; set once for all datasets without ablation.
  • KAN spline order = 3
    Degree of B-splines; chosen by hand without sensitivity analysis.
  • Hidden layer size = [32, 32]
    Two GCN layers with 32 hidden units; fixed for SGCN and KASGCN alike.
  • Learning rate = 0.001
    Fixed for all experiments.
  • Training epochs = 1000
    Fixed for all experiments.
  • Weight decay = 1e-5
    Fixed regularization.
  • KAN scale parameters (scale_noise, scale_base, scale_spline) = 0.1, 1.0, 1.0
    Initialization scales of the KAN layer, set by hand.
  • Random seed = 42
    Seed used for reproducibility; 10 runs are averaged, but the text does not specify whether seeds vary across runs.
assumptions (5)
  • standard math The Kolmogorov-Arnold representation theorem
    Invoked in Eq. 1 to justify KAN's universal representation power.
  • domain assumption Structural balance theory as a model of signed networks
    Section 1.2 builds SGCN on the premise that an even number of negative edges in a cycle defines balance; this assumption is inherited from Derr et al. and not tested.
  • domain assumption Kmeans++ on the concatenated positive and negative embeddings yields meaningful signed communities
    Section 2.3 defines Q = pos_in + neg_out and uses Kmeans++ clusters as the community assignments; this assumes the embedding geometry supports clustering.
  • domain assumption Logistic regression on the embeddings is a valid probe for link sign prediction
    Section 3.2 uses multinomial logistic regression with a 0.2 test split as the evaluation of embedding quality.
  • domain assumption Preprocessing choices preserve signed network semantics
    Section 2.2 treats neutral edges as positive, removes self-loops, and reindexes nodes; these choices alter the graph and are applied uniformly to both models.

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Cite this review

Pith. "Pith review of KAN KAN Buff Signed Graph Neural Networks?." pith.science (2026). https://pith.science/paper/E7GYYWGX

@misc{pith2026250100709,
  author       = {Pith},
  title        = {Pith review of: KAN KAN Buff Signed Graph Neural Networks?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E7GYYWGX}},
  note         = {Machine review of arXiv:2501.00709}
}
read the original abstract

Graph Representation Learning aims to create effective embeddings for nodes and edges that encapsulate their features and relationships. Graph Neural Networks (GNNs) leverage neural networks to model complex graph structures. Recently, the Kolmogorov-Arnold Neural Network (KAN) has emerged as a promising alternative to the traditional Multilayer Perceptron (MLP), offering improved accuracy and interpretability with fewer parameters. In this paper, we propose the integration of KANs into Signed Graph Convolutional Networks (SGCNs), leading to the development of KAN-enhanced SGCNs (KASGCN). We evaluate KASGCN on tasks such as signed community detection and link sign prediction to improve embedding quality in signed networks. Our experimental results indicate that KASGCN exhibits competitive or comparable performance to standard SGCNs across the tasks evaluated, with performance variability depending on the specific characteristics of the signed graph and the choice of parameter settings. These findings suggest that KASGCNs hold promise for enhancing signed graph analysis with context-dependent effectiveness.

Figures

Figures reproduced from arXiv: 2501.00709 by the authors.

Figure 1
Figure 1. Illustration of SGCN and KAN-enhanced SGCN of a signed network of 4 nodes and three edges. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The embedding generation time of SGCN and KASGCN with varying aggregator layers. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. t-SNE visualizations of the embeddings generated by SGCN (Red) and KASGCN (Blue) for different signed [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

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Reference graph

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Reviewed August 10, 2026 · model on record in the stance chip above.