Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.
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Graph Neural Networks (GNNs) with attention have been successfully applied for learning visual feature matching. However, current methods learn with complete graphs, resulting in a quadratic complexity in the number of features. Motivated by a prior observation that self- and cross- attention matrices converge to a sparse representation, we propose ClusterGNN, an attentional GNN architecture which operates on clusters for learning the feature matching task. Using a progressive clustering module we adaptively divide keypoints into different subgraphs to reduce redundant connectivity, and employ a coarse-to-fine paradigm for mitigating miss-classification within images. Our approach yields a 59.7% reduction in runtime and 58.4% reduction in memory consumption for dense detection, compared to current state-of-the-art GNN-based matching, while achieving a competitive performance on various computer vision tasks.
Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes barely any progress alternate with intervals of rapid decrease. These successive phases of learning often take place on very different time scales. Finally, models learnt in an early phase are typically `simpler' or `easier to learn' although in a way that is difficult to formalize. Although theoretical explanations of these phenomena have been put forward, each of them captures at best certain specific regimes. In this paper, we study the gradient flow dynamics of a wide two-layer neural network in high-dimension, when data are distributed according to a single-index model (i.e., the target function depends on a one-dimensional projection of the covariates). Based on a mixture of new rigorous results, non-rigorous mathematical derivations, and numerical simulations, we propose a scenario for the learning dynamics in this setting. In particular, the proposed evolution exhibits separation of timescales and intermittency. These behaviors arise naturally because the population gradient flow can be recast as a singularly perturbed dynamical system.
Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-called meta-paths. Our experiments show that GTNs learn new graph structures, based on data and tasks without domain knowledge, and yield powerful node representation via convolution on the new graphs. Without domain-specific graph preprocessing, GTNs achieved the best performance in all three benchmark node classification tasks against the state-of-the-art methods that require pre-defined meta-paths from domain knowledge.
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.
Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.
Graphs, which describe pairwise relations between objects, are essential representations of many real-world data such as social networks. In recent years, graph neural networks, which extend the neural network models to graph data, have attracted increasing attention. Graph neural networks have been applied to advance many different graph related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytical tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges, the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.
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