Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks

Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively exploit this graph structure. In this work, we leverage graph signal processing to characterize the representation space of graph neural networks (GNNs). We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology. These two properties offer insight about the workings of GNNs and help explain their scalability and transferability properties which, coupled with their local and distributed nature, make GNNs powerful tools for learning in physical networks. We also introduce GNN extensions using edge-varying and autoregressive moving average graph filters and discuss their properties. Finally, we study the use of GNNs in recommender systems and learning decentralized controllers for robot swarms.

Efficient Fusion of Sparse and Complementary Convolutions

We propose a new method to create compact convolutional neural networks (CNNs) by exploiting sparse convolutions. Different from previous works that learn sparsity in models, we directly employ hand-crafted kernels with regular sparse patterns, which result in the computational gain in practice without sophisticated and dedicated software or hardware. The core of our approach is an efficient network module that linearly combines sparse kernels to yield feature representations as strong as those from regular kernels. We integrate this module into various network architectures and demonstrate its effectiveness on three vision tasks, object classification, localization and detection. For object classification and localization, our approach achieves comparable or better performance than several baselines and related works while providing lower computational costs with fewer parameters (on average, a $2-4times$ reduction of convolutional parameters and computation). For object detection, our approach leads to a VGG-16-based Faster RCNN detector that is 12.4$times$ smaller and about 3$times$ faster than the baseline.

Self-Attention Equipped Graph Convolutions for Disease Prediction

Multi-modal data comprising imaging (MRI, fMRI, PET, etc.) and non-imaging (clinical test, demographics, etc.) data can be collected together and used for disease prediction. Such diverse data gives complementary information about the patients condition to make an informed diagnosis. A model capable of leveraging the individuality of each multi-modal data is required for better disease prediction. We propose a graph convolution based deep model which takes into account the distinctiveness of each element of the multi-modal data. We incorporate a novel self-attention layer, which weights every element of the demographic data by exploring its relation to the underlying disease. We demonstrate the superiority of our developed technique in terms of computational speed and performance when compared to state-of-the-art methods. Our method outperforms other methods with a significant margin.

Efficient keyword spotting using dilated convolutions and gating

We explore the application of end-to-end stateless temporal modeling to small-footprint keyword spotting as opposed to recurrent networks that model long-term temporal dependencies using internal states. We propose a model inspired by the recent success of dilated convolutions in sequence modeling applications, allowing to train deeper architectures in resource-constrained configurations. Gated activations and residual connections are also added, following a similar configuration to WaveNet. In addition, we apply a custom target labeling that back-propagates loss from specific frames of interest, therefore yielding higher accuracy and only requiring to detect the end of the keyword. Our experimental results show that our model outperforms a max-pooling loss trained recurrent neural network using LSTM cells, with a significant decrease in false rejection rate. The underlying dataset - Hey Snips utterances recorded by over 2.2K different speakers - has been made publicly available to establish an open reference for wake-word detection.

Node-Variant Graph Filters in Graph Neural Networks

Graph neural networks (GNNs) have been successfully employed in a myriad of applications involving graph-structured data. Theoretical findings establish that GNNs use nonlinear activation functions to create low-eigenvalue frequency content that can be processed in a stable manner by subsequent graph convolutional filters. However, the exact shape of the frequency content created by nonlinear functions is not known, and thus, it cannot be learned nor controlled. In this work, node-variant graph filters (NVGFs) are shown to be capable of creating frequency content and are thus used in lieu of nonlinear activation functions. This results in a novel GNN architecture that, although linear, is capable of creating frequency content as well. Furthermore, this new frequency content can be either designed or learned from data. In this way, the role of frequency creation is separated from the nonlinear nature of traditional GNNs. Extensive simulations are carried out to differentiate the contributions of frequency creation from those of the nonlinearity.