KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning
Authors: Roman Bresson
Giannis Nikolentzos
George Panagopoulos
Michail Chatzianastasis
Jun Pang
Michalis Vazirgiannis
Venue: Accepted by TMLR ()

Abstract: In recent years, Graph Neural Networks (GNNs) have become the de facto tool for learning node and graph representations. Most GNNs typically consist of a sequence of neighborhood aggregation (a.k.a., message-passing) layers, within which the representation of each node is updated based on those of its neighbors. The most expressive message-passing GNNs can be obtained through the use of the sum aggregator and of MLPs for feature transformation, thanks to their universal approximation capabilities. However, the limitations of MLPs recently motivated the introduction of another family of universal approximators, called Kolmogorov-Arnold Networks (KANs) which rely on a different representation theorem. In this work, we compare the performance of KANs against that of MLPs on graph learning tasks. We implement three new KAN-based GNN layers, inspired respectively by the GCN, GAT and GIN layers. We evaluate two different implementations of KANs using two distinct base families of functions, namely B-splines and radial basis functions. We perform extensive experiments on node classification, link prediction, graph classification and graph regression datasets. Our results indicate that KANs are on-par with or better than MLPs on all tasks studied in this paper. We also show that the size and training speed of RBF-based KANs is only marginally higher than for MLPs, making them viable alternatives. Code available at https://github.com/RomanBresson/KAGNN.

Published in Transactions on Machine Learning Research (03/2025)
KAGNNs: Kolmogorov-Arnold Networks meet Graph Learn- ing
Roman Bresson
KTH Royal Institute of Technology, Sweden
bresson@kth.see
Giannis Nikolentzos
University of Peloponnese, Greece
nikolentzos Cuup-.gr
George Panagopoulos
University of Luzembourg, Luzemboury
georgios, hawp::sssaaagoooooooooouaas
Michail Chatzianastasis
École Polytechnique, IP Paris, France
michail hht.saaattaaaattiiiipppeeeeeeeee
Jun Pang
University of Luzzembourg, Luxembowry
jun. Crani lu
Michalis Vazirgiannis
Ecole Polglechnique, IP Paris, France KTH Royal Institute of Technology, Sweden
meazirg polkeeehheee
Reviewed on OpenReview: https: //
// openeviee.. net/ forum? id 03UB
Abstract
In recent years, Graph Neural Networks (GNNs) have become the de facto tool for learning node and graph representations. Most GNNs typically consist of sequence of neighborhood aggregation (a.k.a,, message-passing) layers, within which the representation of each node updated based on those of its neighbors. The most expressive messago- messago-passing GNNs can be obtained through the use of the sum aggregator and of MLPs for feature transformation, thanks their universal approximation capabilities. However, the limitations of ML.Ps recently motivated the introduction of another family of universal approximators, called Kolmogorov-Arnol Networks (KANs) which rely different representation theorem. In this work, we compare the performance of KANs against that of MLPs on graph learning tasks. We implement three new KAN-based GNN layers, inspired respectively by the GCN, GAT and GIN layers. We evaluate two different implementation ions of KANs using two distinct base families of functions, namely B-splines and radial basis functions. We perform extensive experiments on node classification, link prediction, graph classification and graph regression datasets. Our results indicate that KANs are on-par with or better than MLPs on all tasks studied in this paper. We also show that the size and training speed of RBF-based KANs is only marginally higher than for MLPs, making them viable alternatives. Code available at https://githuie com wttgtthubboo//mmaaaaeeeeeee RRossnnresson BaaiaanBrrrsooKKKAAGA KAGNN.

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Published in Transactions on Machine Learning Research (03/2025)
1 Introduction
Graphs are structural representations of information useful for modeling different types of data. They arise naturally in wide range of application domains, and their abstract nature offers increased flexibility, Typically, the nodes of graph represent entities, while the edges capture the interactions between them. For instance, in social networks, nodes represent individuals, and edges represent their social interactions. In chemo-informatics, molecules are commonly modcled as graphs, with nodes corresponding to atoms and edges to chemical bonds. In other settings, molecules can also correspond to nodes, with edges capluring their ability to bond with one another.
In many cases where graph data is available, there exist problems that cannot be solved efficiently using conventional tools (e-g., g., graph algorithms) and require the use of machine learning techniques. For instance, in the field of inemo-informatiis, the standard approach for estimating the quantum mechanical properties of molecules leverages computationally expensive density functional theory computations (Gilmer et al. 2017). Machine learning methods could serve as a more efficient alternative to those methods. Recently, Graph Neural Networks (GNNs) have been established as the dominant approach for learning on graphs (Wu et al., 2020). Most GNNs consist of a series of peessge-passing layers. Within a peessage-pasiing layer, each node updates its feature vector by aggregating the feature vectors of its neighbors and combining the emerging vector with its own representation.
A lot of recent work has focused on investigating the expressive power of GNNs Li and Leskovec 2022 There exist, different definitions of expressive power, however, the most common definition is concerned with the number of pairs of non-isomorphic graphs that a GNN model can distinguish. Two graphs are isomorphic if there exists an pree-preerrving bijection between their respective sets of nodes. In this sctting, model is more expressive than another model if the former can distinguish all pairs of non-isomorphic graphs that the latter can distinguish, along with other pairs that the latter cannot (Morris et al. 2019). Furthermore, equivalence was established between the ability of GNNs to distinguish non-isomorphic graphs and their ability to approximate insights into the limitations of different models (Xu et al. 2019: Nikolentzos et
crrmutation-invariie
functions on graphs (Chen et al.
2019 This line of work gave
al. 2020). but also led to the
development of more powerful architectures (Morris et al. 2019 Maron et al.
2019 Morris et al. 2020a).
Most maximally-expressif GNN models rely on multi-layer perceptrons (MLPs) as their main building blocks, due to their universal approximation capabilities (Cybenko| 1989, Hornik et al. 1989 The theorem states that any continuous function can be approximated by an MLP with at least one hidden layer, given that this layer contains enough neurons. Recently, Kolmogorov-
Networks (KANs) (Liu et al.] 2025) have emerged as promising alternatives to MLPs. They are based on the Kolmogorov- Aaannggooo-Arooldd representation theorem [Kolmogorov] 1957) which states that a continuous multivariate function can be represented by a composition and sum of a fixed number of univariate functions. KANs substitute the learnable weights and pre-defined activation functions of MLPs with learnable activations and summations. The initial results demonstrate that KANs have the potential to be more accurate than MLPs in low dimensions and in settings where regularity is expected.
In this paper, we present a thorough empirical comparison of the performance between GNNs that use KANs to update node representations and GNNs that utilize MLPs to that end. Our intuition is that KANs could exploit the expected regularity underlying the message-passing paradigm to provide compara- tively good performance on graph tasks. Our work is orthogonal to prior work that studies the expressive power of GNNs since we empirically compare models that are theoretically equally expressive in terms of distinguishing non-isomorphic graphs against each other, and we study the impact of the different function approximation modules ei. KANs or MLPs) on the models' performance. We implement two layers, one based on the Graph Convolutional Network (GCN) (Kipf and Welling 2017 and one based on the Graph Isomorphism Network (GIN) (Xu et al.] 2019). We evaluate the different GNN models on several standard node classification, link prediction, graph classification, and graph regression datasets.
The rest of this paper is organized as follows. Section 3 provides an overview of the tasks we address in this paper, as well as a description of message-passing GNNs and Kolmogorov-Arne Arnold networks In Section 4 we introduce the KAGIN KKolmogorov-Arnol Graph Isomorphism Network), KAGCN (Kolmogorov-Ammol
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Graph Convolution Network) and KAGAT (Kolmogorov-Arnold Graph ATtention Network) models, which are variants of existing GNNs, and which leverage KANs to update node features within each layer. In Section 5 we present extensive empirical results comparing the above models with their vanilla counterparts in several tasks, and in Section G we evaluate the time efficiency of our architectures. Finally, Section 7 presents perspectives for future work and Section concludes the paper.
2 Related Work
Kolmogorov-Arnold Networks have recently gained significant attention in the machine learning commu- nity (Somvanshi et al. 2024). Even though KANs were introduced very recently, they have already been applied to different problems such as in the task of satellite image classification (Cheon 2024), for predicting the pressure and flow rate of flexible electrohydrodynamiic pumps (Peng et al. 2024D, and for rumor detec-
tion (Jiang et al., 2024p. So far, most efforts have focused on time series data (Xu et al., 2024aa Barašin et al. 2024). For instance, KANS have been evaluated in the satellite traffic forecasting task (Vaca-Rubio Rubio 2024). Furthermore, they were combined with architectures usually leveraged in time series forecasting tasks such as LSTM networks (Genet and Inzirillo 2024a) and the Transformer (Genet and Inzirillo )
et al.
Recently, KAN-based convolutional neural networks have also been proposed which consist of kernels made of learnable non-linear functions that use splines
(Bodner et al., 2024). These neural networks have been utilized for intrusion detection (Wang et al., 2025). KANs have also paved their way into celebrated archi- fectures such as PointNet (Kashefi 2024). Recent work has focused on improving different aspects of KANs such as making them more parameter-effiienn (Ta et al.
2025). robust to overfitting (Altarabichi 2024), and extending them to the complex domain (Wolff et al. 2025)- More importantly, framework was recently introduced which allows scamless interplay between KANs and science (Liu et al.) 2024). Specifically, multiplication was incorporated as a built-in modularity of KANs. Furthermore, the work strengthened the connection between KANss and scientific problems by highlighting the identification of key features, modular structures, and symbolic formulas.
Note that our study not the only work in the intersection of KANs and graph learning algorithms Kiamari et al. 2024 De Carlo et al.) 2024 Zhang and Zhang 2024 Li al. 2024). : However, while this paper provides an extensive evaluation across different settings and datasets, other works focus on a single task (e. g., node classification) or are limited to small-sized datasets. (Kiamari et al.) 2024] propose two variants of the GCN architecture, where the feed-forward layer which updates node representations is replaced by KAN layers. The two variants differ from each other in how the new node representations are produced. The one transforms node representations before aggregation (and is thus similar to our KAGCN model), while the other after aggregation. However, the two variants are only evaluated on a single node classification dataset. (De Carlo et al.) 2024) propose a neighborhood aggregation layer where splino- based activation functions are applied to the representat ions of the neighbors before aggregation, while another basene activation function is applied to the output of the aggregation. A final spline-based transformation then produces the final node representations. While the proposed model is evaluated in different tasks (i. c., node classification, graph classification and link prediction), all the considered datasets are small-sized. In another recent study, (Zhang and Zhang, 2024) also propose a variant of the GCN architecture, where a KAN is employed to transform node representations after aggregation. The proposed model is only evaluated on a single dataset where a graph is constructed from one-dimensional acoustic signals for axial flow pump fault diagnosis. Recent work has also investigated the ability of GNNs that employ KAN layers to solve problems in chemo- and bio-informatics such as the prediction of properties of molecules (Li ct al. 2024 and the
prediction of the binding alfinity of small molecules to protein targets (Ahnndd and Sifat 2024 ), respectively. Such models were also applied to the problem of graph collaborative filtering (Xu et al. 2024b).
3 Background
3.1 Graph Learning Tasks
Before presenting the tasks on which we focus in this study, we start by introducing some key notation for graphs. Let. N denote the set of natural numbers, i.e., 21, Then, [n] (1,.....) m) N for 2 1.
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Let G EV; be an undirected graph, where V is the vertex set and E is the edge set. We denote by n the number of vertices and by m the number of edges, e.e., [V] and m |E Let g: V + [n] denote a bijective mapping from the space of nodes to set [n]. Let (V()) denote the neighbourhood of vertex v, i.e., the set fu| [e, 2} E E}. The degree of a vertex u is deg(v) = [W()]. Each node u E V is associated with a Teature vector X E Rd, and the feature matrix for all nodes represented as E IRaxd Thus, X, equal to the g(v)-th row of X.
In node classification, each node V is associated with label Uo that represents class. The task is to learn how to map nodes to their class labels, e.e. to learn function fuode such that fu, G, X) Yo. In graph regression/classifiiie /classification, the dataset consists of a collection of N graphs GI...., GN along with their class labels/targets "G...... .G.. The task is then to learn function that maps graphs to their class tabels/targets, i. e., a function fgraph such that fgraph X) yg which can discrete or continuous, for graph classification or graph regression, respectively.
The standard approach for learning such predictors (both for node- and graph-level tasks) is to first embed the nodes of the graph(s) into some vector space. That is, we aim to learn H fembedding (G, E RTxd, where de denotes the embedding dimension. Then, the g(v)-th row of matrix H represents the embedding of node v. Let h, denote this embedding. For node-level tasks, we can use h. to predict directly the class ttbel/target of node v. For graph-level tasks, we also need to apply a readout function on all the representations the graph's nodes to obtain a representation h = freadout (H) for the entire graph. One particularly desirable property of such models is permutation invariance. That is, the embedding heg of a graph needs to be the same regardless of the ordering of its nodes. Indeed, these orderings do not hold any semantic meaning, and different orderings give rise to isomorphic graphs. Permutation invariance is achieved at the readout step by utilizing permutation invariant operation over the rows of H, such as the sum, max, or mean operators.
3.2 Graph Neural Networks
One of the most widely-used paradigms for designing such permutation invariant models is the message- passing framework (Gilmer et al.) 2017] which consists of a sequence of layers and within each layer the embedding of each node is computed as a learnable function of its neighbors' embeddings. Formally, the embedding h Rd at layer l is computed as follows:
h = (00) h
(e-1)
(1)
wEN(e)
where + is a permutation-inaarine aggregation function (e. mean, sum), and Φ(9) is differentiable function (e. g., linear transformation, MLP) that combines and transforms the node's previous embedding with the aggregated vector of its neighbors.
As discussed above, we focus here on the functions that different GNN models employ to update node representations. Some GNNs use a 1-layer perceptron (i.e., linear mapping followed by non-linear activation function) within each neighborhood aggregation layer to update node features (Duvenaud et al, 2015 Kipf and Welling) 2017; /Zhang et al. 2018). For instance, each layer of the Graph Convolutional Network (GCN) (Kipf and Welling 2017) is defined as follows:
h (--1)
h =
w
Σ
(2)
V(de(v)) 1)(deg( + +1)
uEN((ju(u)
where a is a non-linear activation and W(() is a trainable weight matrix.
However, the 1-layer perceptron not a universal approximator of multiset functions (Xu et al. 2019
limiting the expressivity of the model. Thus, more recent models use MLPs instead of 1-layer perceptrons update node representations (Balcilar et al.) 2021 Dasoulas al. 2021 Murphy et al. 2019 Nikolentzos
et al. 2020 Tt. well-known that standard message-passing GNNs bounded in expressiveness by the
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Seiifeiler-Leman (WL) test of isomorphism (Xu et al 2019). While two isomorphic graphs will always be mapped to the same representation by such a GNN, some non-isomorphic graphs might also be assigned identical representations.
A model that can achieve the same expressive power as the WL test, given sufficient width and depth of the MT.P, the Graph Isomorphism Network (GTN) (Xu et al. 2019), which is defined as follows:
(L+c(() h (
h 0 MLP(()
h((-1) mEN(e)
Σ
(3)
where e denotes a trainable paramcter, and MLP(() trainable MLP.
The GIN model can achieve its full potential if proper weights (i.e., for the different MLP(() layers and e()) are learned, which is not guaranteed. This has motivated a series of works that focused on improving the training procedure GNNs. For example, Ortho-GConv is an orthogonal feature transformation that can address GNNs' unstable training (Guo et al.] 2022 Other works have studied how to initialize the weights of the MLPs of the message passing layers of GNNs. It was shown that adopting the weights of converged MLPs as the weights of corresponding GNNs can lead to performance improvements in node classification tasks (Han et al.) 2023). On the other hand, there exist settings where there is no need for complex learning models. This has led to the development of methods for simplifying GNNs. This can be achieved by removing the nonlinearities between the neighborhood aggregation layers and collapsing the resulting function into a single linear transformation (Wu al., 2019) or by feeding the node features into neural network which generates predictions and then propagating those predictions via a personalized PageRank scheme (Gasteiger al. 2019
Finally, the Graph Atlention Network (GAT) Velickovi et al. 2017 leverages the multi-head attention mechanism among nodes to give each neighbor an adapted importance in the aggregation scheme.
h
Σ
( v,a
W(-(())
(4)
uEN(o)U(E}
where ( denotes a single linear layer and
(8) exp (LeakyReLU
(( ('W(OnK w(on!--)))
(5)
auv
EmEN(OOURN) (exp LeakyReLU ((Winn- w(O)(-1)))
are the neighbor-wise attention weights for given head.
3.3
Kolmogorov-rrood Networks
3.3.1
Principle
Presented as an alternative to the MLP, the Kolmogorov-Arnold Network (KAN) attracted lot attention in the machine learning community (Liu et al., 2025 As mentioned above, this model relies on the Kolmogorov-Arnold representation theorem, which states that any multivariate function f [0, 1]d + can be written as:
architecture has recently
2d+1
f(x)
Σ T
Σ dis (x,)
(6)
where all Φ and Φ denote univariate functions, and the sum is the only multivariate operator.
Equation 0 can be seen as a two-step process. First, a different set of univariate non-lincar activation functions applied each dimension of the input, and then the output of those functions are summed up. The authors rely this interpretation to define Kolmogorov-Arnol Network (KAN) layer, which is
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mapping between space A S Rd and a different space B S R (identical in to MLP layer). Such layer consists of d x d' trainable functions (di 1 i s d', S d}. Then, for x E A, we compute its image x' as:
x
(x))
(7)
Stacking two such layers, one with input dimension d and output dimension 2d 1, and another with input dimension 2d++1 and output dimension 1, we obtain Equation [ and the derived model is a universal function approximator. This seemingly offers complexity advantage compared to MLPs, since the number of univariate functions required to represent any multivariate function from [0, 1J to Rd is at most (2d xd'''', whereas the universal approximation theorem for the MLP requires a possibly infinite number of neurons. However, as stated in the original paper, the behavior of such univariate functions might be arbitrarily complex (c. g., fractal, non-smooth), thus leading to them being non-representable and non-lcarnable.
MLPs relax the infinite-width constraint by stacking fiite-wwdtth layers. Likewise, KANs relax the arbitrary complexity constraints on the non-linearities by stacking KAN layers of lower complexity. Thus, the output of function is given by:
y (x) 41 oo.o. -1-1 1 ) where .,,..., &L are KAN layers.
(8)
3.3.2 KAN Implementations and Applications
The original paper that introduced KANs uses splines (i. trainable piccewise-polynomial functions) nonlinearities. This allows to retain a high expressivity for a relatively small number of parameters, at the cost of enforcing some local smoothness. A layer & is thus a de x dz- grid of splines. The degree used for each spline (called spline order), as well as the number splines used for each function (called grid size) are both byperparameters of the architecture. Nonetheless, KANs allow for any function serve as its basc element. Thus, alternative implementations which in particular alleviate some computational bottleneck of splines.
different bases, such radial-basis functions LLi 2024
4 KAN-based GNN Layers
We next derive three KAGNN layers, i.e. variants of the GIN, GCN and GAT models which use KANs to transform the node features instead fully-connected layers or MLPs.
4.1 The KAGIN Layer
To achieve its maximal expressivity, the GIN model relies the MLP architecture and its universal approx- imator property. Since KAN is also universal function approximator, could achieve the same expressive power using KANs in lieu of MLPPs We thus propose the KAGIN model, defined as:
h.5 kAN( (a+t)))n) h(
Σ (e-1) mEN())
h
(9)
With theoretically-sonut KANss ei. with arbitrarily complex components), this architecture is exactly expressive as the vanilla GIN model with infinite layer width. In practice, we employ two different families of functions to serve as the base components, leading to two different layers: BS-KAGIN, based on B-splines, as in the original paper; and RBF-KAGIN, based on radial basis functions (RBFs), which were proposed as more computationalll-offiinn alternative. While these do not guarantce universal approximation, the empirical results in the original paper demonstrate the great expressive power of KANs (Liu al.) 2025). motivating empirical study.

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4.2 The KAGCN Layer
GCN-based architectures have achieved great success in node classification tasks. While in our experiments we evaluate KAGIN on node classification datasets, the objective advantage of GCN over GIN on some of the datasets does not facilitate a fair estimation of KANs' potential in this context. To this end, we also propose a variant the GCN model. Specifically, we substitute the linear transformation of the standard GCN (Kipf
and Welling 2017) model with a single KAN layer (defined Equation obtain the KAGCN layer:
h (E-1)
h =p(()
Σ
(10)
v(deg(u) 1)(deg(u) +
WEN(N)U(U)
where ((() denotes a single KAN layer. In the familiar matrix formulation, where À A +I the adjacency matrix with self-loops and D the diagonal degree matrix of A, the node update rule of KAGCN can be written ( ( D A where the different of H store the representations of the different nodes of the graph. We propose both BS-KAGON and a RBF-KAGON, where + is based respectively on B-splines and RBFs.
4.3
The KAGAT Layer
Finally, we substitute the linear transformation of the standard graph attention network (GAT) et al. 2017 model with single KAN layer (defined in Equation g to obtain the KAGAT layer:
Veeičkkoii
h = Σ
(0) ( (h(--))
(11)
aeu
where ( denotes single KAN layer and
exp LeakyReLU ([0(0) [ (n + x(t) (1! (n!t-1))))
(12)
EuEN(o) (exp [LeakyReLU ([T(() ( (n( + (T() 111 (e((-1)
5 Empirical Evaluation
In this section, compare all three KAGNN models against MLP-based GNNs the following tasks: node classification, link prediction, graph classification, and graph regression. All models are implemented with PoTorc (Paszke et al. 2019). For KAN layers, we rely on publicly available implementations for B-splines and for RBF [ For a given task, all models have consistent architectures, differing as little as possible. All GaT-based models use 4 heads.
5.1
Node classification
Datasets
To evaluate the performance of GNNs with KAN layers in the context of node classification, we use 7 well-known datasets of varying sizes and types, including homophilic (Cora, Citeseer (Kipf and Welling,
2017 and Ogbn-arxiv (Hu et al. 2020)) and heterophilic (Cornell, Texas, Wisconsin, Actor) networks (Zhul el al. 2021 The homophilic networks are already split into training, validation, and test sets, while the heterophilic datasets are accompanied by fixed 10-fold cross-validation indices. Thus, we clone the split for homophilic datasets 10 times in order to have similar number of experiments across all datascts.
Experimental setup. We perform two types of experiments. First, we compare KAGCN model the homophilic datasets to the GCN proposed in the state of the art approach in (Lo et al. 2024). The
httter//shhau.cc///alllaa//ffffe http:://gthab.ccm//iyaa////////

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Table 1: Average classification accuracy (# standard deviation) and model parameters based on Luo et
LLu et al., 2024) using GCN-based models on the Cora, CiteSoer, and Arxiv datasets.
Model
Cora
CiteSeer
Arxiv Accuracy (%)
Accuracy (%)
Params
Accuracy (%)
Params
Params
GCN
81.60 0.40
3,262,983
71.60 + 0.40
6,221,830
71.74
0.29
2,591,784 1,010,432
BS-KAGON
80.84 1.61
3,702,144 144
70.04 1.66
4,317,952
70.58
0.20
RBF-KAGCN
81.72 0.79
3,714,217
68.16 + 0.61
6,258,808
71.39 + 0.28
813,647
Table 2: Average node classification accuracies (= standard deviation).
Model
Cora
Citeseer
Ogbn-arxiv
Cornell
Texas
Wisconsin
Actor
GCN
74.01 + 0.81
57.73 + 1.21
53.21 + 0.13
66.13 + 6.09
72.34 +: 5.92
78.63 = 5.43
32.81 +: 1.11
ES-KAGCN
70.46 = 2.00
56.45 + 1.62
53.76 = 0.31
67.75 + 6,54
72.16 + 5.68
78.63 = 5.26
34.45 + 1.12
RBF-KAGCN
48.06 = 1.40
47.55 + 1.43
53.65 = 0.20
67.75 : 7:24
71.62 + 4.69
77.45 = 4.11
34.77 = 1.20
GAT
76.51 + 0.79
60.91 + 1.04
53.68 + 0.12
66.85 + 5.59
69.01 + 6.14
78.17 + 5.70
32.51 + 1.17
BS-KAGAT
78.28 + 0.83
56.87 + 1.67
55.17 + 0.12
67.66 + 6.94
73.78 + 6.39
78.43 + 5.47
31.66 + 1.23
RBF-KAGAT
72.62 + 1.64
48.65 + 2.39
54.24 + 0.25
64.14 +:
71.71 6.49
76.34
4.34
34.04 0.94
GIN
70.85 + 1.75
47.98 i 0.91
53.58 1 0.74
69.10 1: 4.85
73.51 1 5.87
78.24 +: 4.76
33.46 + 1.38
BS-KAGIN
65.78 + 1.68
55.77 + 1.51
53.05 - 0.55
69.64 7.40
72.97
1 5.63
78.63
5.16
34.26 + 1.06
RBF-KAGIN
72.77 + 1.35
46.87 + 1.93
53.56 1 0.37
67.30 1 6.44
73.60 1 5.05
76.73 = 4.88
34.37 1 0.95
results are shown in Table One can observe that the classical GCN outperforms the KAN-based model in 2 out of 3 datasets, albeit with narrow difference and confidence overlaps in all of the comparisons. Note that the current setting is built to favor the classical GNNs, it relies on techniques such as dropout, jumping knowledge, batch normalization and preliminary linear transformations, Hence, although the MLP-based GCN enjoys a plethora of assistive techniques examined in the past decades, the KAN-based counterpart exhibits a close performance. We should note here that these assistive techniques have not been developed yet for KAN-based architectures, and our results aim at motivating the development of such techniques.
Our second approach compares the vanilla versions of the neural architectures when we replace the MLP with KAN, as delineated in sections 4 In order to clarify the effect of KAN on the model's performance, we only use dropout and batchnorm as additional techniques. Indeed, we aspire to compare the classical MLP-based GNNs as if they were in the same nascent stage as their KAN-based counterparts.
In order for all models to exploit the same quantity information, we fix the number of message message-passing layer datasct-wise, with 2 for Cora and CiteSeer, 3 for Texas, Cornell, Wisconsin, and Ogbn-arxiv and for Actor. All attention-based models used 4 heads.
For every dataset and model, we tune the values of the hyperparameters using the Optuna package (Akiba et al. 2019) with 100 trials (paraneterizatioon)) TPE Sampler and set carly stopping patience to 50. For each parameterizatton, and for each split, we train 3 models in order to mitigate randomness. We then select the parameterization with lowest validation error across all splits and models.
We use a different hyperparameter range for MLP-based models, B-Splines baseides-based based models and RBF-basod models (see Table 8 Indeed, for the same number of 'neurons", KAN-based layer will have a much larger number of parameters than an MLP- layer (sec Appendix C.1 for examples). In order to avoid giving unfair advantage to KAN-based layers, we thus allowed the MLP layers to be larger.
The results are given in Table We see that a B-splines- based variant outperforms other models on 5/7 datascts, and both other architecture win on one dataset each. Nonctheless, these are often by small margins. We also notice poor performance of RBF-KAGCN on Cora, which we attribute to overfitting. Overall, seems to be positive impact of using KAN-based architectures.
Results.
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Table 3: AUC for link prediction of the KAGIN and GIN models on the link-prediction datasets.
Cora
CiteSeer
Cora
CiteSeer
Cora
CiteScer
GCN
95.36 1: 0.23
96.72 1 0.44
GAT
94.02 = 0.48
96.10 1 0.49
GIN
94.97 + 0.40
95.37 1: 0.23
BS-KAGON
94.37 0.46
94.91 + 0.62
BS-KAGAT
94.71 0.65
95,40 + 0.33
B8-KAGIN
94.64 = 0.44
95.75 + 0.39
ABF-KAGCN
94.87 0.45
95.44 + 0.67
RBF-XACAT
94.96 0.42
90.09 14.1
RBF-KACIN
95.07 = 0.27
97.07 = 0.40
5.2 Link Prediction
Datasets and Experimental Setup. In this setting, we focus on the task of link prediction. We use two datasets, Cora and CiteSeer, following the implementation and protocol provided in (Li et al. 2023 Mao et al.) 2024). We performed a grid-search over learning rate, hidden dimension, number of hidden layers, grid size and spline order, each time training models 10 splits. We then selected the model with lowest validation loss to obtain the best configuration, and reported its test ROC-AUC (over all 10 splits).
Results. Table 3 displays the results the link prediction task. We see that GCN is the best performer Cora, and RBF-KAGIN is the best on CiteSeer, albeit with often close scores among models. We also notice some instability of RBF-KAGAT on CiteSeer.
5.3 Graph Classification
Datasets. In this set of experiments, we evaluate the KAGNN models on standard graph elassification benchmark datascts (Morris et al.] 2020b). We experiment with the following 7 datascts: MUTAG, DD, NC11, PROTEINS, ENZYMES, IMDB-B, IMDB-M.
Experimental setup. We follow the experimental protocol proposed in (Errica et al. 2020 We kept our architecture simple: first, a number of message-passing layers extract node representation, whose model is either an MLP (resp. a KAN). We then use pooling (sum-pooling for GINs and GATs, mean-pooling for GCNs) to obtain graph representations. Finally, an MLP (resp. a KAN) with same architecture as those in the messagc-passing layer, is used classifier. A softmax is used for predicting class probabilities. Thus, we perform 10-fold cross-validation, while within each fold model is selected based split of the training set. We use the pre-defined splits provided in (Errica et al. 2020). We use the Optuna package to select the model that achieves the lowest validation cross-entropy loss over 100 iterations. For fair comparison, we fix the number
90%/100
cesssag-passsig layers of all architectures for each dataset. On MUTAG, PROTEINS, IMDB-B and IMDB-M, we set the number of layers to 2. On DD, we set it to 3. On ENZYMES, we set to and finally, on NCI1 we set it to We train each model for 1, 1,000 epochs (early stopping with patience of 20 epochs) by minimizing the cross entropy loss. We use the Adam optimizer for model training (Kingma and Ba 2015). We apply batch normalization (Toffe and Szegedy 2015) and dropout (Srivastava et al.) 2014 to the output of each message-passing layer. The ranges for hyperparameters scarch are given in table I1 Once the best hyperparamcters are found for a given split, we train 3 different. models on the training set of the split and evaluate them on the test set of the split. This yields test accuracies for this split, and we compute their average to obtain the performance for this split.
Results. Table iilustrates the average classification accuracies and the corresponding standard deviations of the three models on the different datasots. We observe that B-splines variants win on 4 datasets, and the MLP-based GIN leads on 3, albeit by small margins wrt. the standard deviation. We notice that, while the MLsebaaed GCN performs poorly (predictably so, since graph-level lasks often require higher complexity than code-classification ones), the KAN-based GCN perform significantly better. This tends to confirm that single KAN layer has much more representation power than fully-conneeted layer.
5.4 Graph Regression
Datasets. We experiment with two molecular datasets: (1) ZINC-12K (Irwin and Shoichet 2005). and
(2) QM9 (Ramakrishnan et al. 2014). ZINC-12K consists of 12, 000 molecules. The task is to predict the

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Published in Transactions on Machine Learning Research (03/2025)
Table 4: Average graph classification accuracy (+ standard deviation).
MUTAG
DD
NCI
PROTEINS
ENZYMES
IMDB-B
IMDB-M
GCN
39.95 +: 8.98
65.87 6.33
60.10 + 4.63
63.10 + 3.75
20.56 + 3.70
68.40 +: 4.01
48,56 +: 3.71
BS-KAGON
71.70 = 7.54
72.74 = 4.16
73.97 = 4.01
75.68 3.49
59.06 + 4.48
72.87 + 5.12
50.04 + 3.99
RBF-KAGOH
77.86 = 9.45
66.78 = 5.91
73.07 = 2.90
73.67 = 3.99
56.83 = 8.37
73.13 + 4.5
49.84 + 3.78
GAT
37.51 + 12.3
71.92 = 5.88
60.42 = 8.21
59.78 + 0.87
18.17 = 1.34
67.37 + 3.83
48.24 + 5.02
BS-KAGAT
82.66 + 4.78
78.27 + 2.37
76.46 + 3.66
72.75 + 2.18
51.33 + 12.9
72.00 + 3.80
50.09 + 4.34
RBF-KAGAT
75.88 +: 12.1
73.42 = 4.76
72.63 i 4.65
71.93 + 4.23
49.78 + 7.65
71.00 1 5.04
48.13 1 4.15
GIN
86.16 + 5.96
74.78
3.82
79.32 + 1.63
70.66 + 3.60
54.72 + 6.55
73.37 + 2.90
50.36 1 4.10
BS-KAGIN
85.79 + 8.06
76.06 5.10
80.34 + 1.46
73.37 + 2.81
44.50 + 8.53
13 + 4.46
50.33 + 3.87
RBF-KAGIN
85.10 + 5.60
75.92 = 3.49
79.19 + 1.81
74.33
1 3.52
44.78 + 9.58
69.93 1 3.84
49.22 1 4.41
Table 5: Average MAE (= standard deviation) of the KAGIN and GIN models on graph regression.
ZINC-12K
QM9
GIN
0.4131 0.0215
0.0969 + 0.0017
BS-KAGIN
0.3000 = 0.0332
0.0618 + 0.0007
RBF-KAGIN
0.3026 = 0.0663 0.0778 + 0.0023
constrained solubility of molecules, important property for designing generative GNNs for molecules. The dataset is already split into training, validation and test sets (10, 000, 1, 000 and 1000 graphs in the training, validation and test sets, respectively). QM9 contains approximately 134, 000 organic molecules. Each molecule consists of Hydrogen, Carbon, Oxygen, Nitrogen, and Flourine atoms and contain up to 9 heavy (non Hydrogen) atoms. The task is to predict 12 target properties for each molecule. The dataset was divided into a training, a validation, and a test set according to 80%/10%/1100 100 split.
Experimental setup. We perform grid search to select values for the different hyperparameters. We choose the number of hidden layers from (2,3,4) for GIN and {1, 2, for KAN. We use different ranges for each model was because wanted to limit the size advantage of KAN against MLP, since a layer with the same width of KAN has more parameters than an MLP one). For both models we search learning rate from (10-3,10-1) For GIN, we choose the hidden dimension size from (32, 64, 128, 256, 512, 1024), while for KAGIN, we choose it from (4, 8, 16, 32, 64, 128, 256]. For KAGIN, we also select the grid size from {1,3, 5, 8, 10} and for BS-KAGIN the spline order from {3, 5). To produce graph representations, we use the sum operator. The emerging graph representations are finally fed to a 2-layer MLP (for GIN) or a 2-layer KAN (for KAGIN) which produces the output. We set the batch size equal to 128 for all models. We train each model for 1, 000 epochs by minimiizing the mean absolute error (MAE). We use the Adam optimizer for model training (Kingma and Ba 2015). We also use early stopping with a patience of 20 epochs. For ZINC-12K, we also use an embedding layer that maps node features into 100-dimensional vectors. We choose the configuration that achioves the lowest validation crror. Once the best configuration is found, we run 10 experiments and report the average performance on the test set. For both datasets and models, we set the number of message-passing layers 4. On QM9, we performed a joint regression of the 12 targets.
Results. The results are shown in Table 5 We observe that on both considered datasets, both KAGIN vari- ants significantly outperform the GLN model. Note that these datasets are significantly larger (in terms of the number of samples) compared to the graph classification datascts of Table 4 The results also indicate that BS-KAGIN outperforms RBF-KAGIN on both ZINC-12K and QM9. However, the difference in performance between the two models is very small. Thus, it appears that both B-splines and RBFs are good candidates as KANs' base components regression tasks. In addition, we should note that the BS-KAGIN model offers an absolute improvement of approximately 0.11 and 0.03 in MAE over GIN. Those improvements suggest that KANs might be more effective than ML.Ps in regression tasks.
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0.82
HIP
Tranipg time (Ahepoch)
0.50
0.60
Accorti
0.78
0.78
MLP bwK bTKKA
HLP bwKoN (bf KAN
0.78
Model pe cermmeters count
Model parameters Count
Train ng time tolepoch)
Figure 1: Parameters count/iizepperfrmmancc comparison, GIN, NCT
6
Analysis of Size and Time
6.1 Setting
Following the above results, and it is legitimate to wonder whether the performance of the KAN models comes from a larger size than their ML.P-based counterparis. We show in this section that it is not the case. Using the graph-classificatin sizo-to-perfort poott---rformancee relation, the size- dize-to-training time relation and the training time-to-porformance relation. Note that these models are the ones selected by the hyperparameter search algorithm, thus exhibiting the best validation performance throughout the architectur-oppiiizztion process.
models trained for the results provided in 5.3, we display here three relations: the
We thus notice an interesting tradeoff, where RBFF-based KANs tend train models with good performance, but smaller size than their based counterparts, allowing them to train almost as quickly. Meanwhile BS-based KANs tend to be slower.
6.2 Discussion
Figures [ shows these relations on dataset NCI1 for the GIN-based models, a setting where the three models have a similar performance. We also show in table G the associated numerical values for this dataset. The rest of the graph classification datasets and models are provided in App. C. We notice that, for the same number of parameters, MLPs are the fastest, followed closely by RBF-bbsed KANs; then BS-based KANs are significantly slower than both others. This confirms the fact that the RBF-based representa- tion alleviates greatly the computational bottlenecks of B-splines. Nonetheless, also notice that, despite the byperparameter search setting allowing them a large size, the performance-driven model selection con- verged towards smaller sizes for KAN-based models than for MLPs. This allows the RBF- version of KAGNN models to train time similar to their ML.P-based counterpart. Nonetheless, the BS-based variant remains significantly slower in almost all settings.
7 Discussion and Perspectives
Prominent application domains. KANs, both in our work and in the recent literature, seem to be a promising alternative to MLPs for regression tasks. They rely on combinations of continuous functions which could explain their improved performance for continuous outputs. Moreover, this property and their empirical performance in regression tasks renders them an ideal candidate for duysics-inspired architectures (Karni- adakis et al. (2021), which address problems of high importance, from climate forecasting (Kashinath et al. 2021) to atomic simulations (Batzner et al.] 2022) and rely heavily on graph-based architectures.
Explainability matters. Recent works on KANs argue that their potential for explainability is higher than that of MLPs with post-hoc methods (e.g. Shapley values, madienttbbseed (Liu et al. (2025). since closed-form symbolic formulas be drawn from the former (Liu et al. 2024), providing complete overview
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Table 6: Average time and parameter sizes for selected models, NCI1
Model
Parameter count
Accuracy
time per epoch (s)
GCN
316588.40
0.60 = 0.04
0.31
BS BS-KAGCN
182464.80
0.74 0.04
0.94
RBF-KAGCN
117043.10
0.73 = 0.03
0.37
GAT
1566334.00
0.60 = 0.08
0.47
BS-KAGAT
1109714.80
0.76 = 0.04
1.42
RBF-KAGAT
1468335.80
0.73 = 0.04
0.53
GIN BS-KAGIN
1557454.00
0.79 + 0.02
0.39
532684.50
0.80 = 0.01
1.70
RBF-KAGIN
107075.40
0.79 + 0.02
0.37
of the underlying computations. Hence, KAN-based models could prove more friendly to practitioners from application fields, such as biology and physics, who tend to be skeptical of the black-box approach.
GNNs for fixed graphs inspired from KANs. Each KAN architecture consists of a set of neurons. Each one of those neurons is connected to other neurons. Thus, KANs can be naturally modeled as graphs where nodes represent neurons and edges represent the connections between them. Each layer of KAN is actually a complete bipartite graph, while KAN has learnable activation functions on the edges of its associated graph. There actually exist datasets that contain multiple graphs which share the same graph structure, but differ in the node and edge features. Two examples such datasets are the MNIST and CIFAR10 graph classification datasets (Dwivedi et al.) 2023). Since the graph structure is fixed (and identical for all graphs), we could associate each edge of the graph with one or more learnable activation functions (shared across graphs), similar to what KANs do. This would allow the model to learn different functions for each edge of the graph, leading potentially to high-quality node and graph representations.
Advantages and future work. Finally, we discuss potential advantages that KANs might have over MLPs, and leave their investigation for future work. First, their ability to accurately fit smooth functions could prove relevant on datasets where variables interact with some regular patterns. Second, their inter- pretability could be leveraged to provide explanations on learned models, giving insights into the nature of interactions among entities. Another study direction could be to extend the KAN architecture more GNN models (e.g. GAT, GraphSAGE, Graph Transformer) develop a wider KAN-based arsenal for graph tasks. Finally, thorough study of the effect of the different hyperparameters could be pursued, allowing to fully exploit the splines or radial basis functions while retaining small workorks
8 Conclusion
In this paper, we have investigated the potential of Kolmogorov-Arool networks in graph learning tasks. Since the KAN architecture is a natural alternative to the MLP, we developed three GNN architectures, KAGCN, KAGAT and KAGIN, respectively analogous to the GCN, GAT and GIN models. We then compared those architectures against. each other both node- and graph-level tasks. For link prediction, as well as graph and node classification, there does not appear to be clear winner. For graph regression, our results indicate that KAN has an advantage over MLP, with the B-spline variant proving superior in terms of performance. Nonetheless, this gain comes at the cost of computational efficiency. In this regard, the RBF-based variant offers a lesser performance improvement, but proves much more efficient in terms of training time.
This paper shows that such KAN-based GNNs are valid alternatives to the traditional MLP-based models. We thus believe that these models deserve the attention of the graph leching- community, and that future work should be carried out to identify their specific advantages and weaknesses, allowing for an enlightened choice between KANs and ML.Ps based on the task and context at hand.
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Acknowledgements
This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation and partner Swedish universities and indus- try. Part of the experiments was enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), partially funded by the Swedish Research Council through grant agree- ment no. 2022-06725. Part of the experiments was also enabled by the Berzelius resouree, which was made possible through application support provided by National Supercompuler Centre at Linköping University.
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Karthik Kashinath, M Mustafa, Adrian Albert, JL Wu, C Jiang, Soheil Esmaeilzadeh, Kamyar Azizzade- nesheli, R Wang, Ashesh Chattopadhyay, A Singh, et al. Physics-infowd informed machine learning: case studies for weather and climate modelling. Philosophical Transactions of the Royal Society A, 379((194):20200099, 2021.
Simon Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E Smidt, and Boris Kozinsky. E (3)-equivariant graph neural networks for data- efficient and accurate interatomic potentials. Nature communications, 13(1):2453, 2022.
Vijay Prakash Dwivedi, Chaitanya K Joshi, Anh Tuan Luu, Thomas Laurent, Yoshua Bengio, and Xavier Bresson. Benchmarking graph neural networks. Journal of Machine Learning Research, 24(43):1 48, 2023.
Vijay Prakash Dwivedi, Ladislav Rampášek, Michael Galkin, Ali Parviz, Guy Wolf, Anh Tuan Luu, and Dominique Beaini. Long range graph benchmark. In Advances in Neural Information Processing Systems, pages 2022.
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A Further Graph Classification Experiments
Besides the graph classification experiments that are presented in the main paper, we also experimented with the Peptides-fure func dataset, a graph classification dataset from the Long Range Graph Benchmark (Dwivedi et al. 2022). The dataset consists of 15, 535 graphs where the average number of nodes per graph is equal to 150.94. We evaluated GIN, BS-KAGIN and RBF-KAGIN on this dataset. We performed a grid search where for all models we chose the learning rate from {0.001, 0.0001}, the number of hidden layers of MLPs and KANs from 21, and the hidden dimension from {64, 128}- We the number of neighborhood aggregation layers to 5 for all models. For both BS-KAGIN and RBF-KAGIN, grid size was chosen from (3,5) 5), and for BS-KAGIN, spline order was chosen from {3,5}. Each experiment run times with 4 different seeds and Table illustrates the average precision achieved by the three models.
Table 7: Average Precision (= standard deviation) of the KAGIN and GIN models on Peptides-fune func
Peptides-func
GIN
55.01 + 0.75
BS-KAGIN
58.71 + 1.02
RBF-XAGIN
57.68 2.05
We observe that BS-KAGIN and RBF-KAGIN outperform GIN the Peptides-func dataset. Both models offer absolute improvement of more than 2.5% in average precision over GIN. Thus, even in tasks where long-range interactions between nodes need to be captured, for fixed receptive field, KAN layers can help the models better capture those interactions.
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B
Hyperparameter search ranges
Table 8: Hyperparameter ranges for node classification (datasets Cora, Cornell, Texas, Wisconsin)
Model
Learning Rate Hidden Layers
Hidden Dim.
Grid Size
Spl. Order
Dropout
GIN
[le 5, le 2]
[144]
[1, 256
NA
NA
[0, 0.9
BS- SS-KAGIN/KACON RBF-KAGIN/KAGGE KAGGN
[e - 5, le 2
[1,4]
[1, 128
[1, [1,8]
[1.
[0, 0.9
[le - 5, le - 2]
[1,4]
[2, 128]
[2, 32]
NA
[0,0.9]
Table Hyperparameter ranges for node classification (datasets CiteSeer, Ogbn-Arxiv, Actor)
Model
Learning Rate Hidden Layers
Hidden Dim.
Grid Size
Spl. Order
Dropout
GIN
[e - 5, le - 2]
[1.4]
[1. 64]
NA
NA
[0, 0.9
BS BS-KAGIN/KAGEN KAGGN KAAKAAIIINKKGO
le - 5, le - 2]
[1,4]
[2, 32]
[]
[1, 3]
0.9
[e - 5, le - 2
[1,4]
[2,32]
[2,4]
NA
[..
Table 10: Hyperparameter ranges for link prediction
Model
Learning Rate
Hidden Layers
Hidden Dim.
Grid Size
Spl. Order
GIN BS-KAGIN/KAGOH RBF-KACIN/KAGON
3, {le 2-12,,1111110 {le 2, le 2 33 [le 2,-
4}
{2, 4]
{16, 512]
NA
NA
[2,4)
{16, 64)
{8}
[2, 3)]
2, le 3]
[2,4]
(16, 512)
(2,
NA
Table 11: Hyperparameter ranges for graph classification Hidden Dim.
Model
Learning Rate
Hidden Layers
Dropout
Grid Size
Spl. Order
GIN AS-KAGIN/KAGON RBF-KAGIN RBF-KAGIN/KAGON /KAGON
le 4, le 2]
[.44]
512]
[0,
NA
NA
le - 4, le - 2
1,4
[2, 64]
[0,0.9
[2, 32)
[1,4]
[e - 4, - 2
[1.4]
[2, 64
[0,0.9]
[2, 16]
NA
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C
Time/Performancc/Acccrry analysis
Figures task.
to
22 and tables
12 to
regarding the fime/size/accuraaee analysis on the graph classification
Table Average time and parameter sizes for selected models, MUTAG
Model
Parameter count
Accuracy
time per epoch (s)
GCN
66421.40
0.60 + 0.09
0.02
BS-XAGON
31991.40
0.72 + 0.07
0.03
RBF-KAGCN
67221.20
0.78 + 0.09
0.02
GAT
1162504.80
0.58 + 0.12
0.02
BS-KAGAT
521626.00
0.83 + 0.05
0.04
RBF-KAGAT
1119860.90
0.76 + 0.11
0.02
GIN
840858.00
0.86 + 0.06
0.02
BS BS-KAGIN
145455.00
0.86 + 0.08
0.05
RBF-KAGIN
82645.40
0.85 + 0.05
0.02
Table 13: Average time and parameter sizes for selected models, DD
Model
Parameter count
Accuracy
time per epoch (s)
GCN
274320.80
0.66 = 0.06
0.24
BS-KAGCN
110847.70
0.73 + 0.04
0.93
RBF-KAGCN
110976.90
0.67 + 0.06
0.24
GAT
224323.60
0.72 + 0.06
0.22
BS-KAGAT
1375974.80
0.78 + 0.02
2.36
RBF-KAGAT
514070.80
0.73 = 0.05
0.38
GIN
281992.60
0.75 + 0.04
0.15
BS BS-KAGIN
189140.10
0.76 0.05
2.24
RBF-KAGIN
62553.50
0.76 + 0.03
0.24
Table 14: Average time and parameter sizes for selected models, PROTEINS full
Model
Parameter count
Accuracy
time per epoch (s)
GCN
14055.70
0.63 + 0.04
0.09
BS-KAGCN
26241.00
0.76 + 0.03
0.15
RBF-KAGCN
77950.00
0.74 + 0.04
0.11
GAT
1217234.00
0.60 + 0.01
0.14
BS-KAGAT
377421.60
0.73 + 0.02
0.28
RBF-KAGAT
406871.00 00
0.72 + 0.04
0.13
GIN
935245.00
0.71 + 0.03
0.10
BS-KAGIN
206523.00
0.73 + 0.03
0.36
KBGIKAGIN
76445.40
0.74 + 0.03
0.14
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Table 15: Average time and parameter sizes for selected models, ENZYMES
Model
Parameter count
Accuracy
time per epoch (s)
GCN
230071.20
0.21 = 0.04
0.06
BS BS-KAGCN
102457.20
0.59 0.04
0.12
RBF-KAGCN
105379.80
0.57 0.08
0.08
GAT
2193344.40
0.18 = 0.01
0.10
BS-KAGAT
734566.80
0.51 = 0.12
0.23
RBF-KAGAT
292237.60
0.50 + 0.07
0.09
GIN
778435.40
0.55 + 0.06
0.07
BS-KAGIN
199432.90
0.44 = 0.08
0.21
RBF-KAGIN
135783.50
0.45 + 0.09
0.10
Table 16: Average time and parameter sizes for selected models, IMDB-BINARY
Model
Parameter count
Accuracy
time per epoch (s)
GCN
106247.80
0.68 + 0.04
0.15
BS- BS-KAGCN
34710.10
0.73 0.05
0.19
RBF-KAGCN
40357.50
0.73 = 0.04
0.17
GAT
1482555.60 6.6
0.67 + 0.04
0.18
BS BS-KAGAT
391572.00
0.72 = 0.04
0.25
RBF-KAGAT
308826.00
0.71 0.05
0.18
GIN
769820.20
0.73 = 0.03
0.16
BS-KAGIN
144101.00
0.73 = 0.04
0.30
RBF-KAGIN
159608.70 70
0.70 - 0.04
0.20
Table 17: Average time and parameter sizes for selected models, IMDB-MULTI
Model
Parameter count
Accuracy
time per epoch (s)
GCN
83223.60
0.49 + 0.04
0.23
BS-KAGCN
50801.41
0.50 0.04
0.29
RBF-KAGCN
25513.00
0.50 + 0.04
0.25
GAT
838081.80
0.48 + 0.05
0.25
BS-KAGAT
129868.00 00
0.50 + 0.04
0.33
RBF-KAGAT
340916.00
0.48 0.04
0.27
GIN
875383.22 20
0.50 + 0.04
0.24
BS-KAGIN
195207.70
0.50 - 0.04
0.38
RBF-KAGIN
40460.40
0.49 = 0.04
0.26
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0.9
H1P
HIP
0.9
MIP (bf GAN
rDf
Trannng time (Vepseh)
X
0.025
Accirto
Actures:
0.929
0.5
0.005
05
X
25000 50000
100000000020000000000 /5000000000
25000 50000
7500010000a 2000 20000000000///0000000000000000
0.00 0,005
2.030
0.013 0.020 0.025 0.030 0.055
Model se mmeters count
Model porameters count
Training time (slepoct)
Figure 2: Parameters count/size/performaaat comparison, GCN, MUTAG
X
KLP
RLP CAN
bs CAN
to KAN C1-AN
0.01
rot GAN
Traning time saupert)
0.00
0.7
0.02
0.5
0.5
0.01
35
4.0
0.00
4,0
1e6
Figure 3: Parameters countssizeeperformann comparison, GAT, MUTAG
0.55
0.55
X
0.05
AgurS3
0.05
Agura2
0.02
0.75
0.75
0.00
025
0.50
6.7%
1.00
1.25
1.50
1.75
0.00
0.25
3.50
0.75
1.60
1:25
3.50
1.75
0.00
3.01
0.02
6:3
0.64
6.0 0.06 0.07 068
Model rermmberrs count
Modil parametees count
Thaiing time colepoch)
Figure 4: Parameters count/size/performanc comparison, GIN, MUTAG
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1.5
MIP (61 GAN
MLP
1.4
0.75
(Svepoch
0.75
Accirso
0.70
0.70
0.8
0.6
100
0.4
0.80
X
0.35
0:55
100000
200000
300000
400000
300000
100000
200000
300000
430000
300000
0.0
0.2
04
0.0
0.8
1.0
122
1.4
1.5
Model parsmeters court
Mode: parmmeters COUnT
Thaining time islesoch))
Figure 5: Parameters count/size/performaane comparison, GCN, DD
0.825
MLP
0.625
0.500
5-
to KGN
0.800
0.775
Tranie One Socportt
0.775
0.725
0.725
0.700
0,700
0.675
0.675
0.560
bo 16F-ONN
0.580
bo KAN
0.825
0.005
(bf MAN
Figure 6: Parameters coum/sizzepeerformauu comparison, GAT, DD
0.800
0.800
10000000 Sime salppech)
0.775
0.775
0.750
0.725
0.725
0.700
0.A75
0.675
0.0
0.4
0.6
3.8
3.0
1.2
1.4
3.5
0.2
0.6
0.6
0.8
1.5
1/2
1.4
Model paramebers count
Model pararratiess rount
Teiting zwme (xlepech))
Figure Parameters countssiz/pperfrrmanc comparison, GIN, DD
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0.10
0.00
1.75
1.50
0.70
0.70
Accuaayy
1.00
%
MLP
0:25
buKoN
(61
woooeoooeeeee0000eoeo ootp://coooooooooooooooooooooo Model ze rerameters count
0.00
0.5
0.50
0.73
1.00
1.25
1.50
1./5
Mode: parsmeters count
Trannnn time (slepoch)
Figure 8: Parameters coumt/sie//peffommance comparison, GCN, NCT1
MLP bo IDSKAN
HLP bs KAN
2.3
126-KAN
2.0
0.70
0,70
Accuacy
0.25
Traasing time
0.05
bo KAN
(bf KAN
0.0
Modal
Figure 9: Parameters coum/siizepperfommanc comparison, GAT, NCI1
0.51
0.61
0.80
0.78
0.78
0.76
0.76
Model zersmeters count
Modiel pww.metees count
Than time (elepoh))
Figure 10: Parameters count/size/performann comparison, GIN, NCI1
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MIP
MIP
0.16
(67
0.75
0.30
0.12
WAY
Acturary
0.75
XXX
0.06
0.65
0.65
0.00
25000 50000
75000 100003
125000 150000 175000
25000
b000s
75000
100003
125000 15:000 175000
0.00
0.52
0.04
0.05
0.08
0.10
0-12
0.14
0.16
Model parameters count
Mode: parameters count
Taininn time Islepoch)
Figure 11: Parameters count/size/performaace comparison, GCN, PROTEINS full
HLP
HLP
Do
0.5
bs CAN
bo KAN
BSAAAN
221-AA
1814 GAN
0.75
0.4
0.7%
Trarsing time
0.1
XXX
$
3.5
0.0
0.2
Figure 12: Parameters count/siee/performant comparison, GAT, PROTEINS full
Baining (anpeec))
0.76
0.5
036
Agor533
0.74
x
0.4
Aruracy
0.74
0.72
0.3
0.72
0.1
0.0
0.5
1.0
1.5
2.0
6.0
0.5
1/0
1.5
2.0
0.0
0.1
0.2
6.3
0.4
0.6
5.7
Model parametens court
Modiel parameties count
Thaining time Istepoch)
Figure 13: Paramcters count/size/performamn comparison, GIN, PROTEINS full
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HIP KAN
0.15
HIP KAN KAN
MIP
0.14
(oFKAN
0.5
05
Accinoo
Accurmy
0.4
0.
0.3
0.3
0.2
02
100000 z00000 s00e00 400000 s00000 500030 700000
102030 200000 J000c0 400000 s00000 600000
ro0000
0.00
0.02
0.04
0.06
0.06
0.30
0.12
0.14
0.15
Model sarameters count
Model parameters count
Trahiing Islepoct
Figure 14: Parameters count/size/performann comparison, GCN, ENZYMES
MEP Do IDSKAN
HLP
X MLP
bs CAN
bo CAN
236-AN
1bS-AA
0.5
Therting time Noepect
0.6-
0.4
XX
0.0
parameters
Figure 15: Parameters count/size/perforaacc comparison, GAT, ENZYMES
0:35
0.50
0.60
Taiting (WPEreN))
23
0.30
0.20
0.50
0.40
0.40
36
0.30
0.30
0.0
0.5
1.5
2.5
2.5
0.0
0.5
1.5
2.0
2.5
3.00
0.09
3.10
0.15
0.20
3:35
0.30
0.55
Model za remeeers count
Model parametees count
Thiinng time (olepoch)
Figure 16: Parameters count/size/performannt comparison, GIN, ENZYMES
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MIP
0.200
CAN
Accinso
0.725
0.125
0.675
0.675
0.650
X
0.00
0.590
0.525
8.525
50000
100000
150003
200000
230000
30000
100000
1b:0000
200000
250000
5.000
0.025 0.000
5.75 2.100 0.125 5.130 0.175 0:200
Model parsmeters count
Model parameteers count
Tririing time idleocc))
Figure 17: Parameters count/size/performmncc comparison, GCN, IMDR-BINARY
KLP
MLP
WEP
bs-KAN
bS-KAN (N6KAN
SuKAN I69KAN
ro6KAN
0.25
0.74
Traping 1aseea
0.74
0.72
0.72
Ascurasy
0.70
0.35
0.10
0.66
X
0.30
0.66
0.64
0.64
0.62
0.62
0.00
le6
Figure 18: Parameters countssize/eeroommann comparison, GAT, IMDB-BINARY
0.40
0.35
0.755
0.775
brining time rangpec))
0,30
0.725
0.725
0.700
X
0.700
0.675
0.650-
0.650
0.00
6.5
0.50
0.75
3.00
1.25
3.50
1.75
5.00
0.5
0.50
0.75
1.00
1.25
1.50
1.75
0.00
0.05
5.10
615
020
0.25
0.30
0.35
0.40
Model paramaters.commmmmm count
Model paramattiess count
Trithing wwwiingimm..oo (xlepect))
Figure 19: Parameters coumt/sizo/peeformaaa comparison, GIN, IMDB-BINARY
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0.36
HIP
0.56
MIP
0.34
0.54
K00
0.52
theerrn (Arepent))
0.25
0.52
0.50
0.50
0.20
0.45
0.40
30200
100000
1:0000
200003
30000
100000
150000
200000
0.00
0.05
0.30
0.25
0.20
0.25
0.30
Model remeters count
Model parsmeters count
Train ng time (slepoch)
Figure 20: Parameters count/sixe/pperformamne comparison, GCN, MUDB-MULTI
0.550
0.40
0.550
0.525
0.55
0.525
0.30
0.475
0.25
0.475
0.450
0.450
0.425
0.425
0.400
0.400
0.375
0.375
X
0.0
055
1.0
1.5
2.5
3.5
0.0
055
1.0
3.5
2.0
2.5
3.0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
D.35
D-1D
Model parameterss count
166
Model paraametiess count
1c6
Tramiing time (ulepecn)
Figure 21: Parameters count/size/performanc comparison, GAT, IMDB-MULTI
0.5
0.550
0.550
0.525
0.525
AccusO
0.500
0.3
0.500
0.473
0.415
0.2
0.450
0.450
0.400
0.400
0.0
0.5
1.5
1.5
2.0
2.5
0.5
0.5
3.0
1.5
2.0
2.5
0.0
0.1
0.2
0.3
0.4
Model parameters count
165
Model pararreciees couutt
1c6
Teiting time (clepezc))
Figure 22: Parameters count/size/performannd comparison, GIN, IMDB-MULTI
C.1
Training Times Graph Classification
We give in Table I8 the training time per epoch for different configurations of the BS-KAGIN, RBF-XAGIN and GIN models hidden dimension size, GIN is the fastest, followed by RBF-KAGIN, BS-KAGIN is noticcably slower than the others. It suffers doubly: its parameter count. increases much quicker than both other models for same hyperparameters: but even for similar numbers of parameters, BS-KAGIN is by far the slowest. Spline order soems to have a larger impact on running time than grid size. This shows that RBFs do alleviate some the computational bottlenecks of the B-splines from the original KAN paper. Table 19 Appendix C.2 shows similar observations node-level task.
graph-level task. We observe that for given number of message-
layers and
27

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Published in Transactions on Machine Learning Research (03/2025)
Table 18: Training time per epoch on NCI1 dataset. message- pesssag-passsnn layers.
batch size to 128.
Hidden
Hidden Layers
Training time (s/epoch)
Architecture
Grid Size
Spline Order # Parameters
Dimension
GIN
256
2
NA
NA
670722
0.303
GTN
256
4
NA
NA
1465346
0.390
GIN
512
2
NA
NA
2652162
0.541
GIN
512
4
NA
NA
5814274
0.951
RBF-KAGIN
256
1
NA
822872
0.386
RBF-KAGIN
256
1
4
NA
1639274
0.599
RBF-KAGIN
256
3
NA
3191408
0.783
RBF-KAGIN
256
3
4
NA
6367142
1.577
RBF-KAGIN
512
1
NA
3218520
0.807
RBF-KAGIN
512
NA
6424170
1.441
RBF-KAGIN
512
NA
12674160
2.198
RBF-KAGIN
3
NA
2531 7030
4.429
BS-KAGIN
256
1
1091072
0.446
BS-KAGIN
256
4
1907456
2.964
BS-KAGIN
256
1
1
1907456
0.720
BS-KAGIN
256
2723840
4.240
BS-KAGIN
256
3
4236800
0.937
BS-KAGIN
256
3
4
7412480
9.703
BS-KAGIN
256
3
4
7412480
1.963
BS- BS-KAGIN
256
3
4
4
10588160
14.572
C.2 Training Times Node Classification
Table 19: Training time per epoch on the node-classification task (Cora dataset, 3 MP-layers).
Hidden Dimension
Hidden Layers
Training time (s/epoch)
Architecture
Grid Size
Spline Order
# Parameters
GCN
256
NA
NA
NA
378934
0.003
GCN
1024
NA
NA
NA
1485622
0.005
BS-KAGCN
256
NA
1
1514684
0.017
BS-KAGCN
256
NA
1
2650697
0.160
BS-KAGCN
256
NA
2650697
0.031
BS-KAGCN
256
NA
3786710
0.222
BS BS-KAGCN
512
NA
1
2989244
0.020
BS BS-KAGCN
512
NA
1
4
5231177
0.179
BS-KAGCN
512
NA
4
5231177
0.039
BS-KAGCN
512
NA
4
7473110
0.254
RBF-KAGCN
256
NA
NA
1142524
0.016
RBF-KAGCN
256
NA
4
NA
2278543
0.031
RBF-KAGCN
1024
NA
1
NA
4462588
0.029
RBF-KAGON
1024
NA
4
NA
8916367
0.057
GIN
256
2
NA
NA
867335
0.007
GIN
256
4
NA
NA
1130503
0.008
GIN
1024
2
NA
NA
5042183 83
0.020
GIN
1024
4
NA
NA
9240583
0.033
28

---

Published in Transactions on Machine Learning Research (03/2025)
BS-KAGIN
256
1
1
1514684
0.017
BS-KAGIN
256
1
2650697
0.158
BS-KAGIN
256
1
4
2650697
0.032
BS-KAGIN
256
3786710
0.224
BS-KAGIN
256
3990528
0.025
BS-KAGIN
256
6983424
0.229
ES-KAGIN
256
3
6983424
0.051
BS-KAGIN
256
3
4
9976320
0.334
BS-KAGIN
512
1
2989244
0.021
BS-KAGIN
512
1
4
5231177
0.184
BS-KAGIN
512
4
5231177
0.041
BS-KAGIN
512
7473110
0.261
BS-KAGIN
512
10078208
0.046
BS-KAGIN
512
3
17636864
0.354
BS-KAGIN
512
3
4
17636864
0.089
BS-KAGIN
512
3
4
25195520
0.499
RBF-KAGIN
NA
1142524
0.017
RBF-KAGIN
256
NA
2278543
0.032
RBF-KAGIN
256
3
1
NA
3002487
0.023
RBF-KAGIN
256
3
4
NA
5995401
0.046
RBF-KAGIN
1024
1
NA
4462588
0.03
RBF-KAGIN
1024
1
4
NA
8916367
0.057
RBF-KAGIN
1024
3
1
NA
21429879
0.091
RBF-KAGIN
1024
NA
42838665
0.185
29


Reviews:
[{"review_id": "Lw10wk9Xj7", "reviewer": "Reviewer_KEvU", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. The paper offers a thorough comparison between KANs and MLPs within GNN frameworks, shedding light on their respective advantages.\n\n2. The manuscript is well-written, clearly structured, and easy to follow, which facilitates comprehension of the concepts and results.\n\n\nWeaknesses: \n\n\n1. The motivation for the study requires further clarification. The authors aim to enhance the expressiveness of GNNs by incorporating KANs. However, it is unclear how this aligns with the standard definition of GNN expressiveness, particularly the constraints imposed by the 1-WL test in basic message-passing GNNs. A detailed discussion of how KANs address these limitations or extend GNN expressiveness is necessary.\n\n2. The paper’s main contribution is somewhat ambiguous. While the authors evaluate KAN-based GNNs against MLP-based GNNs, the specific novelty or advancement introduced by the KAN architecture is not explicitly emphasized. Clarifying the unique insights or techniques brought forth by this work would strengthen its impact.\n\n3. In Section 6, the authors assert that KANs offer superior explainability compared to MLPs. However, no empirical evidence or qualitative examples are provided to substantiate this claim. Supporting this assertion with experiments, visualizations, or real-world examples would significantly enhance the credibility and relevance of this argument.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper presents a comprehensive comparison between Multilayer Perceptrons (MLPs) and Kernel Attention Networks (KANs) within the context of Graph Neural Networks (GNNs). Specifically, the authors introduce modifications to the GCN and GIN architectures, replacing the original MLP layers with KANs to create KAGCN and KAGIN. They conduct extensive experiments on both node classification and graph classification tasks to demonstrate that KANs are more parameter-efficient and achieve better performance than MLPs.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Elaborate on the motivation behind replacing MLPs with KANs, explicitly addressing how KANs improve expressiveness in ways relevant to the constraints of traditional GNNs (e.g., the 1-WL test).\n\n2. Clearly articulate the contributions of the paper. Emphasize the unique aspects of KANs and their integration into GNNs beyond the evaluation of their performance.\n\n3. Provide empirical evidence or illustrative examples to support the claim that KANs are more explainable than MLPs, as stated in Section 6. This could include case studies, attention heatmaps, or other interpretability analyses.", "broader_impact_concerns": "n/a", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "5cZnmCSoJG", "reviewer": "Reviewer_ywSt", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n* Novel use of KANs in GNNs\n* Detailed experimental evaluation: The study conducts carries out an evaluation across multiple datasets for node and graph classification, providing empirical support for their claims.\n* Clear insights into computational trade-offs: The paper discusses the advantages and disadvantages, providing practitioners with guidance for selecting the appropriate KAN variants.\n* Practical relevance: The work has potential applications in tasks requiring smooth function approximations or interpretable models.\n\nWeaknesses:\n\nThe strength of this work lies in its empirical evaluation. However, the evaluation is somewhat limited:\n\n* Task scope:  The study focuses on node and graph classification tasks but omits link prediction, though it is an important application for GNNs.\n* GNN architectures: The comparisons are limited to basic GNN variants (GIN and GCN), without benchmarking against more advanced models such as Graph Attention Networks (GAT).\n\nThese limitations reduce the generality of the findings but are straightforward to address.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes replacing Multi-Layer Perceptrons (MLPs) with Kolmogorov-Arnold Networks (KANs) as the update function in Graph Neural Networks (GNNs). The authors introduce two KAN-based GNN variants (KAGIN and KAGCN) and use two types of KANs (B-Splines and RBFs). Experiments are conducted on node and graph classification tasks, demonstrating that KAN-based GNNs perform competitively with or better than their MLP-based counterparts, particularly in regression-tasks.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "* (critical) Include experiments on link prediction.\n* (critical) Add comparisons with more GNN architecture, at least, e.g., with Graph Attention Networks (GAT).\n* (critical) Expand Table 9 and similar with model performance.", "broader_impact_concerns": "n/a", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ck1Ky5YT0e", "reviewer": "Reviewer_jhqf", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Although the experiments are extensive, I believe this work has limited novelty. Since KANs are known for its interpretability, in my opinion, this work should have focused on that aspect. For example, how the learned activations can explain the interactions between features as well as nodes. What kind of activations are prominent in social networks and what activations are prominent in molecular networks. The chosen activations are as in KAN paper, what about exploring domain specific activations in the context of graph learning tasks? Overall, without these insights, the paper just seems to be a accuray tables and benchmarks by replacing MLPs with KANs. I see that these questions have been mentioned in the future work section, but this should have been the focus of this paper in my opinion.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Graph neural networks perform two operations in each layer: feature transformation and feature aggregation. Traditionally, MLP shave been used for feature transformation. This paper replaces MLPs with recently proposed Kolmogorov-Arnold Networks (KANs) for feature transformation. It provides empirical evaluations on various graph related tasks including node classification and graph classification/regression. Its a great problem to study in the context of graph learning. However, this paper has limited novelty.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "It would be great if the authors can explore more on interpretability part as mentioned above, at least for some tasks. \n\nAlso, there is loose sentence in abstract \" Our results indicate that KANs are on-par with or better than MLPs on all studied tasks,...\" it should be in terms of graph learning, not generic.", "broader_impact_concerns": "n/a", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper proposes modifications to the GCN and GIN architectures by substituting the original MLP layers with KANs, resulting in the KAGCN and KAGIN models. Extensive experiments on node and graph classification tasks demonstrate that KANs are more parameter-efficient and outperform baseline methods. It is interesting and new to add KANs to GNNs and improve their performance. The experiments and the paper writing are overall good. It is necessary to further improve the work by adding elaborated motivations behind replacing MLPs with KANs, providing link prediction results, and exploring more architectures like GAT.
Decision: Accept (poster)