scholarly journals Path integral based convolution and pooling for graph neural networks*

2021 ◽  
Vol 2021 (12) ◽  
pp. 124011
Author(s):  
Zheng Ma ◽  
Junyu Xuan ◽  
Yu Guang Wang ◽  
Ming Li ◽  
Pietro Liò
Keyword(s):  
Neural Networks ◽  
Path Integral ◽  
State Of The Art ◽  
Graph Laplacian ◽  
Maximal Entropy ◽  
Optimized Design ◽  
Graph Classification ◽  
Physical Sciences ◽  
Special Cases ◽  
Graph Neural Networks

Abstract Graph neural networks (GNNs) extend the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose path integral-based GNNs (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix that we call the maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus leading to a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics that we propose to boost applications of GNN in physical sciences.

scholarly journals Coloring Graph Neural Networks for Node Disambiguation

2020 ◽  
Author(s):  
George Dasoulas ◽  
Ludovic Dos Santos ◽  
Kevin Scaman ◽  
Aladin Virmaux
Keyword(s):  
Neural Networks ◽  
Message Passing ◽  
State Of The Art ◽  
Structural Characteristics ◽  
Expressive Power ◽  
Continuous Functions ◽  
Graph Classification ◽  
Node Attributes ◽  
Graph Neural Networks ◽  
Coloring Graph

In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks (MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node attributes, and show that this representation is a universal approximator of continuous functions on graphs with node attributes. Our method relies on separability, a key topological characteristic that allows to extend well-chosen neural networks into universal representations. Finally, we show experimentally that CLIP is capable of capturing structural characteristics that traditional MPNNs fail to distinguish, while being state-of-the-art on benchmark graph classification datasets.

scholarly journals GSSNN: Graph Smoothing Splines Neural Networks

2020 ◽  
Vol 34 (04) ◽  
pp. 7007-7014
Author(s):  
Shichao Zhu ◽  
Lewei Zhou ◽  
Shirui Pan ◽  
Chuan Zhou ◽  
Guiying Yan ◽  
...  
Keyword(s):  
Neural Networks ◽  
State Of The Art ◽  
Representation Learning ◽  
Smoothing Splines ◽  
Graph Representation ◽  
Graph Classification ◽  
Topological Information ◽  
Graph Representations ◽  
The Arts ◽  
Graph Neural Networks

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in many graph data analysis tasks. However, they still suffer from two limitations for graph representation learning. First, they exploit non-smoothing node features which may result in suboptimal embedding and degenerated performance for graph classification. Second, they only exploit neighbor information but ignore global topological knowledge. Aiming to overcome these limitations simultaneously, in this paper, we propose a novel, flexible, and end-to-end framework, Graph Smoothing Splines Neural Networks (GSSNN), for graph classification. By exploiting the smoothing splines, which are widely used to learn smoothing fitting function in regression, we develop an effective feature smoothing and enhancement module Scaled Smoothing Splines (S3) to learn graph embedding. To integrate global topological information, we design a novel scoring module, which exploits closeness, degree, as well as self-attention values, to select important node features as knots for smoothing splines. These knots can be potentially used for interpreting classification results. In extensive experiments on biological and social datasets, we demonstrate that our model achieves state-of-the-arts and GSSNN is superior in learning more robust graph representations. Furthermore, we show that S3 module is easily plugged into existing GNNs to improve their performance.

scholarly journals K-plex cover pooling for graph neural networks

2021 ◽  
Author(s):  
Davide Bacciu ◽  
Alessio Conte ◽  
Roberto Grossi ◽  
Francesco Landolfi ◽  
Andrea Marino
Keyword(s):  
Neural Networks ◽  
Graph Theory ◽  
State Of The Art ◽  
Graph Classification ◽  
Topological Information ◽  
Community Discovery ◽  
Connectivity Patterns ◽  
Graph Neural Networks ◽  
Pruning Heuristics ◽  
Non Parametric

AbstractGraph pooling methods provide mechanisms for structure reduction that are intended to ease the diffusion of context between nodes further in the graph, and that typically leverage community discovery mechanisms or node and edge pruning heuristics. In this paper, we introduce a novel pooling technique which borrows from classical results in graph theory that is non-parametric and generalizes well to graphs of different nature and connectivity patterns. Our pooling method, named KPlexPool, builds on the concepts of graph covers and k-plexes, i.e. pseudo-cliques where each node can miss up to k links. The experimental evaluation on benchmarks on molecular and social graph classification shows that KPlexPool achieves state of the art performances against both parametric and non-parametric pooling methods in the literature, despite generating pooled graphs based solely on topological information.

scholarly journals SketchGNN: Semantic Sketch Segmentation with Graph Neural Networks

2021 ◽  
Vol 40 (3) ◽  
pp. 1-13
Author(s):  
Lumin Yang ◽  
Jiajie Zhuang ◽  
Hongbo Fu ◽  
Xiangzhi Wei ◽  
Kun Zhou ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Large Scale ◽  
State Of The Art ◽  
Semantic Segmentation ◽  
Structure Information ◽  
Graph Neural Networks ◽  
Node Labels ◽  
Point Level

We introduce SketchGNN , a convolutional graph neural network for semantic segmentation and labeling of freehand vector sketches. We treat an input stroke-based sketch as a graph with nodes representing the sampled points along input strokes and edges encoding the stroke structure information. To predict the per-node labels, our SketchGNN uses graph convolution and a static-dynamic branching network architecture to extract the features at three levels, i.e., point-level, stroke-level, and sketch-level. SketchGNN significantly improves the accuracy of the state-of-the-art methods for semantic sketch segmentation (by 11.2% in the pixel-based metric and 18.2% in the component-based metric over a large-scale challenging SPG dataset) and has magnitudes fewer parameters than both image-based and sequence-based methods.

Active and Semi-supervised Graph Neural Networks for Graph Classification

2022 ◽  
pp. 1-1
Author(s):  
Yu Xie ◽  
Shengze Lv ◽  
Yuhua Qian ◽  
Chao Wen ◽  
Jiye Liang
Keyword(s):  
Neural Networks ◽  
Graph Classification ◽  
Graph Neural Networks

scholarly journals Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

2020 ◽  
Author(s):  
Luís C. Lamb ◽  
Artur d’Avila Garcez ◽  
Marco Gori ◽  
Marcelo O.R. Prates ◽  
Pedro H.C. Avelar ◽  
...  
Keyword(s):  
Neural Networks ◽  
Constraint Satisfaction ◽  
State Of The Art ◽  
Relational Reasoning ◽  
Widespread Application ◽  
Symbolic Computing ◽  
Industry Research ◽  
Optimization Constraint ◽  
The Subject ◽  
Graph Neural Networks

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNNs) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as their relationship to current developments in neural-symbolic computing.

scholarly journals Multi-View Attribute Graph Convolution Networks for Clustering

2020 ◽  
Author(s):  
Jiafeng Cheng ◽  
Qianqian Wang ◽  
Zhiqiang Tao ◽  
Deyan Xie ◽  
Quanxue Gao
Keyword(s):  
Neural Networks ◽  
State Of The Art ◽  
Graph Embedding ◽  
Structured Data ◽  
Attention Networks ◽  
Graph Data ◽  
Graph Reconstruction ◽  
Node Attributes ◽  
Graph Neural Networks ◽  
Geometric Relationship

Graph neural networks (GNNs) have made considerable achievements in processing graph-structured data. However, existing methods can not allocate learnable weights to different nodes in the neighborhood and lack of robustness on account of neglecting both node attributes and graph reconstruction. Moreover, most of multi-view GNNs mainly focus on the case of multiple graphs, while designing GNNs for solving graph-structured data of multi-view attributes is still under-explored. In this paper, we propose a novel Multi-View Attribute Graph Convolution Networks (MAGCN) model for the clustering task. MAGCN is designed with two-pathway encoders that map graph embedding features and learn the view-consistency information. Specifically, the first pathway develops multi-view attribute graph attention networks to reduce the noise/redundancy and learn the graph embedding features for each multi-view graph data. The second pathway develops consistent embedding encoders to capture the geometric relationship and probability distribution consistency among different views, which adaptively finds a consistent clustering embedding space for multi-view attributes. Experiments on three benchmark graph datasets show the superiority of our method compared with several state-of-the-art algorithms.

scholarly journals Active Learning for Node Classification: An Evaluation

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1164
Author(s):  
Kaushalya Madhawa ◽  
Tsuyoshi Murata
Keyword(s):  
Neural Networks ◽  
Active Learning ◽  
State Of The Art ◽  
Learning Algorithms ◽  
Classification Performance ◽  
Data Types ◽  
Neural Network Models ◽  
Attributed Graph ◽  
Attributed Graphs ◽  
Graph Neural Networks

Current breakthroughs in the field of machine learning are fueled by the deployment of deep neural network models. Deep neural networks models are notorious for their dependence on large amounts of labeled data for training them. Active learning is being used as a solution to train classification models with less labeled instances by selecting only the most informative instances for labeling. This is especially important when the labeled data are scarce or the labeling process is expensive. In this paper, we study the application of active learning on attributed graphs. In this setting, the data instances are represented as nodes of an attributed graph. Graph neural networks achieve the current state-of-the-art classification performance on attributed graphs. The performance of graph neural networks relies on the careful tuning of their hyperparameters, usually performed using a validation set, an additional set of labeled instances. In label scarce problems, it is realistic to use all labeled instances for training the model. In this setting, we perform a fair comparison of the existing active learning algorithms proposed for graph neural networks as well as other data types such as images and text. With empirical results, we demonstrate that state-of-the-art active learning algorithms designed for other data types do not perform well on graph-structured data. We study the problem within the framework of the exploration-vs.-exploitation trade-off and propose a new count-based exploration term. With empirical evidence on multiple benchmark graphs, we highlight the importance of complementing uncertainty-based active learning models with an exploration term.

scholarly journals Fast and Deep Graph Neural Networks

2020 ◽  
Vol 34 (04) ◽  
pp. 3898-3905 ◽  
Author(s):  
Claudio Gallicchio ◽  
Alessio Micheli
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
State Of The Art ◽  
Input Graph ◽  
Sparse Networks ◽  
Set Up ◽  
The Stability ◽  
Graph Neural Networks ◽  
Architectural Organization

We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural network), and leverages a deep architectural organization of the recurrent units. Efficiency is gained by many aspects, including the use of small and very sparse networks, where the weights of the recurrent units are left untrained under the stability condition introduced in this work. This can be viewed as a way to study the intrinsic power of the architecture of a deep GNN, and also to provide insights for the set-up of more complex fully-trained models. Through experimental results, we show that even without training of the recurrent connections, the architecture of small deep GNN is surprisingly able to achieve or improve the state-of-the-art performance on a significant set of tasks in the field of graphs classification.

scholarly journals Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks

2019 ◽  
Vol 33 ◽  
pp. 4602-4609 ◽  
Author(s):  
Christopher Morris ◽  
Martin Ritzert ◽  
Matthias Fey ◽  
William L. Hamilton ◽  
Jan Eric Lenssen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Multiple Scales ◽  
Graph Isomorphism ◽  
Higher Order ◽  
Point Of View ◽  
Theoretical Point ◽  
Graph Classification ◽  
Graph Neural Networks ◽  
Vector Representations

In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically—showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the 1-dimensional Weisfeiler-Leman graph isomorphism heuristic (1-WL). We show that GNNs have the same expressiveness as the 1-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called k-dimensional GNNs (k-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.

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