scholarly journals Learning to Solve NP-Complete Problems: A Graph Neural Network for Decision TSP

2019 ◽  
Vol 33 ◽  
pp. 4731-4738 ◽  
Author(s):  
Marcelo Prates ◽  
Pedro H. C. Avelar ◽  
Henrique Lemos ◽  
Luis C. Lamb ◽  
Moshe Y. Vardi
Keyword(s):  
Neural Networks ◽  
Message Passing ◽  
Ground Truth ◽  
Problem Instance ◽  
Target Cost ◽  
Complete Problems ◽  
Np Complete ◽  
Route Cost ◽  
Numeric Data ◽  
Graph Neural Networks

Graph Neural Networks (GNN) are a promising technique for bridging differential programming and combinatorial domains. GNNs employ trainable modules which can be assembled in different configurations that reflect the relational structure of each problem instance. In this paper, we show that GNNs can learn to solve, with very little supervision, the decision variant of the Traveling Salesperson Problem (TSP), a highly relevant NP-Complete problem. Our model is trained to function as an effective message-passing algorithm in which edges (embedded with their weights) communicate with vertices for a number of iterations after which the model is asked to decide whether a route with cost < C exists. We show that such a network can be trained with sets of dual examples: given the optimal tour cost C∗, we produce one decision instance with target cost x% smaller and one with target cost x% larger than C∗. We were able to obtain 80% accuracy training with −2%,+2% deviations, and the same trained model can generalize for more relaxed deviations with increasing performance. We also show that the model is capable of generalizing for larger problem sizes. Finally, we provide a method for predicting the optimal route cost within 2% deviation from the ground truth. In summary, our work shows that Graph Neural Networks are powerful enough to solve NP-Complete problems which combine symbolic and numeric data.

scholarly journals Deep Generative Probabilistic Graph Neural Networks for Scene Graph Generation

2020 ◽  
Vol 34 (07) ◽  
pp. 11237-11245
Author(s):  
Mahmoud Khademi ◽  
Oliver Schulte
Keyword(s):  
Neural Networks ◽  
Message Passing ◽  
Question Answering ◽  
Ground Truth ◽  
Mass Function ◽  
Probability Mass Function ◽  
Scene Graph ◽  
Probabilistic Graph ◽  
Graph Neural Networks ◽  
Graph Generation

We propose a new algorithm, called Deep Generative Probabilistic Graph Neural Networks (DG-PGNN), to generate a scene graph for an image. The input to DG-PGNN is an image, together with a set of region-grounded captions and object bounding-box proposals for the image. To generate the scene graph, DG-PGNN constructs and updates a new model, called a Probabilistic Graph Network (PGN). A PGN can be thought of as a scene graph with uncertainty: it represents each node and each edge by a CNN feature vector and defines a probability mass function (PMF) for node-type (object category) of each node and edge-type (predicate class) of each edge. The DG-PGNN sequentially adds a new node to the current PGN by learning the optimal ordering in a Deep Q-learning framework, where states are partial PGNs, actions choose a new node, and rewards are defined based on the ground-truth. After adding a node, DG-PGNN uses message passing to update the feature vectors of the current PGN by leveraging contextual relationship information, object co-occurrences, and language priors from captions. The updated features are then used to fine-tune the PMFs. Our experiments show that the proposed algorithm significantly outperforms the state-of-the-art results on the Visual Genome dataset for scene graph generation. We also show that the scene graphs constructed by DG-PGNN improve performance on the visual question answering task, for questions that need reasoning about objects and their interactions in the scene context.

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 UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks

2021 ◽  
Author(s):  
Jing Huang ◽  
Jie Yang
Keyword(s):  
Neural Networks ◽  
Message Passing ◽  
State Of The Art ◽  
Representation Learning ◽  
Graph Representation ◽  
Challenging Problem ◽  
Unified Framework ◽  
Real World Datasets ◽  
Graph Neural Networks ◽  
Research Domains

Hypergraph, an expressive structure with flexibility to model the higher-order correlations among entities, has recently attracted increasing attention from various research domains. Despite the success of Graph Neural Networks (GNNs) for graph representation learning, how to adapt the powerful GNN-variants directly into hypergraphs remains a challenging problem. In this paper, we propose UniGNN, a unified framework for interpreting the message passing process in graph and hypergraph neural networks, which can generalize general GNN models into hypergraphs. In this framework, meticulously-designed architectures aiming to deepen GNNs can also be incorporated into hypergraphs with the least effort. Extensive experiments have been conducted to demonstrate the effectiveness of UniGNN on multiple real-world datasets, which outperform the state-of-the-art approaches with a large margin. Especially for the DBLP dataset, we increase the accuracy from 77.4% to 88.8% in the semi-supervised hypernode classification task. We further prove that the proposed message-passing based UniGNN models are at most as powerful as the 1-dimensional Generalized Weisfeiler-Leman (1-GWL) algorithm in terms of distinguishing non-isomorphic hypergraphs. Our code is available at https://github.com/OneForward/UniGNN.

scholarly journals TSI-GNN: Extending Graph Neural Networks to Handle Missing Data in Temporal Settings

2021 ◽  
Vol 4 ◽  
Author(s):  
David Gordon ◽  
Panayiotis Petousis ◽  
Henry Zheng ◽  
Davina Zamanzadeh ◽  
Alex A.T. Bui
Keyword(s):  
Neural Networks ◽  
Missing Data ◽  
Bipartite Graph ◽  
Message Passing ◽  
Representation Learning ◽  
Temporal Information ◽  
Graph Representation ◽  
Sequence Information ◽  
Novel Approach ◽  
Graph Neural Networks

We present a novel approach for imputing missing data that incorporates temporal information into bipartite graphs through an extension of graph representation learning. Missing data is abundant in several domains, particularly when observations are made over time. Most imputation methods make strong assumptions about the distribution of the data. While novel methods may relax some assumptions, they may not consider temporality. Moreover, when such methods are extended to handle time, they may not generalize without retraining. We propose using a joint bipartite graph approach to incorporate temporal sequence information. Specifically, the observation nodes and edges with temporal information are used in message passing to learn node and edge embeddings and to inform the imputation task. Our proposed method, temporal setting imputation using graph neural networks (TSI-GNN), captures sequence information that can then be used within an aggregation function of a graph neural network. To the best of our knowledge, this is the first effort to use a joint bipartite graph approach that captures sequence information to handle missing data. We use several benchmark datasets to test the performance of our method against a variety of conditions, comparing to both classic and contemporary methods. We further provide insight to manage the size of the generated TSI-GNN model. Through our analysis we show that incorporating temporal information into a bipartite graph improves the representation at the 30% and 60% missing rate, specifically when using a nonlinear model for downstream prediction tasks in regularly sampled datasets and is competitive with existing temporal methods under different scenarios.

scholarly journals Message Passing Attention Networks for Document Understanding

2020 ◽  
Vol 34 (05) ◽  
pp. 8544-8551 ◽  
Author(s):  
Giannis Nikolentzos ◽  
Antoine Tixier ◽  
Michalis Vazirgiannis
Keyword(s):  
Neural Networks ◽  
Text Classification ◽  
Message Passing ◽  
State Of The Art ◽  
Structured Data ◽  
Attention Networks ◽  
Document Understanding ◽  
Standard Text ◽  
Graph Neural Networks ◽  
The Impact

Graph neural networks have recently emerged as a very effective framework for processing graph-structured data. These models have achieved state-of-the-art performance in many tasks. Most graph neural networks can be described in terms of message passing, vertex update, and readout functions. In this paper, we represent documents as word co-occurrence networks and propose an application of the message passing framework to NLP, the Message Passing Attention network for Document understanding (MPAD). We also propose several hierarchical variants of MPAD. Experiments conducted on 10 standard text classification datasets show that our architectures are competitive with the state-of-the-art. Ablation studies reveal further insights about the impact of the different components on performance. Code is publicly available at: https://github.com/giannisnik/mpad.

scholarly journals Reinforced Neighborhood Selection Guided Multi-Relational Graph Neural Networks

2022 ◽  
Vol 40 (4) ◽  
pp. 1-46
Author(s):  
Hao Peng ◽  
Ruitong Zhang ◽  
Yingtong Dou ◽  
Renyu Yang ◽  
Jingyi Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Message Passing ◽  
Representation Learning ◽  
Graph Representations ◽  
Graph Data ◽  
Neighborhood Information ◽  
Neighborhood Selection ◽  
Graph Neural Networks

Graph Neural Networks (GNNs) have been widely used for the representation learning of various structured graph data, typically through message passing among nodes by aggregating their neighborhood information via different operations. While promising, most existing GNNs oversimplify the complexity and diversity of the edges in the graph and thus are inefficient to cope with ubiquitous heterogeneous graphs, which are typically in the form of multi-relational graph representations. In this article, we propose RioGNN , a novel Reinforced, recursive, and flexible neighborhood selection guided multi-relational Graph Neural Network architecture, to navigate complexity of neural network structures whilst maintaining relation-dependent representations. We first construct a multi-relational graph, according to the practical task, to reflect the heterogeneity of nodes, edges, attributes, and labels. To avoid the embedding over-assimilation among different types of nodes, we employ a label-aware neural similarity measure to ascertain the most similar neighbors based on node attributes. A reinforced relation-aware neighbor selection mechanism is developed to choose the most similar neighbors of a targeting node within a relation before aggregating all neighborhood information from different relations to obtain the eventual node embedding. Particularly, to improve the efficiency of neighbor selecting, we propose a new recursive and scalable reinforcement learning framework with estimable depth and width for different scales of multi-relational graphs. RioGNN can learn more discriminative node embedding with enhanced explainability due to the recognition of individual importance of each relation via the filtering threshold mechanism. Comprehensive experiments on real-world graph data and practical tasks demonstrate the advancements of effectiveness, efficiency, and the model explainability, as opposed to other comparative GNN models.

Neural networks for NP-complete problems

1997 ◽  
Vol 30 (3) ◽  
pp. 1617-1624 ◽  
Author(s):  
Marco Budinich
Keyword(s):  
Neural Networks ◽  
Complete Problems ◽  
Np Complete

scholarly journals Learning from the Past: Continual Meta-Learning with Bayesian Graph Neural Networks

2020 ◽  
Vol 34 (04) ◽  
pp. 5021-5028 ◽  
Author(s):  
Yadan Luo ◽  
Zi Huang ◽  
Zheng Zhang ◽  
Ziwei Wang ◽  
Mahsa Baktashmotlagh ◽  
...  
Keyword(s):  
Neural Networks ◽  
Message Passing ◽  
Shot Classification ◽  
The Past ◽  
Meta Learning ◽  
Error Accumulation ◽  
Effectiveness And Efficiency ◽  
Graph Neural Networks ◽  
Continual Learning

Meta-learning for few-shot learning allows a machine to leverage previously acquired knowledge as a prior, thus improving the performance on novel tasks with only small amounts of data. However, most mainstream models suffer from catastrophic forgetting and insufficient robustness issues, thereby failing to fully retain or exploit long-term knowledge while being prone to cause severe error accumulation. In this paper, we propose a novel Continual Meta-Learning approach with Bayesian Graph Neural Networks (CML-BGNN) that mathematically formulates meta-learning as continual learning of a sequence of tasks. With each task forming as a graph, the intra- and inter-task correlations can be well preserved via message-passing and history transition. To remedy topological uncertainty from graph initialization, we utilize Bayes by Backprop strategy that approximates the posterior distribution of task-specific parameters with amortized inference networks, which are seamlessly integrated into the end-to-end edge learning. Extensive experiments conducted on the miniImageNet and tieredImageNet datasets demonstrate the effectiveness and efficiency of the proposed method, improving the performance by 42.8% compared with state-of-the-art on the miniImageNet 5-way 1-shot classification task.

scholarly journals Learning Multi-Task Communication with Message Passing for Sequence Learning

2019 ◽  
Vol 33 ◽  
pp. 4360-4367 ◽  
Author(s):  
Pengfei Liu ◽  
Jie Fu ◽  
Yue Dong ◽  
Xipeng Qiu ◽  
Jackie Chi Kit Cheung
Keyword(s):  
Neural Networks ◽  
Transfer Learning ◽  
Text Classification ◽  
Sequence Learning ◽  
Message Passing ◽  
Ad Hoc ◽  
General Graph ◽  
Learning Framework ◽  
Task Learning ◽  
Graph Neural Networks

We present two architectures for multi-task learning with neural sequence models. Our approach allows the relationships between different tasks to be learned dynamically, rather than using an ad-hoc pre-defined structure as in previous work. We adopt the idea from message-passing graph neural networks, and propose a general graph multi-task learning framework in which different tasks can communicate with each other in an effective and interpretable way. We conduct extensive experiments in text classification and sequence labelling to evaluate our approach on multi-task learning and transfer learning. The empirical results show that our models not only outperform competitive baselines, but also learn interpretable and transferable patterns across tasks.

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