# PAN: Path Integral Based Convolution for Deep Graph Neural Networks

arXiv: https://arxiv.org/abs/1904.10996 · HTML: https://mlsanity.com/paper/1904.10996/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 5 of 5)

- [A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling](https://mlsanity.com/paper/2110.03442/) (2021)
- [YOLOv1 to YOLOv10: A comprehensive review of YOLO variants and their application in the agricultural domain](https://mlsanity.com/paper/2406.10139/) (2024)
- [FlowGNN: A Dataflow Architecture for Real-Time Workload-Agnostic Graph Neural Network Inference](https://mlsanity.com/paper/2204.13103/) (2022)
- [Respecting Time Series Properties Makes Deep Time Series Forecasting Perfect](https://mlsanity.com/paper/2207.10941/) (2022)
- [YotoR-You Only Transform One Representation](https://mlsanity.com/paper/2405.19629/) (2024)

## Abstract (arXiv)

Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph convolution framework that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. PAN generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Most previous graph convolutional network architectures can be adapted to our framework, and many variations and derivatives based on the path integral idea can be developed. Experimental results show that the path integral based graph neural networks have great learnability and fast convergence rate, and achieve state-of-the-art performance on benchmark tasks.