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archwalker / archwalker.github.io

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https://archwalker.github.io
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GNN 教程：Weisfeiler-Leman 算法 - ArchWalker #11

Open archwalker opened 5 years ago

archwalker commented 5 years ago

https://archwalker.github.io/blog/2019/06/22/GNN-Theory-WL.html

一、引言前面的文章中，我们介绍了GNN的三个基本模型GCN、GraphSAGE、GAT，分析了经典的GCN逐层传播公式是如何由谱图卷积推导而来的。GNN模型现在正处于学术研究的热点话题，那么我们不经想问，GNN模型到底有多强呢？我们的目的是分析GNN的表达能力，我们需要一个模型作为衡量标准。比如说如果我们想衡量G...

hotchilipowder commented 4 years ago

Hello, it looks like that step1 is not right if I understand it correctly. In step1, for the node 4, it gets (1, 14) not (1, 4).

archwalker commented 4 years ago

@h12345jack Hello, it looks like that step1 is not right if I understand it correctly. In step1, for the node 4, it gets (1, 14) not (1, 4).

node index after comma are all neighbor nodes' indices, thus 1 is excluded.

hotchilipowder commented 4 years ago

@archwalker

@h12345jack Hello, it looks like that step1 is not right if I understand it correctly. In step1, for the node 4, it gets (1, 14) not (1, 4).

node index after comma are all neighbor nodes' indices, thus 1 is excluded.

I am sorry, I mean if some nodes are not labeled correctly. 2020-04-09-2.14.35.png

archwalker commented 4 years ago

@h12345jack

@archwalker

@h12345jack Hello, it looks like that step1 is not right if I understand it correctly. In step1, for the node 4, it gets (1, 14) not (1, 4).

node index after comma are all neighbor nodes' indices, thus 1 is excluded.

I am sorry, I mean if some nodes are not labeled correctly. 2020-04-09-2.14.35.png

you are right, I have fix the problem, thanks

liangchen1ceeee commented 3 years ago

请问为什么后话部分说“单层感知机不是单射函数”呀？单层感知机由矩阵乘法、激活函数组成，矩阵乘法是单调函数，激活函数如果也是单调的（比如tanh、sigmoid），那么由于单调函数一定是单射函数，单层感知机就是单设函数啊？

archwalker commented 3 years ago

@liangchen1ceeee 请问为什么后话部分说“单层感知机不是单射函数”呀？单层感知机由矩阵乘法、激活函数组成，矩阵乘法是单调函数，激活函数如果也是单调的（比如tanh、sigmoid），那么由于单调函数一定是单射函数，单层感知机就是单设函数啊？

您好，矩阵乘法不一定是单射的，矩阵乘法单射的充要条件是矩阵为列满秩矩阵。