[CCGridW 2023]Performance Modelling of Graph Neural Networks

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

1. 心得

2. 论文逐段精读

2.1. Abstract

2.2. Introduction

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.

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