[CCGridW 2023]Performance Modelling of Graph Neural Networks

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#深度学习 #人工智能 #计算机视觉 #神经网络 #机器学习 #算法 #图论

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论文网址：Performance Modelling of Graph Neural Networks | IEEE Conference Publication | IEEE Xplore

英文是纯手打的！论文原文的summarizing and paraphrasing。可能会出现难以避免的拼写错误和语法错误，若有发现欢迎评论指正！文章偏向于笔记，谨慎食用

2.3. Background and Related Work

2.4. GNN Forward Pass Computational Cost

2.5. Empirical Evaluation

2.6. Conclusion and Future Work

3. Reference

1. 心得

（1）猝死ing

（2）把我读的这么多论文全部献祭给下一篇投的！！！

2. 论文逐段精读

2.1. Abstract

①Evaluation the computational costs of GNNs

2.2. Introduction

①This study calculated the computational cost of forward propagation in GraphConv and GraphSAGE

2.3. Background and Related Work

①Time complexity of standard GCN:

$\mathcal{O}=(L\|A\|_0F+LNF^2)$

time complexity of standard GraphSAGE:

$\mathcal{O}(r^LNF^2)$

where $L$ is the number of layers, $N$ denotes number of nodes, $\|A\|_0$ denotes number of non-zero values in adjacency matrix, $F$ denotes the number of features, $r$ denotes number of aggregated neighbours per node

2.4. GNN Forward Pass Computational Cost

①Define a graph $G=\left ( V,E \right )$ , where $\left | V \right |$ is the number of vertex, $\left | E \right |$ denotes number of edge

②Node feature: $h_i^l\in\mathcal{R}^{d\times1}$ in the $l$ -th layer

③Updating function of GCN:

$h_i^{l+1}=ReLU\left(U^l\frac{1}{\deg_i}\sum_{j\in N_{\dot{x}}}h_j^l\right)$

where $U^l\in\mathcal{R}^{d^{\prime}\times d}$ denotes learnable matrix（原文写的leamable mamx，看不懂一点，我猜就似乎俩都一起写错了？？是什么外文简单表示法吗？）, which get:

$((\deg_i+1)d+2dd^{\prime})$

FLOPs per node per layer

④FLOPs of each GConv layer:

$ExpectedFLOPs=2d|E|+\left(d+2dd^{\prime}\right)|V|$

⑤Updating function of GraphSAGE:

$\begin{aligned} & \hat{h}_{i}^{l+1}=\mathrm{ReLU}\left(U^l\mathrm{concat}\left(h_i^l,\mathrm{Mean}_{j\in\mathcal{N}_i}h_j^l\right)\right) \\ & h_{i}^{l+1}=\frac{\hat{h}_i^{l+1}}{\left\|\hat{h}_i^{l+1}\right\|_2} \end{aligned}$

where $U^l\in\mathcal{R}^{d^{\prime}\times2d}$ denotes learnable matrix, $\|\cdot\|_{2}$ is Euclidean norm, and its FLOPs per node per layer is:

$((\deg_i+1)d+3d^{\prime}+4dd^{\prime}+1)$

and FLOPs per layer is:

$ExpectedFLOPs=2d|E|+(1+d+3d^{\prime}+4dd^{\prime})|V|$

⑥FLOPs of two GNNs with 3 layers, $d_{in}\times d_{in}$ , $d_{in}\times d_{in}$ and $d_{in}\times C$ :

where $C$ denotes the number of classes

2.5. Empirical Evaluation

①10 datasets:

②CPU time of 2 models

2.6. Conclusion and Future Work

3. Reference

Naman,P. & Simmhan, Y. (2023) Performance Modelling of Graph Neural Networks, IEEE/ACM 23rd International Symposium on Cluster, Cloud and Internet Computing Workshops (CCGridW). Bangalore, India.