Graph convolutional networks (GCNs) can successfully learn the graph signal representation by graph convolution. The graph convolution depends on the graph filter, which contains the topological dependency of data and propagates data features. However, the estimation errors in the propagation matrix (e.g., the adjacency matrix) can have a significant impact on graph filters and GCNs. In this paper, we study the effect of a probabilistic graph error model on the performance of the GCNs. We prove that the adjacency matrix under the error model is bounded by a function of graph size and error probability. We further analytically specify the upper bound of a normalized adjacency matrix with self-loop added. Finally, we illustrate the error bounds by running experiments on a synthetic dataset and study the sensitivity of a simple GCN under this probabilistic error model on accuracy.

Graph convolutional networks (GCNs) are becoming increasingly popular as they overcome the limited applicability of prior neural networks. A GCN takes as input an arbitrarily structured graph and executes a series of layers which exploit the graph's structure to calculate their output features. One recent trend in GCNs is the use of deep network architectures. As opposed to the traditional GCNs which only span around two to five layers deep, modern GCNs now incorporate tens to hundreds of layers with the help of residual connections. From such deep GCNs, we find an important characteristic that they exhibit very high intermediate feature sparsity. We observe that with deep layers and residual connections, the number of zeros in the intermediate features sharply increases. This reveals a new opportunity for accelerators to exploit in GCN executions that was previously not present. In this paper, we propose SGCN, a fast and energy-efficient GCN accelerator which fully exploits the sparse intermediate features of modern GCNs. SGCN suggests several techniques to achieve significantly higher performance and energy efficiency than the existing accelerators. First, SGCN employs a GCN-friendly feature compression format. We focus on reducing the off-chip memory traffic, which often is the bottleneck for GCN executions. Second, we propose microarchitectures for seamlessly handling the compressed feature format. Third, to better handle locality in the existence of the varying sparsity, SGCN employs sparsity-aware cooperation. Sparsity-aware cooperation creates a pattern that exhibits multiple reuse windows, such that the cache can capture diverse sizes of working sets and therefore adapt to the varying level of sparsity. We show that SGCN achieves 1.71x speedup and 43.9% higher energy efficiency compared to the existing accelerators.

Morphological attributes from histopathological images and molecular profiles from genomic data are important information to drive diagnosis, prognosis, and therapy of cancers. By integrating these heterogeneous but complementary data, many multi-modal methods are proposed to study the complex mechanisms of cancers, and most of them achieve comparable or better results from previous single-modal methods. However, these multi-modal methods are restricted to a single task (e.g., survival analysis or grade classification), and thus neglect the correlation between different tasks. In this study, we present a multi-modal fusion framework based on multi-task correlation learning (MultiCoFusion) for survival analysis and cancer grade classification, which combines the power of multiple modalities and multiple tasks. Specifically, a pre-trained ResNet-152 and a sparse graph convolutional network (SGCN) are used to learn the representations of histopathological images and mRNA expression data respectively. Then these representations are fused by a fully connected neural network (FCNN), which is also a multi-task shared network. Finally, the results of survival analysis and cancer grade classification output simultaneously. The framework is trained by an alternate scheme. We systematically evaluate our framework using glioma datasets from The Cancer Genome Atlas (TCGA). Results demonstrate that MultiCoFusion learns better representations than traditional feature extraction methods. With the help of multi-task alternating learning, even simple multi-modal concatenation can achieve better performance than other deep learning and traditional methods. Multi-task learning can improve the performance of multiple tasks not just one of them, and it is effective in both single-modal and multi-modal data.

Graph Convolutional Networks (GCNs) have achieved impressive empirical advancement across a wide variety of graph-related applications. Despite their great success, training GCNs on large graphs suffers from computational and memory issues. A potential path to circumvent these obstacles is sampling-based methods, where at each layer a subset of nodes is sampled. Although recent studies have empirically demonstrated the effectiveness of sampling-based methods, these works lack theoretical convergence guarantees under realistic settings and cannot fully leverage the information of evolving parameters during optimization. In this paper, we describe and analyze a general \textbf{\textit{doubly variance reduction}} schema that can accelerate any sampling method under the memory budget. The motivating impetus for the proposed schema is a careful analysis for the variance of sampling methods where it is shown that the induced variance can be decomposed into node embedding approximation variance (\emph{zeroth-order variance}) during forward propagation and layerwise-gradient variance (\emph{first-order variance}) during backward propagation. We theoretically analyze the convergence of the proposed schema and show that it enjoys an $\mathcal{O}(1/T)$ convergence rate. We complement our theoretical results by integrating the proposed schema in different sampling methods and applying them to different large real-world graphs. Code is public available at~\url{https://github.com/CongWeilin/SGCN.git}.

Graph convolutional networks (GCNs) have gained popularity due to high performance achievable on several downstream tasks including node classification. Several architectural variants of these networks have been proposed and investigated with experimental studies in the literature. Motivated by a recent work on simplifying GCNs, we study the problem of designing other variants and propose a framework to compose networks using building blocks of GCN. The framework offers flexibility to compose and evaluate different networks using feature and/or label propagation networks, linear or non-linear networks, with each composition having different computational complexity. We conduct a detailed experimental study on several benchmark datasets with many variants and present observations from our evaluation. Our empirical experimental results suggest that several newly composed variants are useful alternatives to consider because they are as competitive as, or better than the original GCN.