Timely accurate traffic forecast is crucial for urban traffic control and guidance. Due to the high nonlinearity and complexity of traffic flow, traditional methods cannot satisfy the requirements of mid-and-long term prediction tasks and often neglect spatial and temporal dependencies. In this paper, we propose a novel deep learning framework, Spatio-Temporal Graph Convolutional Networks (STGCN), to tackle the time series prediction problem in traffic domain. Instead of applying regular convolutional and recurrent units, we formulate the problem on graphs and build the model with complete convolutional structures, which enable much faster training speed with fewer parameters. Experiments show that our model STGCN effectively captures comprehensive spatio-temporal correlations through modeling multi-scale traffic networks and consistently outperforms state-of-the-art baselines on various real-world traffic datasets.

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science applications such as link, relation and motif prediction. However, current SGRL approaches suffer from scalability issues since they require extracting subgraphs for each training or test query. Recent solutions that scale up canonical GNNs may not apply to SGRL. Here, we propose a novel framework SUREL for scalable SGRL by co-designing the learning algorithm and its system support. SUREL adopts walk-based decomposition of subgraphs and reuses the walks to form subgraphs, which substantially reduces the redundancy of subgraph extraction and supports parallel computation. Experiments over six homogeneous, heterogeneous and higher-order graphs with millions of nodes and edges demonstrate the effectiveness and scalability of SUREL. In particular, compared to SGRL baselines, SUREL achieves 10X speed-up with comparable or even better prediction performance; while compared to canonical GNNs, SUREL achieves 50% prediction accuracy improvement.

Graph neural networks (GNN) have shown great advantages in many graph-based learning tasks but often fail to predict accurately for a task based on sets of nodes such as link/motif prediction and so on. Many works have recently proposed to address this problem by using random node features or node distance features. However, they suffer from either slow convergence, inaccurate prediction or high complexity. In this work, we revisit GNNs that allow using positional features of nodes given by positional encoding (PE) techniques such as Laplacian Eigenmap, Deepwalk, etc.. GNNs with PE often get criticized because they are not generalizable to unseen graphs (inductive) or stable. Here, we study these issues in a principled way and propose a provable solution, a class of GNN layers termed PEG with rigorous mathematical analysis. PEG uses separate channels to update the original node features and positional features. PEG imposes permutation equivariance w.r.t. the original node features and rotation equivariance w.r.t. the positional features simultaneously. Extensive link prediction experiments over 8 real-world networks demonstrate the advantages of PEG in generalization and scalability. 1

Graph neural networks (GNNs) have shown superiority in many prediction tasks over graphs due to their impressive capability of capturing nonlinear relations in graph-structured data. However, for node classification tasks, often, only marginal improvement of GNNs over their linear counterparts has been observed. Previous works provide very few understandings of this phenomenon. In this work, we resort to Bayesian learning to deeply investigate the functions of non-linearity in GNNs for node classification tasks. Given a graph generated from the statistical model CSBM, we observe that the max-a-posterior estimation of a node label given its own and neighbors' attributes consists of two types of non-linearity, a possibly nonlinear transformation of node attributes and a ReLU-activated feature aggregation from neighbors. The latter surprisingly matches the type of non-linearity used in many GNN models. By further imposing Gaussian assumption on node attributes, we prove that the superiority of those ReLU activations is only significant when the node attributes are far more informative than the graph structure, which nicely matches many previous empirical observations. A similar argument can be achieved when there is a distribution shift of node attributes between the training and testing datasets. Finally, we verify our theory on both synthetic and real-world networks.Preprint. Under review.

Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science applications such as link, relation and motif prediction. However, current SGRL approaches suffer from a scalability issue since they require extracting subgraphs for each training and testing query. Recent solutions that scale up canonical GNNs may not apply to SGRL. Here, we propose a novel framework SUREL for scalable SGRL by co-designing the learning algorithm and its system support. SUREL adopts walk-based decomposition of subgraphs and reuses the walks to form subgraphs, which substantially reduces the redundancy of subgraph extraction and supports parallel computation. Experiments over seven homogeneous, heterogeneous and higherorder graphs with millions of nodes and edges demonstrate the effectiveness and scalability of SUREL. In particular, compared to SGRL baselines, SUREL achieves 10× speed-up with comparable or even better prediction performance; while compared to canonical GNNs, SUREL achieves 50% prediction accuracy improvement. SUREL is also applied to the brain vessel prediction task. SUREL significantly outperforms the state-of-the-art baseline in both prediction accuracy and efficiency.

Model Checking is widely applied in verifying the correctness of complex and concurrent systems against a specification. Pure symbolic approaches while popular, still suffer from the state space explosion problem that makes them impractical for large scale systems and/or specifications. In this paper, we propose to use graph representation learning (GRL) for solving linear temporal logic (LTL) model checking, where the system and the specification are expressed by a Büchi automaton and an LTL formula respectively. A novel GRL-based framework OCTAL, is designed to learn the representation of the graph-structured system and specification, which reduces the model checking problem to binary classification in the latent space. The empirical experiments show that OCTAL achieves comparable accuracy against canonical SOTA model checkers on three different datasets, with up to 5× overall speedup and above 63× for satisfiability checking alone.Preprint. Under review.

Subgraph-based graph representation learning (SGRL) has recently emerged as a powerful tool in many prediction tasks on graphs due to its advantages in model expressiveness and generalization ability. Most previous SGRL models face computational issues associated with the high cost of extracting subgraphs for each training or testing query. Recently, SUREL has been proposed as a new framework to accelerate SGRL, which samples random walks offline and joins these walks as subgraphs online for prediction. Due to the reusability of sampled walks across different queries, SUREL achieves state-of-the-art performance in both scalability and prediction accuracy. However, SUREL still suffers from high computational overhead caused by node redundancy in sampled walks. In this work, we propose a novel framework SUREL+ that upgrades SUREL by using node sets instead of walks to represent subgraphs. This set-based representation avoids node duplication by definition, but the sizes of node sets can be irregular. To address this issue, we design a dedicated sparse data structure to efficiently store and fast index node sets, and provide a specialized operator to join them in parallel batches. SUREL+ is modularized to support multiple types of set samplers, structural features, and neural encoders to complement the loss of structural information due to the reduction from walks to sets. Extensive experiments have been performed to validate SUREL+ in the prediction tasks of links, relation types, and higher-order patterns. SUREL+ achieves 3-11× speedups of SUREL while maintaining comparable or even better prediction performance; compared to other SGRL baselines, SUREL+ achieves ∼20× speedups and significantly improves the prediction accuracy.

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