FourierKAN-GCF: Fourier Kolmogorov-Arnold Network - An Effective and Efficient Feature Transformation for Graph Collaborative Filtering

Introduction

This is the Pytorch implementation for our FourierKAN-GCF paper:

FourierKAN-GCF: Fourier Kolmogorov-Arnold Network - An Effective and Efficient Feature Transformation for Graph Collaborative Filtering

Discussion

Rethinking feature transformation component in GCNs in recommendation field!

LightGCN simplifies NGCF by remove feature transformation, formally:

NGCF

$$\begin{aligned} \mathbf{e}_u^{(l+1)} & =\sigma(\mathbf{W}_1 \mathbf{e}_u^{(l)}+\sum_{i \in \mathcal{N}_u} \frac{\mathbf{W}_1 \mathbf{e}_i^{(l)}+\mathbf{W}_2(\mathbf{e}_i^{(l)} \odot \mathbf{e}_u^{(l)})}{\sqrt{|\mathcal{N}_u||\mathcal{N}_i|}}), \\ \mathbf{e}_i^{(l+1)} & =\sigma(\mathbf{W}_1 \mathbf{e}_i^{(l)}+\sum_{u \in \mathcal{N}_i} \frac{\mathbf{W}_1 \mathbf{e}_u^{(l)}+\mathbf{W}_2(\mathbf{e}_u^{(l)} \odot \mathbf{e}_i^{(l)})}{\sqrt{|\mathcal{N}_u||\mathcal{N}_i|}}). \end{aligned}$$

LightGCN

$$\mathbf{e}_u^{(l+1)} =\sum_{i \in \mathcal{N}_u} \frac{\mathbf{e}_i^{(l)}}{\sqrt{|\mathcal{N}_u||\mathcal{N}_i|}}, \quad \mathbf{e}_i^{(l+1)} =\sum_{u \in \mathcal{N}_i} \frac{\mathbf{e}_u^{(l)}}{\sqrt{|\mathcal{N}_u||\mathcal{N}_i|}}.$$

We point out that $\mathbf{W}_1$ is unnecessary, but interaction part $\mathbf{W}_2(\mathbf{e}_i^{(l)} \odot \mathbf{e}_u^{(l)})$ is valuable for recommendation task, but it's hard to train on sparsity dataset.

Thanks to the original implementations KAN and FourierKAN.

We use single-layer FourierKAN to replace MLP in feature transformation component and achieve better results than LightGCN and NGCF on MOOC and Amazon Games datasets. Formally:

FourierKAN-GCF

$$\phi_F(\mathbf{x})=\sum_{i=1}^{d} \sum_{k=1}^{g}\left(\cos \left(k \mathbf{x}_i\right) \cdot a_{i k}+\sin \left(k \mathbf{x}_i\right) \cdot b_{i k}\right).$$ $$\begin{aligned} \mathbf{e}_u^{(l+1)} & =\sigma(\mathbf{e}_u^{(l)}+\sum_{i \in \mathcal{N}_u} \frac{\mathbf{e}_i^{(l)}+\phi_F(\mathbf{e}_i^{(l)} \odot \mathbf{e}_u^{(l)})}{\sqrt{|\mathcal{N}_u||\mathcal{N}_i|}}), \\ \mathbf{e}_i^{(l+1)} & =\sigma(\mathbf{e}_i^{(l)}+\sum_{u \in \mathcal{N}_i} \frac{\mathbf{e}_u^{(l)}+\phi_F(\mathbf{e}_u^{(l)} \odot \mathbf{e}_i^{(l)})}{\sqrt{|\mathcal{N}_u||\mathcal{N}_i|}}). \end{aligned}$$

More datasets are yet to be tested, and this work is just a taste of whether KAN can be used for recommendation.

Structure

Environment Requirement

• Python 3.9
• Pytorch 2.1.0

Dataset

Two public datasets: MOOC, Games

Training

cd ./src
python main.py

Thanks for simplifies Recbole repo. ImRec.

Citing if this repo. useful:

@article{xu2024fourierkan,
  title={FourierKAN-GCF: Fourier Kolmogorov-Arnold Network--An Effective and Efficient Feature Transformation for Graph Collaborative Filtering},
  author={Xu, Jinfeng and Chen, Zheyu and Li, Jinze and Yang, Shuo and Wang, Wei and Hu, Xiping and Ngai, Edith C-H},
  journal={arXiv preprint arXiv:2406.01034},
  year={2024}
}