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KA-GNN: Kolmogorov-Arnold Graph Neural Networks for Molecular Property Prediction

Longlong Li, Yipeng Zhang, Guanghui Wang, Kelin Xia

TL;DR

This work addresses molecular property prediction with graph neural networks by introducing KA-GNNs, which embed Kolmogorov-Arnold Networks (KAN) into GCN and GAT architectures to optimize node embedding, message passing, and readout. A Fourier-series variant of KAN is developed, and its robust approximation capability is theoretically supported. Empirically, KA-GNNs achieve state-of-the-art ROC-AUC across seven MoleculeNet datasets, with notable gains on challenging tasks and improved efficiency due to the Fourier basis. The results establish a new geometric-deep-learning framework for non-Euclidean data and demonstrate how Fourier-based KAN can enhance both accuracy and computational performance in molecular-property prediction.

Abstract

As key models in geometric deep learning, graph neural networks have demonstrated enormous power in molecular data analysis. Recently, a specially-designed learning scheme, known as Kolmogorov-Arnold Network (KAN), shows unique potential for the improvement of model accuracy, efficiency, and explainability. Here we propose the first non-trivial Kolmogorov-Arnold Network-based Graph Neural Networks (KA-GNNs), including KAN-based graph convolutional networks(KA-GCN) and KAN-based graph attention network (KA-GAT). The essential idea is to utilizes KAN's unique power to optimize GNN architectures at three major levels, including node embedding, message passing, and readout. Further, with the strong approximation capability of Fourier series, we develop Fourier series-based KAN model and provide a rigorous mathematical prove of the robust approximation capability of this Fourier KAN architecture. To validate our KA-GNNs, we consider seven most-widely-used benchmark datasets for molecular property prediction and extensively compare with existing state-of-the-art models. It has been found that our KA-GNNs can outperform traditional GNN models. More importantly, our Fourier KAN module can not only increase the model accuracy but also reduce the computational time. This work not only highlights the great power of KA-GNNs in molecular property prediction but also provides a novel geometric deep learning framework for the general non-Euclidean data analysis.

KA-GNN: Kolmogorov-Arnold Graph Neural Networks for Molecular Property Prediction

TL;DR

This work addresses molecular property prediction with graph neural networks by introducing KA-GNNs, which embed Kolmogorov-Arnold Networks (KAN) into GCN and GAT architectures to optimize node embedding, message passing, and readout. A Fourier-series variant of KAN is developed, and its robust approximation capability is theoretically supported. Empirically, KA-GNNs achieve state-of-the-art ROC-AUC across seven MoleculeNet datasets, with notable gains on challenging tasks and improved efficiency due to the Fourier basis. The results establish a new geometric-deep-learning framework for non-Euclidean data and demonstrate how Fourier-based KAN can enhance both accuracy and computational performance in molecular-property prediction.

Abstract

As key models in geometric deep learning, graph neural networks have demonstrated enormous power in molecular data analysis. Recently, a specially-designed learning scheme, known as Kolmogorov-Arnold Network (KAN), shows unique potential for the improvement of model accuracy, efficiency, and explainability. Here we propose the first non-trivial Kolmogorov-Arnold Network-based Graph Neural Networks (KA-GNNs), including KAN-based graph convolutional networks(KA-GCN) and KAN-based graph attention network (KA-GAT). The essential idea is to utilizes KAN's unique power to optimize GNN architectures at three major levels, including node embedding, message passing, and readout. Further, with the strong approximation capability of Fourier series, we develop Fourier series-based KAN model and provide a rigorous mathematical prove of the robust approximation capability of this Fourier KAN architecture. To validate our KA-GNNs, we consider seven most-widely-used benchmark datasets for molecular property prediction and extensively compare with existing state-of-the-art models. It has been found that our KA-GNNs can outperform traditional GNN models. More importantly, our Fourier KAN module can not only increase the model accuracy but also reduce the computational time. This work not only highlights the great power of KA-GNNs in molecular property prediction but also provides a novel geometric deep learning framework for the general non-Euclidean data analysis.

Paper Structure

This paper contains 17 sections, 6 theorems, 30 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Kolmogorov-Arnold Network (KAN)
  4. Kolmogorov-Arnold Network (KAN)
  5. Fourier-series KAN model
  6. Kolmogorov-Arnold Network-based Graph Neural Network Models
  7. KA-GCN Model
  8. KA-GAT Model
  9. KA-GNNs for Molecular Property Analysis
  10. Performance and comparison of KA-GNNs
  11. Importance of Fourier series for KA-GNNs
  12. Methods
  13. Approximation Capability of Fourier KAN
  14. Benchmark Datasets
  15. Baseline Models
  16. ...and 2 more sections

Key Result

Theorem 1

Let $\mathbf{Z}^n$ denote the $n$-dimensional integer lattice, and let $Z_N^n = \{1, 2, \ldots, N\}^n \subset \mathbf{Z}^n$. Then for the function $f \in L^2([0, 2\pi]^n)$ and its Fourier expansion: where $x\in [0, 2\pi]^n \text{ and } L^2([0, 2\pi]^n)$ denotes the space of square-integrable functions on $[0, 2\pi]^n$, which consists of all functions $f$ such that $\int_{[0, 2\pi]^n} |f(\vec{\ma

Figures (3)

  • Figure 1: Overview of the KA-GNN model architecture. The flowchart illustrates the modified components within the GNN: node embedding, message-passing, pooling and prediction modules.
  • Figure 2: The comparison the computational efficiency of KA-GNNs based on B-spline, polynomial, and Fourier series. A. Running time of KA-GCN model for 100 epochs across different datasets. B. Running time of KA-GAT Model for 100 epochs across different datasets.
  • Figure 3: Fourier-series KAN and two-layers MLP fit six different functions: A. Linear function $y = 3x + 5$, $K = 200$ in Fourier-series KAN; B. Exponential function $y = 3\exp(\frac{1}{2}x)$, $K = 120$ in Fourier-series KAN; C. Logarithmic function $y = 2\log(x) + 3$, $K = 100$ in Fourier-series KAN; D. Polynomial function $y = 2x^2 - 4x + 1$, $K = 500$ in Fourier-series KAN; E. Sin function $y = 2\sin(3x) + 1$, $K = 100$ in Fourier-series KAN; F. Sin and Cos function $y = 3\sin(x) + 2\cos(2x) + 1$, $K = 100$ in Fourier-series KAN.

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6