Quantum Graph Neural Networks (QGNNs) present a promising approach for combining quantum computing with graph-structured data processing. While classical Graph Neural Networks (GNNs) are renowned for their scalability and robustness, existing QGNNs often lack flexibility due to graph-specific quantum circuit designs, limiting their applicability to a narrower range of graph-structured problems, falling short of real-world scenarios. To address these limitations, we propose a versatile QGNN framework inspired by the classical GraphSAGE approach, utilizing quantum models as aggregators. In this work, we integrate established techniques for inductive representation learning on graphs with parametrized quantum convolutional and pooling layers, effectively bridging classical and quantum paradigms. The convolutional layer is flexible, enabling tailored designs for specific problems. Benchmarked on a node regression task with the QM9 dataset, we demonstrate that our framework successfully models a non-trivial molecular dataset, achieving performance comparable to classical GNNs. In particular, we show that our quantum approach exhibits robust generalization across molecules with varying numbers of atoms without requiring circuit modifications, slightly outperforming classical GNNs. Furthermore, we numerically investigate the scalability of the QGNN framework. Specifically, we demonstrate the absence of barren plateaus in our architecture as the number of qubits increases, suggesting that the proposed quantum model can be extended to handle larger and more complex graph-based problems effectively.
Graph neural networks (GNNs) are powerful tools for developing scalable, decentralized artificial intelligence in large-scale networked systems, such as wireless networks, power grids, and transportation networks. Currently, GNNs in networked systems mostly follow a paradigm of `centralized training, distributed execution', which limits their adaptability and slows down their development cycles. In this work, we fill this gap for the first time by developing a communication-efficient, fully distributed online training approach for GNNs applied to large networked systems. For a mini-batch with $B$ samples, our approach of training an $L$-layer GNN only adds $L$ rounds of message passing to the $LB$ rounds required by GNN inference, with doubled message sizes. Through numerical experiments in graph-based node regression, power allocation, and link scheduling in wireless networks, we demonstrate the effectiveness of our approach in training GNNs under supervised, unsupervised, and reinforcement learning paradigms.
Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. To gain some insight into the performance of various estimators for this task, we perform a theoretical study in a context where the graph is random. Specifically, we assume that the graph is generated by a Latent Position Model, where each node of the graph has a latent position, and the probability that two nodes are connected depend on the distance between the latent positions of the two nodes. In this context, we begin by studying the simplest possible estimator for graph regression, which consists in averaging the value of the label at all neighboring nodes. We show that in Latent Position Models this estimator tends to a Nadaraya Watson estimator in the latent space, and that its rate of convergence is in fact the same. One issue with this standard estimator is that it averages over a region consisting of all neighbors of a node, and that depending on the graph model this may be too much or too little. An alternative consists in first estimating the true distances between the latent positions, then injecting these estimated distances into a classical Nadaraya Watson estimator. This enables averaging in regions either smaller or larger than the typical graph neighborhood. We show that this method can achieve standard nonparametric rates in certain instances even when the graph neighborhood is too large or too small.
Scalability of Graph Neural Networks (GNNs) remains a significant challenge, particularly when dealing with large-scale graphs. To tackle this, coarsening-based methods are used to reduce the graph into a smaller graph, resulting in faster computation. Nonetheless, prior research has not adequately addressed the computational costs during the inference phase. This paper presents a novel approach to improve the scalability of GNNs by reducing computational burden during both training and inference phases. We demonstrate two different methods (Extra-Nodes and Cluster-Nodes). Our study also proposes a unique application of the coarsening algorithm for graph-level tasks, including graph classification and graph regression, which have not yet been explored. We conduct extensive experiments on multiple benchmark datasets in the order of $100K$ nodes to evaluate the performance of our approach. The results demonstrate that our method achieves competitive performance in tasks involving classification and regression on nodes and graphs, compared to traditional GNNs, while having single-node inference times that are orders of magnitude faster. Furthermore, our approach significantly reduces memory consumption, allowing training and inference on low-resource devices where traditional methods struggle.
The challenge of effectively learning inter-series correlations for multivariate time series forecasting remains a substantial and unresolved problem. Traditional deep learning models, which are largely dependent on the Transformer paradigm for modeling long sequences, often fail to integrate information from multiple time series into a coherent and universally applicable model. To bridge this gap, our paper presents ForecastGrapher, a framework reconceptualizes multivariate time series forecasting as a node regression task, providing a unique avenue for capturing the intricate temporal dynamics and inter-series correlations. Our approach is underpinned by three pivotal steps: firstly, generating custom node embeddings to reflect the temporal variations within each series; secondly, constructing an adaptive adjacency matrix to encode the inter-series correlations; and thirdly, augmenting the GNNs' expressive power by diversifying the node feature distribution. To enhance this expressive power, we introduce the Group Feature Convolution GNN (GFC-GNN). This model employs a learnable scaler to segment node features into multiple groups and applies one-dimensional convolutions with different kernel lengths to each group prior to the aggregation phase. Consequently, the GFC-GNN method enriches the diversity of node feature distribution in a fully end-to-end fashion. Through extensive experiments and ablation studies, we show that ForecastGrapher surpasses strong baselines and leading published techniques in the domain of multivariate time series forecasting.
Estimating causal effects in e-commerce tends to involve costly treatment assignments which can be impractical in large-scale settings. Leveraging machine learning to predict such treatment effects without actual intervention is a standard practice to diminish the risk. However, existing methods for treatment effect prediction tend to rely on training sets of substantial size, which are built from real experiments and are thus inherently risky to create. In this work we propose a graph neural network to diminish the required training set size, relying on graphs that are common in e-commerce data. Specifically, we view the problem as node regression with a restricted number of labeled instances, develop a two-model neural architecture akin to previous causal effect estimators, and test varying message-passing layers for encoding. Furthermore, as an extra step, we combine the model with an acquisition function to guide the creation of the training set in settings with extremely low experimental budget. The framework is flexible since each step can be used separately with other models or treatment policies. The experiments on real large-scale networks indicate a clear advantage of our methodology over the state of the art, which in many cases performs close to random, underlining the need for models that can generalize with limited supervision to reduce experimental risks.
This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width Neural Networks are connecting Deep Learning to Gaussian Processes and Kernels, both Machine Learning Frameworks with long traditions and extensive theoretical foundations. Gaussian Processes and Kernels have much less hyperparameters then Neural Networks and can be used for uncertainty estimation, making them more user friendly for applications. This works extends the increasing amount of research connecting Gaussian Processes and Kernels to Neural Networks. The Kernel and Gaussian Process closed forms are derived for a variety of architectures, namely the standard Graph Neural Network, the Graph Neural Network with Skip-Concatenate Connections and the Graph Attention Neural Network. All architectures are evaluated on a variety of datasets on the task of transductive Node Regression and Classification. Additionally, a Spectral Sparsification method known as Effective Resistance is used to improve runtime and memory requirements. Extending the setting to inductive graph learning tasks (Graph Regression/ Classification) is straightforward and is briefly discussed in 3.5.
In recent years, there has been an increasing interest in the use of graph neural networks (GNNs) for analyzing dynamic graphs, which are graphs that evolve over time. However, there is still a lack of understanding of how different temporal graph neural network (TGNs) configurations can impact the accuracy of predictions on dynamic graphs. Moreover, the hunt for benchmark datasets for these TGNs models is still ongoing. Up until recently, Pytorch Geometric Temporal came up with a few benchmark datasets but most of these datasets have not been analyzed with different TGN models to establish the state-of-the-art. Therefore, this project aims to address this gap in the literature by performing a qualitative analysis of spatial-temporal dependence structure learning on dynamic graphs, as well as a comparative study of the effectiveness of selected TGNs on node and edge prediction tasks. Additionally, an extensive ablation study will be conducted on different variants of the best-performing TGN to identify the key factors contributing to its performance. By achieving these objectives, this project will provide valuable insights into the design and optimization of TGNs for dynamic graph analysis, with potential applications in areas such as disease spread prediction, social network analysis, traffic prediction, and more. Moreover, an attempt is made to convert snapshot-based data to the event-based dataset and make it compatible with the SOTA model namely TGN to perform node regression task.
Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of large-graph GNNs using graph neural tangent kernels (GNTKs) and graphons. In the limit of large width, optimization of an overparametrized NN is equivalent to kernel regression on the NTK. Here, we investigate how the GNTK evolves as another independent dimension is varied: the graph size. We use graphons to define limit objects -- graphon NNs for GNNs, and graphon NTKs for GNTKs -- , and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK. We further prove that the spectrum of the GNTK, which is related to the directions of fastest learning which becomes relevant during early stopping, converges to the spectrum of the graphon NTK. This implies that in the large-graph limit, the GNTK fitted on a graph of moderate size can be used to solve the same task on the large graph, and to infer the learning dynamics of the large-graph GNN. These results are verified empirically on node regression and classification tasks.
Graph Neural Networks (GNNs) have shown remarkable effectiveness in capturing abundant information in graph-structured data. However, the black-box nature of GNNs hinders users from understanding and trusting the models, thus leading to difficulties in their applications. While recent years witness the prosperity of the studies on explaining GNNs, most of them focus on static graphs, leaving the explanation of dynamic GNNs nearly unexplored. It is challenging to explain dynamic GNNs, due to their unique characteristic of time-varying graph structures. Directly using existing models designed for static graphs on dynamic graphs is not feasible because they ignore temporal dependencies among the snapshots. In this work, we propose DGExplainer to provide reliable explanation on dynamic GNNs. DGExplainer redistributes the output activation score of a dynamic GNN to the relevances of the neurons of its previous layer, which iterates until the relevance scores of the input neuron are obtained. We conduct quantitative and qualitative experiments on real-world datasets to demonstrate the effectiveness of the proposed framework for identifying important nodes for link prediction and node regression for dynamic GNNs.
Rule-based fine-grained IP geolocation methods are hard to generalize in computer networks which do not follow hypothetical rules. Recently, deep learning methods, like multi-layer perceptron (MLP), are tried to increase generalization capabilities. However, MLP is not so suitable for graph-structured data like networks. MLP treats IP addresses as isolated instances and ignores the connection information, which limits geolocation accuracy. In this work, we research how to increase the generalization capability with an emerging graph deep learning method -- Graph Neural Network (GNN). First, IP geolocation is re-formulated as an attributed graph node regression problem. Then, we propose a GNN-based IP geolocation framework named GNN-Geo. GNN-Geo consists of a preprocessor, an encoder, messaging passing (MP) layers and a decoder. The preprocessor and encoder transform measurement data into the initial node embeddings. MP layers refine the initial node embeddings by modeling the connection information. The decoder maps the refined embeddings to nodes' locations and relieves the convergence problem by considering prior knowledge. The experiments in 8 real-world IPv4/IPv6 networks in North America, Europe and Asia show the proposed GNN-Geo clearly outperforms the state-of-art rule-based and learning-based baselines. This work verifies the great potential of GNN for fine-grained IP geolocation.
Recent years have witnessed a rise in real-world data captured with rich structural information that can be conveniently depicted by multi-relational graphs. While inference of continuous node features across a simple graph is rather under-studied by the current relational learning research, we go one step further and focus on node regression problem on multi-relational graphs. We take inspiration from the well-known label propagation algorithm aiming at completing categorical features across a simple graph and propose a novel propagation framework for completing missing continuous features at the nodes of a multi-relational and directed graph. Our multi-relational propagation algorithm is composed of iterative neighborhood aggregations which originate from a relational local generative model. Our findings show the benefit of exploiting the multi-relational structure of the data in several node regression scenarios in different settings.
Understanding how information propagates in real-life complex networks yields a better understanding of dynamic processes such as misinformation or epidemic spreading. The recently introduced branch of machine learning methods for learning node representations offers many novel applications, one of them being the task of spreading prediction addressed in this paper. We explore the utility of the state-of-the-art node representation learners when used to assess the effects of spreading from a given node, estimated via extensive simulations. Further, as many real-life networks are topologically similar, we systematically investigate whether the learned models generalize to previously unseen networks, showing that in some cases very good model transfer can be obtained. This work is one of the first to explore transferability of the learned representations for the task of node regression; we show there exist pairs of networks with similar structure between which the trained models can be transferred (zero-shot), and demonstrate their competitive performance. To our knowledge, this is one of the first attempts to evaluate the utility of zero-shot transfer for the task of node regression.