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

@article{Ma2019PANPI, title={PAN: Path Integral Based Convolution for Deep Graph Neural Networks}, author={Zheng Ma and Ming Li and Yuguang Wang}, journal={ArXiv}, year={2019}, volume={abs/1904.10996} }

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…

## 18 Citations

### Path integral based convolution and pooling for graph neural networks

- Computer ScienceNeurIPS
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This work proposes path integral-based GNNs (PAN), a versatile framework that can be tailored for different graph data with varying sizes and structures, and achieves state-of-the-art performance on various graph classification/regression tasks.

### Graph Neural Networks with Haar Transform-Based Convolution and Pooling: A Complete Guide

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### Haar Graph Pooling

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A new graph pooling operation based on compressive Haar transforms -- HaarPooling is proposed, which synthesizes the features of any given input graph into a feature vector of uniform size.

### Adaptive Graph Diffusion Networks with Hop-wise Attention

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This work proposes Adaptive Graph Diffusion Networks with Hop-wise Attention (AGDNs-HA), which stacks multi-hop neighborhood aggregations of different orders into single layer with the help of hop-wise attention, which is learnable and adaptive for each node.

### HAARPOOLING: GRAPH POOLING

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This work proposes a new graph pooling operation based on compressive Haar transforms, called HaarPooling, which achieves state-of-the-art performance on diverse graph classification problems.

### HaarPooling: Graph Pooling with Compressive Haar Basis

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A new graph pooling operation based on compressive Haar transforms, called HaarPooling, is proposed, which achieves state-of-the-art performance on diverse graph classification problems.

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