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Register a new userMultipath Graph Convolutional Neural Networks
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Added by
Saumik Bhattacharya
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Graph convolution networks have recently garnered a lot of attention for representation learning on non-Euclidean feature spaces. Recent research has focused on stacking multiple layers like in convolutional neural networks for the increased expressive power of graph convolution networks. However, simply stacking multiple graph convolution layers lead to issues like vanishing gradient, over-fitting and over-smoothing. Such problems are much less when using shallower networks, even though the shallow networks have lower expressive power. In this work, we propose a novel Multipath Graph convolutional neural network that aggregates the output of multiple different shallow networks. We train and test our model on various benchmarks datasets for the task of node property prediction. Results show that the proposed method not only attains increased test accuracy but also requires fewer training epochs to converge. The full implementation is available at https://github.com/rangan2510/MultiPathGCN
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Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCN operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1% in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the Pubmed dataset.
Convolutional neural networks (CNNs) have proven to be highly successful at a range of image-to-image tasks. CNNs can be computationally expensive, which can limit their applicability in practice. Model pruning can improve computational efficiency by sparsifying trained networks. Common methods for pruning CNNs determine what convolutional filters to remove by ranking filters on an individual basis. However, filters are not independent, as CNNs consist of chains of convolutions, which can result in sub-optimal filter selection. We propose a novel pruning method, LongEst-chAiN (LEAN) pruning, which takes the interdependency between the convolution operations into account. We propose to prune CNNs by using graph-based algorithms to select relevant chains of convolutions. A CNN is interpreted as a graph, with the operator norm of each convolution as distance metric for the edges. LEAN pruning iteratively extracts the highest value path from the graph to keep. In our experiments, we test LEAN pruning for several image-to-image tasks, including the well-known CamVid dataset. LEAN pruning enables us to keep just 0.5%-2% of the convolutions without significant loss of accuracy. When pruning CNNs with LEAN, we achieve a higher accuracy than pruning filters individually, and different pruned substructures emerge.
Although group convolution operators are increasingly used in deep convolutional neural networks to improve the computational efficiency and to reduce the number of parameters, most existing methods construct their group convolution architectures by a predefined partitioning of the filters of each convolutional layer into multiple regular filter groups with an equal spatial group size and data-independence, which prevents a full exploitation of their potential. To tackle this issue, we propose a novel method of designing self-grouping convolutional neural networks, called SG-CNN, in which the filters of each convolutional layer group themselves based on the similarity of their importance vectors. Concretely, for each filter, we first evaluate the importance value of their input channels to identify the importance vectors, and then group these vectors by clustering. Using the resulting emph{data-dependent} centroids, we prune the less important connections, which implicitly minimizes the accuracy loss of the pruning, thus yielding a set of emph{diverse} group convolution filters. Subsequently, we develop two fine-tuning schemes, i.e. (1) both local and global fine-tuning and (2) global only fine-tuning, which experimentally deliver comparable results, to recover the recognition capacity of the pruned network. Comprehensive experiments carried out on the CIFAR-10/100 and ImageNet datasets demonstrate that our self-grouping convolution method adapts to various state-of-the-art CNN architectures, such as ResNet and DenseNet, and delivers superior performance in terms of compression ratio, speedup and recognition accuracy. We demonstrate the ability of SG-CNN to generalise by transfer learning, including domain adaption and object detection, showing competitive results. Our source code is available at https://github.com/QingbeiGuo/SG-CNN.git.
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 networks 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.
Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their success, there is a dearth of theoretical explorations of GCNN models such as their generalization properties. In this paper, we take a first step towards developing a deeper theoretical understanding of GCNN models by analyzing the stability of single-layer GCNN models and deriving their generalization guarantees in a semi-supervised graph learning setting. In particular, we show that the algorithmic stability of a GCNN model depends upon the largest absolute eigenvalue of its graph convolution filter. Moreover, to ensure the uniform stability needed to provide strong generalization guarantees, the largest absolute eigenvalue must be independent of the graph size. Our results shed new insights on the design of new & improved graph convolution filters with guaranteed algorithmic stability. We evaluate the generalization gap and stability on various real-world graph datasets and show that the empirical results indeed support our theoretical findings. To the best of our knowledge, we are the first to study stability bounds on graph learning in a semi-supervised setting and derive generalization bounds for GCNN models.
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