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GKAN: Graph Kolmogorov-Arnold Networks
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We introduce Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of the recently proposed Kolmogorov-Arnold Networks (KAN) to graph-structured data. By adopting the unique characteristics of KANs, notably the use of learnable univariate functions instead of fixed linear weights, we develop a powerful model for graph-based learning tasks. Unlike traditional Graph Convolutional Networks (GCNs) that rely on a fixed convolutional architecture, GKANs implement learnable spline-based functions between layers, transforming the way information is processed across the graph structure. We present two different ways to incorporate KAN layers into GKAN: architecture 1 -- where the learnable functions are applied to input features after aggregation and architecture 2 -- where the learnable functions are applied to input features before aggregation. We evaluate GKAN empirically using a semi-supervised graph learning task on a real-world dataset (Cora). We find that architecture generally performs better. We find that GKANs achieve higher accuracy in semi-supervised learning tasks on graphs compared to the traditional GCN model. For example, when considering 100 features, GCN provides an accuracy of 53.5 while a GKAN with a comparable number of parameters gives an accuracy of 61.76; with 200 features, GCN provides an accuracy of 61.24 while a GKAN with a comparable number of parameters gives an accuracy of 67.66. We also present results on the impact of various parameters such as the number of hidden nodes, grid-size, and the polynomial-degree of the spline on the performance of GKAN.
Forward citations
Cited by 12 Pith papers
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KAN-SAs: Efficient Acceleration of Kolmogorov-Arnold Networks on Systolic Arrays
A systolic-array accelerator that tabulates B-splines and exploits B-spline local support achieves ~100% PE utilization and a 2x cycle reduction for KAN inference compared with a conventional systolic array.
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A Kolmogorov-Arnold Surrogate Model for Chemical Equilibria: Application to Solid Solutions
Kolmogorov-Arnold networks trained on GEM-Selektor output accurately approximate chemical equilibria for cement and radium-sulfate solid-solution systems, outperforming MLPs on the cement benchmark and cutting evaluat...
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Khan-GCL: Kolmogorov-Arnold Network Based Graph Contrastive Learning with Hard Negatives
Khan-GCL combines KAN encoders with coefficient-based critical feature identification to generate hard negatives and reports state-of-the-art graph classification results.
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On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimators
The paper claims spline-parameterized KAN least-squares estimators achieve the minimax univariate regression rate O(n^{-2r/(2r+1)}) for additive and multiplicative KAN structures, independent of dimension.
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Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement
Training in a B-spline KAN basis is equivalent to preconditioned gradient descent on a multichannel ReLU MLP, and geometric refinement plus trainable knots accelerate and improve training.
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KAA: Kolmogorov-Arnold Attention for Enhancing Attentive Graph Neural Networks
Swapping attentive GNN score mappings for a single-layer Kolmogorov-Arnold Network improves benchmark performance and, on a specially constructed input matrix, provably achieves zero maximum ranking error.
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Kolmogorov-Arnold Recurrent Network for Short Term Load Forecasting Across Diverse Consumers
KARN, a recurrent network with spline-based learnable edge activations, reports better or comparable load forecasting accuracy than RNN, LSTM, and GRU across ten building datasets.
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Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning
Conformal prediction applied to ensembles of KANs, FBKANs, and MFKANs yields prediction intervals that empirically hit the target 95% coverage on four synthetic problems.
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EMK-KEN: A High-Performance Approach for Assessing Knowledge Value in Citation Network
EMK-KEN, a Mamba-KAN hybrid classifier, is reported to outperform six baselines on knowledge-value classification across ten citation datasets.
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Kolmogorov-Arnold Networks for Time Series Granger Causality Inference
KANGCI applies Kolmogorov-Arnold Networks with group-lasso penalties on first-layer base weights to infer Granger causality from time series, plus a time-reversal fusion heuristic to reduce spurious links.
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KAN KAN Buff Signed Graph Neural Networks?
Replacing the weight matrix in SGCN with a KAN layer yields competitive but generally not superior performance on signed community detection and link sign prediction, with high variance across datasets.
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PowerMLP: An Efficient Version of KAN
PowerMLP is a ReLU-power MLP that trains about 40x faster than KAN in the reported benchmarks and often beats it, but the main proof that KANs are contained in PowerMLPs at the same depth is flawed.
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