Neural network of zero basis multi map detailed map

Reference link ：
https://www.bilibili.com/video/BV1iT4y1d7zP?share_source=copy_web

1. Preface ：

primary coverage ： What modules are needed to build a graph neural network , What's the idea behind it

The nodes on the upper layer of a graph are composed of neighbor nodes on the lower layer of the graph

Graphics are everywhere . Researchers have developed neural networks that operate on graphical data （ It is called graphical neural network , or GNN） More than 10 years. . Recent developments have improved their ability to express . We Start Found in antibacterial 、 physical simulation 、 Fake news detection 、 Traffic prediction and recommendation systems see practical applications .（ Fig. neural networks are just beginning to be applied ）

This paper explores and explains modern graphical neural networks . We divide the work into four parts ：
First , Let's see what kind of data is most naturally expressed as a graph , And some common examples
secondly , We will explore what makes a graph different from other types of data , And some special choices that must be made when using graphics
Third , We built a modern GNN, Browse through each part of the model , Start with historical modeling innovation in this field . We are gradually moving from a simple implementation to the most advanced GNN Model .
Fourth , Provides a GNN Playground , ad locum , You can play a real word Tasks and datasets , To build a stronger intuition , understand GNN How each component of the model contributes to its predictions .

2. What is a graph? ：

** chart ：** Represents a collection of entities （ node ） The relationship between （ edge ）

U： Represents another node , Global information

Directed graph / Undirected graph

Represent the picture as a graph

A pixel maps to a node
Represent the text as a graph

The molecular graph is represented as a graph

Represent the social network as a graph

3. What problems can be defined on the graph ：

Graph level 、 Node level and edge level
1. In graph level tasks , We predict the individual properties of the entire graph
2. For node level tasks , We predict some properties of each node in the graph
3. For side level tasks , We want to predict the properties or existence of edges in the graph

On the layer surface ： Identify two rings ？/ Classify the graph

At the vertex level ：

On the edge layer ：

4. The challenges of applying machine learning to graphs ：

The most important question ： How to represent our graph , Make them compatible
Represents the connection properties ： Adjacency matrix （ Too much space is used ）(x)
Adjacency list (√)：

5. Figure neural network （GNN）

GNN Is all the properties of the graph （ node 、 edge 、 Global context ） Optimized transformation of , It preserves the symmetry of the graph （ Permutation invariance ）.
For each level of the graph （ The vertices , edge , overall situation ） All use multi-layer perceptrons （MLP）, Three make up a layer of the graph

By gathering information GNN forecast

All nodes share a full connection layer
When the node has no information to predict , We use a Collect information from edges and provide it to nodes for prediction Methods
There are two steps to collect revenue ：1. For each project to be merged , Collect each of their embeddings and connect them to a matrix .2. then , Typically, the collected embeddedness is aggregated by summation .

example ： Only edge vectors , No node vector , Through a convergence layer , From edge to vertex , This is that each vertex gets its own vector , Finally, the output of vertices is obtained through the output layer shared between vertices

Empathy ： You can also converge vertices to edges

Converge to a graph through vertices

The simplest GNN Model

Give an input graph , Enter a series of gnn layer （ spot , edge , overall situation ）, Get a processed output that preserves the graph structure , To predict attributes, add some corresponding output layers , The missing information is added to the corresponding aggregation layer , Finally get the prediction

In this simplest GNN In the formula , We're not at all GNN Use the structure information of the graph in the layer . Each node and each edge and the global context are handled independently . We only use connectivity when pooling information for forecasting .

Information transmission
1. For each node in the graph , Collect all neighboring nodes to embed （ Or news ）
2. Through aggregate functions （ Such as sum） Aggregate all messages
3. All aggregated messages are passed through an update function

By passing to GNN Layers of messages are stacked together , Nodes can eventually merge information throughout the drawing

Use the data set of edges for representation learning
Our data sets do not always contain all types of information （ node 、 Edge and global context ）.
When we want to predict nodes , But when our dataset has only side information , We showed above how to use the pool to route information from the edge to the node , But only in the final prediction step of the model .
We can use Messages are delivered in GNN Information is shared between nodes and edges within the layer . We can merge information from adjacent edges in the same way as we used adjacent node information before , First merge the edge information , Use the update function to convert it and store .
however , The node and edge information stored in the drawing may not have the same size or shape , So it is not clear how to combine them . One way is to learn the linear mapping from edge space to node space , vice versa . perhaps , Can be in update Functions before connecting them together .

Nodes and edges exchange information with each other at the same time , This eliminates the need to consider nodes and edges , Which is the first to exchange information between edges and nodes

How to add global information
up to now , There is a flaw in the network we describe ： Nodes far away from each other in the graph may never be able to effectively transfer information to each other , Even if we apply messaging many times . For a node , If we had k layer , Most information spread k Step . When the prediction task depends on nodes or node groups far away , It could be a problem . One solution is to enable all nodes to pass information to each other . Unfortunately , For large graphics , This quickly becomes computationally expensive （ Although this is called “ Virtual edge ” The method of has been used for small graphics , Such as molecules ）. Of this question One solution is to use diagrams （U） Global representation of , It is sometimes referred to as the master node or context vector . The global context vector is connected to all other nodes and edges in the network , And can be used as a bridge between them , Create a representation for the entire graph . This will create a richer than other methods 、 More complex graphical representation .

For a node , We can consider from adjacent nodes 、 Information connecting edges and global information . In order to embed the new node into all these possible information sources , We can simply connect them . Besides , We can also map them to the same space by linear mapping , And add them or apply feature modulation layers , This can be regarded as a characteristic intelligent attention mechanism .

6.GNN Playground

Explore the impact of different parameters on the model （ The specific content is omitted ）

7.GNNs Sampling plots and batch processing in

The graph has enough levels , The final node may contain more information , Intermediate variables need to be stored , It may cause the calculation to be unbearable , therefore We need to take samples , A common way to train neural networks is to use them in training data （ Small batch ） Of Random constant size （ Batch size ） The gradient calculated on the subset is used to update the network parameters




GNN Assumptions ： No matter how the graph is transformed , All graphs maintain symmetry

8. Conclusion

Graphics is a powerful 、 Structured data types , It has distinct advantages and challenges from images and texts . In this paper , We outline some of the milestones that researchers have achieved in building a graphics processing model based on neural networks . We have seen some important design choices that must be made when using these architectures , hope GNN The amusement park can intuitively understand the empirical results of these design choices .GNNs The success of recent years has created a huge opportunity for a wide range of new problems , We are pleased to see what this area will bring .