GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers

Guansong Pang; Guoguo Ai; Hezhe Qiao; Hui Yan; Yuan Gao

REVIEW 4 major objections 5 minor 17 references

GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers

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

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Pith's one-line read A learnable Fourier-series filter over Laplacian eigenvalue powers is claimed to make polynomial and Specformer graph filters special cases.

desk verdict A Fourier-series spectral filter for graph transformers that wins on heterophilic benchmarks, but the paper's expressiveness proofs overclaim: the special-case containment is asserted, not derived. read the letter →

arxiv 2411.17296 v3 pith:N6ID2ZND submitted 2024-11-26 cs.LG cs.AI

Guoguo Ai , Guansong Pang , Hezhe Qiao , Yuan Gao , Hui Yan This is my paper · ORCID

classification cs.LGcs.AI

keywords graphtransformersspectralfiltersFourierseriesKolmogorov-Arnoldnetworksheterophilicgraphsfrequency-adaptivefilteringnodeclassification

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

Self-attention, the core of graph Transformers, behaves as a low-pass filter and therefore suppresses the high-frequency node-difference signals that matter on heterophilic graphs. GrokFormer addresses this by adding a spectral convolution whose frequency response is a learnable Fourier series over powers of the Laplacian eigenvalues, with learnable coefficients for both the spectral order and the spectrum. The paper claims that this filter contains existing polynomial filters and Specformer's first-order learnable filter as special cases, which would make it strictly more expressive than prior spectral graph filters. If that is right, one model can fit low-pass, high-pass, band, comb, and low-comb filters without hand-designing the frequency response, and the reported node and graph classification gains follow from that flexibility.

What carries the argument

The load-bearing object is the Graph Fourier KAN filter, a learnable spectral response written as a truncated Fourier series in the powers $\lambda^k$ of each Laplacian eigenvalue. Fourier coefficients $a_{km}$ and $b_{km}$ shape the spectrum at each order, and order coefficients $\alpha_k$ weight how much each order contributes; the result is applied as $U\mathrm{diag}(h(\lambda))U^\top X$ and added to the output of efficient self-attention inside a Transformer layer. The Fourier representation does triple duty: sine and cosine orthogonality gives stable coefficient learning, Fourier approximation theory supplies a convergence guarantee for continuous filters, and the sum over orders lets the filter attend to all eigenvalues across the first through $K$-th spectral planes rather than only to Specformer's first-order spectrum.

What would settle it

Fit a polynomial target such as $h(\lambda)=\lambda^3$ using GrokFormer with small finite $M$ (for example $M=1,2,4$) and measure the residual; if the filter cannot reproduce the polynomial to numerical precision as $M$ grows, the containment claim is false. A complementary check is to constrain GrokFormer to $K=1$ and verify that its learned response matches Specformer's fitted filter on the same eigenvalues; any mismatch would falsify the special-case claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that a graph filter built as a Fourier-series expansion over the order-$K$ spectrum of the graph Laplacian is more expressive than all prior learnable spectral filters. The filter is $$h(\$\lambda$)=\sum_{k=1}^{K}\alpha_k\sum_{m=0}^{M}\left(\cos(m\$\lambda$^k)a_{km}+\sin(m\$\lambda$^k)b_{km}\right),$$ applied to node features through $U\mathrm{diag}(h(\lambda))U^\top X$ and combined in parallel with efficient self-attention. The argument is that $\alpha_k$ adapts the spectral order while $a_{km}$ and $b_{km}$ adapt the spectrum itself; that removing the learnable nonlinearity reduces the filter to $\sum_k \alpha_k \lambda^k$ and therefore contains every polynomial filter; that at $K=1$ the same formula contains Specformer's first-order filter; and that the uniform convergence of Fourier series makes the filter able to approximate any continuous function on $[0,2]$ while the spectral convolution remains permutation-equivariant. The empirical counterpart is the synthetic filter-fitting study, where fixed polynomial bases saturate at large error on comb-like targets while the Fourier-series filter continues to shrink the error.

Load-bearing premise

The claim that every polynomial filter is a special case assumes that the learnable nonlinearity in the Fourier-series filter can be eliminated to leave exactly $\sum_k \alpha_k \lambda^k$; Appendix C asserts this equivalence rather than deriving it, and it is exact only with infinitely many Fourier terms.

Editorial extensions

If this is right

Any filter that a polynomial GNN or polynomial graph Transformer can express, including FeTA and PolyFormer, is reproducible by GrokFormer's filter, so those models cannot be strictly more expressive.
Specformer's spectrum-adaptive first-order filter is a special case, so adding higher-order Fourier terms extends spectral adaptivity beyond Specformer's first-order spectrum without its quadratic attention over eigenvalues.
On heterophilic graphs the same architecture can learn high-pass or comb-like responses, which matches the gains reported on Chameleon, Squirrel, Actor, and Texas.
The synthetic filter-fitting results imply that complex targets such as comb and low-comb filters, which fixed polynomial bases fail to fit, are learnable in practice and not merely representable in principle.
The model's flexibility is controlled by the order $K$ and the Fourier grid size $M$, and the order-adaptivity analysis shows the learned $\alpha_k$ weights concentrate on small $k$ for homophilic graphs and spread to larger $k$ for heterophilic ones.

Reading between the lines

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

The paper does not discuss this, but the Graph Fourier KAN filter is transportable: the same $U\mathrm{diag}(h(\lambda))U^\top$ convolution could replace the fixed polynomial filter in non-Transformer spectral GNNs, and the containment argument would carry over unchanged.
A consequence the authors leave implicit is that the learned order weights $\alpha_k$ can double as a heterophily diagnostic; concentrated small-$k$ mass indicates a mostly low-pass task, while mass spreading to large $k$ signals a complex frequency response.
A concrete extension the authors do not explore is replacing the real sine/cosine basis with complex exponentials $e^{im\lambda^k}$, which would extend the construction to directed or asymmetric graph operators with complex spectra, at the cost of re-proving the convergence and containment statements.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is an empirically solid graph transformer paper with a genuinely new filter parameterization, but the theoretical "special cases" claims do not hold up as written. The experiments are the contribution; the proofs in Appendix C are not.

What's new: the filter h(λ)=Σ_k α_k Σ_m (cos(mλ^k)a_km + sin(mλ^k)b_km) — a finite Fourier series in λ^k with learnable order weights — inside a transformer with an efficient attention module. That combination is new relative to Specformer, FeTA, and PolyFormer. The paper reports broad node classification results across 11 datasets, with clear wins on heterophilic graphs (Squirrel, Texas, Chameleon) while staying competitive on homophilic ones, plus graph classification and efficiency numbers. Code is public. The synthetic filter-fitting experiment (Table 4) is a nice sanity check: GrokFormer fits comb and low-comb filters with SSE an order of magnitude lower than BernNet and Specformer. That is real evidence that the parameterization is expressive.

Soft spots. The theoretical section overreaches. Proposition 4.2's proof in Appendix C simply asserts Eq. (13) (h(λ)=Σα_k λ^k) after "eliminating the learnable nonlinear function." That is not a consequence of Eq. (9); a finite trigonometric series in cos(mλ^k) and sin(mλ^k) cannot exactly equal a monomial on an interval. Proposition 4.3 similarly reduces Specformer to an identity-attention case and uses the approximation a0λ ≈ R sin(λ+φ), which is not exact. So the claim that GrokFormer contains polynomial and Specformer filters is unproven. The synthetic results give empirical support for expressiveness, but not the containment theorem. Proposition 4.4 (universal approximation of continuous functions) is actually true — trig polynomials are dense in C[0,2] via Stone-Weierstrass — but the proof cites Fourier series uniform convergence without addressing periodicity, so it is misstated. Minor things: the abstract says 10 real-world node classification datasets while Table 2 has 11; the Penn94 result (83.59 vs Specformer's 84.32) undercuts the blanket "outperforms state-of-the-art" phrasing; and the synthetic hyperparameter search for GrokFormer is wider than for baselines, so the fitting table is suggestive, not a controlled comparison.

Who this is for: anyone building spectral graph filters or graph transformers for heterophilic graphs. The filter is simple, competitive, and public; it deserves to be a baseline. The theory needs to be corrected or cut. I would send it to review with a request to rewrite the theoretical claims and fix the abstract. A serious referee can do that without throwing out the empirical contribution.

Referee Report

4 major / 5 minor

Summary. The paper proposes GrokFormer, a graph Transformer that augments multi-head self-attention with a spectral convolution module whose filter is parameterized as a learnable Fourier series over powers of the Laplacian eigenvalues. The filter is claimed to be adaptive in both spectral order and graph spectrum, and the paper argues theoretically that polynomial filters and Specformer's filter are special cases, while empirically reporting strong results on 11 node-classification datasets, 5 graph-classification datasets, synthetic filter-fitting tasks, ablations, and efficiency measurements. The Appendix contains the proofs of the four propositions, additional experiments, and hyperparameter details.

Significance. If the expressiveness claims were rigorously established, the paper would offer a useful unifying perspective on spectral graph filters and a practical architecture that combines spatial and spectral Transformer branches. The empirical study is broad and carefully structured: 11 node and 5 graph datasets, synthetic filter fitting with a low-comb target, ablations isolating the self-attention and Graph Fourier KAN components, and wall-clock/memory comparisons against Specformer and PolyFormer. The code is released. The synthetic fitting results in Table 4 are particularly informative and demonstrate that the proposed parameterization can fit complex frequency responses such as comb and low-comb filters better than the compared baselines. However, the theoretical containment arguments in Appendix C are not valid as written, and the empirical claims are overstated in places; the core contribution is nevertheless defensible after a substantive revision.

major comments (4)

[Appendix C, Proposition 4.2] The proof of Proposition 4.2 asserts, in Eq. (13), that the GrokFormer filter h(λ) = Σ_k α_k Σ_m (cos(mλ^k)a_km + sin(mλ^k)b_km) simplifies to the polynomial h(λ) = Σ_k α_k λ^k by 'eliminating the learnable nonlinear function over the spectrum.' This reduction is not derived and is not a consequence of Eq. (9). A finite trigonometric series cannot equal a monomial exactly on an interval; for example, the function λ has a nonzero projection onto the orthogonal complement of span{cos(mλ), sin(mλ)}_{m=0}^M for any finite M. Therefore Proposition 4.2 does not establish that polynomial filters are special cases of the GrokFormer filter. The claim should be weakened to an approximation statement with an explicit density argument and a bound involving M, or the proof must show an exact coefficient assignment that the current family does not admit.
[Appendix C, Proposition 4.3] The proof of Proposition 4.3 reduces Specformer to the case where the self-attention matrix is the identity, which is not the Specformer filter used in practice, and then relies on Eq. (19), a₀λ = R sin(λ + φ), which is not an identity on [0,2] since the left-hand side is linear while the right-hand side is bounded and nonlinear. Consequently, the statement that 'the graph filter in Specformer is a simplified variant of our graph filter' is unproven. At best the argument suggests a loose approximation in a restricted setting. The proposition and the surrounding text in Section 4.1 should be revised to state an approximation relationship, and the proof must either handle the actual Specformer attention mechanism or explicitly restrict the claim.
[Section 4.1, Proposition 4.4 and Appendix C] The proof of Proposition 4.4 invokes the uniform convergence theorem for Fourier series to conclude that the GrokFormer filter can approximate any continuous function in [0,2]. This does not follow from the cited theorem. First, for K > 1 the family contains terms cos(mλ^k) and sin(mλ^k), which are not standard Fourier series terms, so uniform convergence of ordinary trigonometric series does not directly apply. Second, the parameterization uses finite M and finite K, giving a finite-dimensional function class, which cannot contain all continuous functions or approximate every continuous function to arbitrary accuracy unless M and K are allowed to grow. The proof as written only states that some Fourier series exists; it does not show that the specific family in Eq. (9) has the claimed uniform approximation property. A correct argument should specify the function class (e.g., K = 1 with M → ∞ and Stone-Weierstrass) and state the approximation up to ε, not exact containment.
[Section 5.1, Table 2] The text states that GrokFormer 'outperforms state-of-the-art baselines in both homophilic and heterophilic datasets,' but Table 2 shows that on Penn94, Specformer achieves 84.32±0.32 while GrokFormer achieves 83.59±0.26, so the claim is not supported by the reported results. Similarly, the Appendix B.4 results show that GrokFormer underperforms GRIT and GraphGPS on ZINC, CIFAR10, and Peptides-func. The empirical claims should be qualified to specify the datasets and settings in which GrokFormer is superior, and the main text should not claim universal superiority over all compared methods.

minor comments (5)

[Abstract and Contributions] The abstract says '10 real-world node classification datasets' while the contributions and experiments report 11; please correct the inconsistency.
[Figure 1 caption] The caption contains a typo: 'GorkFormer' should be 'GrokFormer.'
[Notation in Eqs. (6) and (9)] The coefficients are written as am and bm in Eq. (6) but as akm and bkm in Eq. (9); please clarify the correspondence between the per-order basis in Eq. (6) and the full filter in Eq. (9).
[Section 5.2] The text contains the typo 'comepting models' and should read 'competing models.'
[Appendix B.4] The section title and text refer to 'GrokFomer' once; please fix the spelling.

Circularity Check

2 steps flagged · score 6.0 of 10

The special-case expressiveness proof is stipulated, not derived: Eq. (13) redefines the GrokFormer filter as a polynomial, and Prop. 4.3 assumes a0λ = R sin(λ+ϕ); the theoretical containment claim is therefore circular.

self definitional [Appendix C, Proof of Proposition 4.1, Eq. (13); Proof of Proposition 4.2, Eqs. (15)-(16)]
"In Eq. (9), we eliminate the learnable nonlinear function over the spectrum and define our GrokFormer filter function as follows: h(λ) = PK k=0 αkλk, (13) ... Therefore, these polynomial filters are the case of a simplified variant of our GrokFormer filter."

Equation (9) is h(λ) = Σ_k α_k Σ_m (cos(mλ^k)a_km + sin(mλ^k)b_km). To prove that polynomial filters are contained, one must exhibit, for every polynomial Σα_k λ^k, finite-M coefficients satisfying Eq. (9) exactly. A finite trigonometric series cannot exactly equal a monomial on an interval. Eq. (13) simply redefines h as the polynomial by 'eliminating the learnable nonlinear function,' so the containment conclusion is assumed rather than derived. This makes the central claim that existing polynomial filters are special cases true by construction, not by proof.
self definitional [Appendix C, Proof of Proposition 4.3, Eqs. (17)-(23)]
"In Eq. (18), the term a0λ can be combined into sine and cosine terms in an approximate manner. Suppose that constants R and ϕ can be found such that: a0λ = R sin(λ + ϕ). (19) ... Comparing Eq. (21) and Eq. (23), it is clear that the Specformer filter is a simplified variant of our GrokFormer filter."

The proof reduces Specformer to the identity-attention case and then assumes the linear term a0λ equals R sin(λ+ϕ), which is not an identity on [0,2] (the left side is linear and unbounded, the right side is bounded and nonlinear). The comparison of Eq. (21) with Eq. (23) therefore exhibits a form that was assumed into existence, not derived from either Specformer or the GrokFormer filter of Eq. (9). The claimed containment of Specformer is stipulated, not established.

full rationale

The paper's empirical contributions are self-contained and not circular: the synthetic filter-fitting comparison (Table 4), the node and graph classification benchmarks (Tables 2 and 3), ablations, and complexity measurements stand independently of the theoretical containment proof. The load-bearing theoretical claim, however, is the assertion that 'existing advanced filters are special cases of our GrokFormer filter, showing its better universality and flexibility' (Section 4.1), supported by Propositions 4.2 and 4.3. Both proofs reduce by construction: Proposition 4.2's proof defines the GrokFormer filter to be the polynomial filter it is supposed to contain (Eq. 13), and Proposition 4.3's proof assumes a0λ = R sin(λ+ϕ) and considers only the identity-attention Specformer case. Neither is a valid derivation from Eq. (9), so the theoretical superiority claim is partly circular. The self-citation to A2GCN (Ai et al., 2024) is not load-bearing and does not affect the score. Because the central theoretical claim is stipulated while the empirical evidence remains independent, a score of 6 is appropriate.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard Fourier analysis plus a domain assumption about the meaning of spectral orders. The only free parameters are the hyperparameters K and M that control the filter's capacity.

free parameters (2)

K = tuned per dataset (range 1-10)
Maximum spectral order in the filter; tuned on validation splits for each dataset, central to the order-adaptivity claim.
M = tuned per dataset (range 16-256)
Number of Fourier series expansion terms; tuned on validation splits, controls filter expressiveness.

assumptions (4)

standard math The normalized graph Laplacian is diagonalizable with eigenvalues in [0, 2].
Used throughout Section 3.2 and in the convergence argument in Appendix C.
standard math Fourier series can uniformly approximate continuous functions with piecewise continuous derivative on [0,2].
Invoked in Appendix C, proof of Prop 4.4, to claim the filter can approximate any continuous function.
domain assumption Powers of the Laplacian eigenvalues (λ^k) correspond to meaningful spectral orders for graph filtering.
This is the core modeling assumption inherited from polynomial GNNs, used throughout Section 4.1 to justify order-adaptivity.
domain assumption The KAN-inspired Fourier parameterization with finite M and K retains enough expressiveness on real graphs.
The paper tunes K and M on validation sets; the practical expressiveness claim depends on the chosen hyperparameter ranges.

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Cite this review

Pith. "Pith review of GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers." pith.science (2026). https://pith.science/paper/N6ID2ZND

@misc{pith2026241117296,
  author       = {Pith},
  title        = {Pith review of: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N6ID2ZND}},
  note         = {Machine review of arXiv:2411.17296}
}

read the original abstract

Graph Transformers (GTs) have demonstrated remarkable performance in graph representation learning over popular graph neural networks (GNNs). However, self--attention, the core module of GTs, preserves only low-frequency signals in graph features, leading to ineffectiveness in capturing other important signals like high-frequency ones. Some recent GT models help alleviate this issue, but their flexibility and expressiveness are still limited since the filters they learn are fixed on predefined graph spectrum or spectral order. To tackle this challenge, we propose a Graph Fourier Kolmogorov-Arnold Transformer (GrokFormer), a novel GT model that learns highly expressive spectral filters with adaptive graph spectrum and spectral order through a Fourier series modeling over learnable activation functions. We demonstrate theoretically and empirically that the proposed GrokFormer filter offers better expressiveness than other spectral methods. Comprehensive experiments on 10 real-world node classification datasets across various domains, scales, and graph properties, as well as 5 graph classification datasets, show that GrokFormer outperforms state-of-the-art GTs and GNNs. Our code is available at https://github.com/GGA23/GrokFormer

Figures

Figures reproduced from arXiv: 2411.17296 by the authors.

**Figure 1.** (a) The frequency response range of K filter bases {b1(λ), b2(λ), · · · , bk=K(λ)}, k ∈ [1, K] for GrokFormer, Specformer, and polynomial filters at the spectrum λ w.r.t. spectral order k, where colors represent the varying frequency components of spectrum at different orders. Polynomial filters typically have fixed bases, e.g., λ, λ2 , · · · , λK, corresponding to the K filter curves that capture the specific cu… view at source ↗

**Figure 2.** Overview of GrokFormer. In addition to the use of self-attention to capture global information in the spatial [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Filters learned by our GrokFormer on Cora and [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: Illustrations of six filters and their approximations learned by our GrokFormer filter, BernNet, and Specformer. [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

**Figure 6.** Figure 6: Filters learned from real-world datasets with varying graph properties by our GrokFormer. [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: Order adaptivity analysis results [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 9 canonical work pages

[4]

Y ., and Tegmark, M

Liu, Z., Wang, Y ., Vaidya, S., Ruehle, F., Halver- son, J., Solja ˇci´c, M., Hou, T. Y ., and Tegmark, M. Kan: Kolmogorov-arnold networks. arXiv preprint arXiv:2404.19756,

arXiv
[5]

However, polynomial filter of BernNet is difficult to fit these filters, especially other complex filters beyond low-pass and high-pass filters

In general, GrokFormer filter can learn a precise approximation of these filters. However, polynomial filter of BernNet is difficult to fit these filters, especially other complex filters beyond low-pass and high-pass filters. Although Specformer has been well fitted, our proposed filter can perform much better, especially on filters with more complex pat...

work page 2021
[6]

Pitfalls of graph neural network evaluation

Shchur, O., Mumme, M., Bojchevski, A., and G¨unnemann, S. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868,

arXiv
[8]

Graph convolutional networks using heat kernel for semi- supervised learning

Xu, B., Shen, H., Cao, Q., Cen, K., and Cheng, X. Graph convolutional networks using heat kernel for semi- supervised learning. In Proceedings of the 28th Inter- national Joint Conference on Artificial Intelligence, pp. 1928–1934,

work page 1928
[10]

Graph-bert: Only attention is needed for learning graph representations

Zhang, J., Zhang, H., Xia, C., and Sun, L. Graph-bert: Only attention is needed for learning graph representations. arXiv preprint arXiv:2001.05140,

arXiv 2001
[11]

EXPERIMENTAL DETAILS A.1

13 GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers A. EXPERIMENTAL DETAILS A.1. DATASETS Table 7: Statistics of node classification datasets. Datasets Cora Citeseer Pubmed Photo WikiCS Physics Penn94 Chameleon Squirrel Actor Texas #Nodes 2,708 3,327 19,717 7,650 11701 34,493 41,554 2,277 5,201 7,600 183 #Edges 5,429 4,732 44,338 238,163 216,123 2...

work page 2020
[13]

For other datasets, we run the experiments ten times, each with a different random split

provides five official splits, so we run it five times to report the mean accuracy. For other datasets, we run the experiments ten times, each with a different random split. Moreover, due to the increased number of nodes and edges, we set K = 10 for Penn94. The hyper-parameter ranges we used for tuning on each dataset are as follows: • Number of layers: {...

work page 2020
[15]

As a result, GrokFormer learns to adaptively use a larger K to capture a broader range of frequency components, rather than restricting itself to a small K

are required. As a result, GrokFormer learns to adaptively use a larger K to capture a broader range of frequency components, rather than restricting itself to a small K. Moreover, we can find that GrokFormer filter assign the largest order coefficient ak to K ≤ 3 order filter basis on these datasets that expect simple filters (low-pass, all-pass, high-pa...

work page 2012

Show all 17 references

[16]

and PolyFormer (Ma et al., 2024). 18 GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers First of all, the polynomial filter functions in Table 11 can be uniformly written as follows: h(λ) = α0 + α1λ + α2λ2 + · · ·αKλK = KX k=0 αkλk, (15) where α is a learnable parameter....

2024
[17]

ai and bi are learnable parameters

learns graph filters hs(λ) via eigenvalue encoding, which can be treated as a linear combination of position encoding in graph Transformer when the self-attention matrix is set to the identity matrix: hs(λ) = a0λ + d/2X i=1 aisin( ϵλ 100002i/d ) + d/2X i=1 bicos( ϵλ 100002i/d ...

2011
[2005]

and Laurent, T

Bresson, X. and Laurent, T. Residual gated graph convnets. arXiv preprint arXiv:1711.07553,

arXiv
[2015]

We run the experiments with 2,000 epochs and stop the training in advance if the validation loss does not continuously decrease for 200 epochs

following previous works (Bo et al., 2021; 2023). We run the experiments with 2,000 epochs and stop the training in advance if the validation loss does not continuously decrease for 200 epochs. Classification accuracy is used as a metric to evaluate the performance of all mode...

2021
[2019]

Xu, J., Chen, Z., Li, J., Yang, S., Wang, W., Hu, X., and Ngai, E. C.-H. Fourierkan-gcf: Fourier kolmogorov- arnold network–an effective and efficient feature transfor- mation for graph collaborative filtering. arXiv preprint arXiv:2406.01034,

arXiv
[2020]

D., Kramer, S., and Helma, C

Toivonen, H., Srinivasan, A., King, R. D., Kramer, S., and Helma, C. Statistical evaluation of the predictive tox- icology challenge 2000–2001. Bioinformatics, 19(10): 1183–1193,

2000
[2021]

Dwivedi, V . P. and Bresson, X. A generalization of transformer networks to graphs. arXiv preprint arXiv:2012.09699,

2012 arXiv
[2022]

Nagphormer: A tokenized graph transformer for node classification in large graphs

Chen, J., Gao, K., Li, G., and He, K. Nagphormer: A tokenized graph transformer for node classification in large graphs. In The Eleventh International Conference on Learning Representations, 2023a. Chen, J., Li, G., Hopcroft, J. E., and He, K. Signgt: Signed attention-based gr...

arXiv
[2023]

Molecule attention transformer

Maziarka, Ł., Danel, T., Mucha, S., Rataj, K., Tabor, J., and Jastrzebski, S. Molecule attention transformer. arXiv preprint arXiv:2002.08264,

2002 arXiv

Pith tools

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

[1] [4]

Y ., and Tegmark, M

Liu, Z., Wang, Y ., Vaidya, S., Ruehle, F., Halver- son, J., Solja ˇci´c, M., Hou, T. Y ., and Tegmark, M. Kan: Kolmogorov-arnold networks. arXiv preprint arXiv:2404.19756,

arXiv

[2] [5]

However, polynomial filter of BernNet is difficult to fit these filters, especially other complex filters beyond low-pass and high-pass filters

In general, GrokFormer filter can learn a precise approximation of these filters. However, polynomial filter of BernNet is difficult to fit these filters, especially other complex filters beyond low-pass and high-pass filters. Although Specformer has been well fitted, our proposed filter can perform much better, especially on filters with more complex pat...

work page 2021

[3] [6]

Pitfalls of graph neural network evaluation

Shchur, O., Mumme, M., Bojchevski, A., and G¨unnemann, S. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868,

arXiv

[4] [8]

Graph convolutional networks using heat kernel for semi- supervised learning

Xu, B., Shen, H., Cao, Q., Cen, K., and Cheng, X. Graph convolutional networks using heat kernel for semi- supervised learning. In Proceedings of the 28th Inter- national Joint Conference on Artificial Intelligence, pp. 1928–1934,

work page 1928

[5] [10]

Graph-bert: Only attention is needed for learning graph representations

Zhang, J., Zhang, H., Xia, C., and Sun, L. Graph-bert: Only attention is needed for learning graph representations. arXiv preprint arXiv:2001.05140,

arXiv 2001

[6] [11]

EXPERIMENTAL DETAILS A.1

13 GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers A. EXPERIMENTAL DETAILS A.1. DATASETS Table 7: Statistics of node classification datasets. Datasets Cora Citeseer Pubmed Photo WikiCS Physics Penn94 Chameleon Squirrel Actor Texas #Nodes 2,708 3,327 19,717 7,650 11701 34,493 41,554 2,277 5,201 7,600 183 #Edges 5,429 4,732 44,338 238,163 216,123 2...

work page 2020

[7] [13]

For other datasets, we run the experiments ten times, each with a different random split

provides five official splits, so we run it five times to report the mean accuracy. For other datasets, we run the experiments ten times, each with a different random split. Moreover, due to the increased number of nodes and edges, we set K = 10 for Penn94. The hyper-parameter ranges we used for tuning on each dataset are as follows: • Number of layers: {...

work page 2020

[8] [15]

As a result, GrokFormer learns to adaptively use a larger K to capture a broader range of frequency components, rather than restricting itself to a small K

are required. As a result, GrokFormer learns to adaptively use a larger K to capture a broader range of frequency components, rather than restricting itself to a small K. Moreover, we can find that GrokFormer filter assign the largest order coefficient ak to K ≤ 3 order filter basis on these datasets that expect simple filters (low-pass, all-pass, high-pa...

work page 2012