# Graph Structure of Neural Networks

international conference on machine learning, 2020.

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Abstract:

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require a model to learn from graph inputs. In other domains such as learning from non-structural data like texts a...More

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Introduction

- Graphs are a kind of data structure which models a set of objects and their relationships.
- As a unique non-Euclidean data structure for machine learning, graph analysis focuses on node classification, link prediction, and clustering.
- Graph neural networks (GNNs) are deep learning based methods that operate on graph domain.
- Due to its convincing performance and high interpretability, GNN has been a widely applied graph analysis method recently.
- The authors will illustrate the fundamental motivations of graph neural networks

Highlights

- Graphs are a kind of data structure which models a set of objects and their relationships
- There exist several comprehensive reviews on graph neural networks. [22] proposed a unified framework, MoNet, to generalize CNN architectures to non-Euclidean domains and the framework could generalize several spectral methods on graphs [2], [23] as well as some models on manifolds [24], [25]. [26] provides a thorough review of geometric deep learning, which presents its problems, difficulties, solutions, applications and future directions. [22] and [26] focus on generalizing convolutions to graphs or manifolds, in this paper we only focus on problems defined on graphs and we investigate other mechanisms used in graph neural networks such as gate mechanism, attention mechanism and skip connection. [27] proposed the message passing neural network (MPNN) which could generalize several graph neural network and graph convolutional network approaches. [28] proposed the non-local neural network (NLNN) which unifies several “self-attention”-style methods
- We introduce graph convolutional networks and graph attention networks in Section 2.2.2 as they contribute to the propagation step
- This paper presents an extensive survey of graph neural networks with the following contributions
- For Graph neural networks models, we introduce its variants categorized by graph types, propagation types, and training types
- We suggest four open problems indicating the major challenges and future research directions of graph neural networks, including model depth, scalability, the ability to deal with dynamic graphs and non-structural scenarios

Methods

- 1st-order model Single parameter GCN Neural FPs. Graph Attention Networks GAT Aggregator Nk = Tk(L )X N0 = X.
- The original graph convolutional neural network has several drawbacks in training and optimization methods.
- To solve the problems mentioned above, GraphSAGE replaced full graph Laplacian with learnable aggregation functions, which are key to perform message passing and generalize to unseen nodes.
- With learned aggregation and propagation functions, GraphSAGE could generate embeddings for unseen nodes.
- GraphSAGE uses neighbor sampling to alleviate receptive field expansion

Conclusion

- Over the past few years, graph neural networks have become powerful and practical tools for machine learning tasks in graph domain.
- This progress owes to advances in expressive power, model flexibility, and training algorithms.
- In this survey, the authors conduct a comprehensive review of graph neural networks.
- The authors suggest four open problems indicating the major challenges and future research directions of graph neural networks, including model depth, scalability, the ability to deal with dynamic graphs and non-structural scenarios

Summary

## Introduction:

Graphs are a kind of data structure which models a set of objects and their relationships.- As a unique non-Euclidean data structure for machine learning, graph analysis focuses on node classification, link prediction, and clustering.
- Graph neural networks (GNNs) are deep learning based methods that operate on graph domain.
- Due to its convincing performance and high interpretability, GNN has been a widely applied graph analysis method recently.
- The authors will illustrate the fundamental motivations of graph neural networks
## Methods:

1st-order model Single parameter GCN Neural FPs. Graph Attention Networks GAT Aggregator Nk = Tk(L )X N0 = X.- The original graph convolutional neural network has several drawbacks in training and optimization methods.
- To solve the problems mentioned above, GraphSAGE replaced full graph Laplacian with learnable aggregation functions, which are key to perform message passing and generalize to unseen nodes.
- With learned aggregation and propagation functions, GraphSAGE could generate embeddings for unseen nodes.
- GraphSAGE uses neighbor sampling to alleviate receptive field expansion
## Conclusion:

Over the past few years, graph neural networks have become powerful and practical tools for machine learning tasks in graph domain.- This progress owes to advances in expressive power, model flexibility, and training algorithms.
- In this survey, the authors conduct a comprehensive review of graph neural networks.
- The authors suggest four open problems indicating the major challenges and future research directions of graph neural networks, including model depth, scalability, the ability to deal with dynamic graphs and non-structural scenarios

- Table1: Notations used in this paper
- Table2: Different variants of graph neural networks
- Table3: Applications of graph neural networks

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