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Graph Structure of Neural Networks
TL;DR: A novel graph-based representation of neural networks called relational graph is developed, where layers of neural network computation correspond to rounds of message exchange along the graph structure, which shows that a "sweet spot" of relational graphs leads to neural networks with significantly improved predictive performance.
Abstract: Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its predictive performance. Here we systematically investigate how does the graph structure of neural networks affect their predictive performance. To this end, we develop a novel graph-based representation of neural networks called relational graph, where layers of neural network computation correspond to rounds of message exchange along the graph structure. Using this representation we show that: (1) a "sweet spot" of relational graphs leads to neural networks with significantly improved predictive performance; (2) neural network's performance is approximately a smooth function of the clustering coefficient and average path length of its relational graph; (3) our findings are consistent across many different tasks and datasets; (4) the sweet spot can be identified efficiently; (5) top-performing neural networks have graph structure surprisingly similar to those of real biological neural networks. Our work opens new directions for the design of neural architectures and the understanding on neural networks in general.
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TL;DR: The structural principle, the characteristics, and some kinds of classic models of deep learning, such as stacked auto encoder, deep belief network, deep Boltzmann machine, and convolutional neural network are described.
408 citations
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TL;DR: This work defines and systematically study the architectural design space for GNNs which consists of 315,000 different designs over 32 different predictive tasks, and offers a principled and scalable approach to transition from studying individual GNN designs for specific tasks, to systematically studying the GNN design space and the task space.
Abstract: The rapid evolution of Graph Neural Networks (GNNs) has led to a growing number of new architectures as well as novel applications. However, current research focuses on proposing and evaluating specific architectural designs of GNNs, as opposed to studying the more general design space of GNNs that consists of a Cartesian product of different design dimensions, such as the number of layers or the type of the aggregation function. Additionally, GNN designs are often specialized to a single task, yet few efforts have been made to understand how to quickly find the best GNN design for a novel task or a novel dataset. Here we define and systematically study the architectural design space for GNNs which consists of 315,000 different designs over 32 different predictive tasks. Our approach features three key innovations: (1) A general GNN design space; (2) a GNN task space with a similarity metric, so that for a given novel task/dataset, we can quickly identify/transfer the best performing architecture; (3) an efficient and effective design space evaluation method which allows insights to be distilled from a huge number of model-task combinations. Our key results include: (1) A comprehensive set of guidelines for designing well-performing GNNs; (2) while best GNN designs for different tasks vary significantly, the GNN task space allows for transferring the best designs across different tasks; (3) models discovered using our design space achieve state-of-the-art performance. Overall, our work offers a principled and scalable approach to transition from studying individual GNN designs for specific tasks, to systematically studying the GNN design space and the task space. Finally, we release GraphGym, a powerful platform for exploring different GNN designs and tasks. GraphGym features modularized GNN implementation, standardized GNN evaluation, and reproducible and scalable experiment management.
154 citations
Cites background from "Graph Structure of Neural Networks"
...The idea of transferring architecture search results across tasks has been studied in the context of computer vision tasks [43, 53]....
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17 Mar 2021
TL;DR: In this article, a taxonomy for interpretability of DNNs is proposed, as well as applications of interpretability in medicine and future research directions, such as in relation to fuzzy logic and brain science.
Abstract: Deep learning as performed by artificial deep neural networks (DNNs) has achieved great successes recently in many important areas that deal with text, images, videos, graphs, and so on. However, the black-box nature of DNNs has become one of the primary obstacles for their wide adoption in mission-critical applications such as medical diagnosis and therapy. Because of the huge potentials of deep learning, the interpretability of DNNs has recently attracted much research attention. In this article, we propose a simple but comprehensive taxonomy for interpretability, systematically review recent studies on interpretability of neural networks, describe applications of interpretability in medicine, and discuss future research directions, such as in relation to fuzzy logic and brain science.
124 citations
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TL;DR: GRAPE is proposed, a graph-based framework for feature imputation as well as label prediction that yields 20% lower mean absolute error for imputation tasks and 10% lower for label prediction tasks, compared with existing state-of-the-art methods.
Abstract: Machine learning with missing data has been approached in two different ways, including feature imputation where missing feature values are estimated based on observed values, and label prediction where downstream labels are learned directly from incomplete data. However, existing imputation models tend to have strong prior assumptions and cannot learn from downstream tasks, while models targeting label prediction often involve heuristics and can encounter scalability issues. Here we propose GRAPE, a graph-based framework for feature imputation as well as label prediction. GRAPE tackles the missing data problem using a graph representation, where the observations and features are viewed as two types of nodes in a bipartite graph, and the observed feature values as edges. Under the GRAPE framework, the feature imputation is formulated as an edge-level prediction task and the label prediction as a node-level prediction task. These tasks are then solved with Graph Neural Networks. Experimental results on nine benchmark datasets show that GRAPE yields 20% lower mean absolute error for imputation tasks and 10% lower for label prediction tasks, compared with existing state-of-the-art methods.
68 citations
Cites background from "Graph Structure of Neural Networks"
...As is discussed in [57], an MLP can in fact be viewed as a GNN over a complete graph, where the message function is matrix multiplication....
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Posted Content•
TL;DR: A general framework that unifies state-of-the-art graph neural networks (GNNs) through the concept of EdgeNet is put forth and it is shown that GATs are GCNNs on a graph that is learned from the features, which opens the doors to develop alternative attention mechanisms for improving discriminatory power.
Abstract: Driven by the outstanding performance of neural networks in the structured Euclidean domain, recent years have seen a surge of interest in developing neural networks for graphs and data supported on graphs. The graph is leveraged at each layer of the neural network as a parameterization to capture detail at the node level with a reduced number of parameters and computational complexity. Following this rationale, this paper puts forth a general framework that unifies state-of-the-art graph neural networks (GNNs) through the concept of EdgeNet. An EdgeNet is a GNN architecture that allows different nodes to use different parameters to weigh the information of different neighbors. By extrapolating this strategy to more iterations between neighboring nodes, the EdgeNet learns edge- and neighbor-dependent weights to capture local detail. This is a general linear and local operation that a node can perform and encompasses under one formulation all existing graph convolutional neural networks (GCNNs) as well as graph attention networks (GATs). In writing different GNN architectures with a common language, EdgeNets highlight specific architecture advantages and limitations, while providing guidelines to improve their capacity without compromising their local implementation. An interesting conclusion is the unification of GCNNs and GATs -- approaches that have been so far perceived as separate. In particular, we show that GATs are GCNNs on a graph that is learned from the features. This particularization opens the doors to develop alternative attention mechanisms for improving discriminatory power.
65 citations
Cites background from "Graph Structure of Neural Networks"
...In particular, they all share the reuse of parameters across all neighborhoods of a graph as well as indifference towards the values of different neighbors –see also [31]....
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References
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27 Jun 2016
TL;DR: In this article, the authors proposed a residual learning framework to ease the training of networks that are substantially deeper than those used previously, which won the 1st place on the ILSVRC 2015 classification task.
Abstract: Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.
123,388 citations
Proceedings Article•
03 Dec 2012TL;DR: The state-of-the-art performance of CNNs was achieved by Deep Convolutional Neural Networks (DCNNs) as discussed by the authors, which consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax.
Abstract: We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overriding in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.
73,978 citations
Proceedings Article•
01 Jan 2015TL;DR: In this paper, the authors investigated the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting and showed that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 layers.
Abstract: In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth using an architecture with very small (3x3) convolution filters, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. These findings were the basis of our ImageNet Challenge 2014 submission, where our team secured the first and the second places in the localisation and classification tracks respectively. We also show that our representations generalise well to other datasets, where they achieve state-of-the-art results. We have made our two best-performing ConvNet models publicly available to facilitate further research on the use of deep visual representations in computer vision.
49,914 citations
01 Jan 1998
TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
Abstract: Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.
42,067 citations
07 Jun 2015
TL;DR: Inception as mentioned in this paper is a deep convolutional neural network architecture that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14).
Abstract: We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.
40,257 citations