In this paper, we focus on multi-task classification, where related classification tasks share the same label space and are learned simultaneously. In particular, we tackle a new setting, which is more realistic than currently addressed in the literature, where categories shift from training to test data. Hence, individual tasks do not contain complete training data for the categories in the test set. To generalize to such test data, it is crucial for individual tasks to leverage knowledge from related tasks. To this end, we propose learning an association graph to transfer knowledge among tasks for missing classes. We construct the association graph with nodes representing tasks, classes and instances, and encode the relationships among the nodes in the edges to guide their mutual knowledge transfer. By message passing on the association graph, our model enhances the categorical information of each instance, making it more discriminative. To avoid spurious correlations between task and class nodes in the graph, we introduce an assignment entropy maximization that encourages each class node to balance its edge weights. This enables all tasks to fully utilize the categorical information from related tasks. An extensive evaluation on three general benchmarks and a medical dataset for skin lesion classification reveals that our method consistently performs better than representative baselines.
Graph neural network (GNN)-based graph learning has been popular in natural language and programming language processing, particularly in text and source code classification. Typically, GNNs are constructed by incorporating alternating layers which learn transformations of graph node features, along with graph pooling layers that use graph pooling operators (e.g., Max-pooling) to effectively reduce the number of nodes while preserving the semantic information of the graph. Recently, to enhance GNNs in graph learning tasks, Manifold-Mixup, a data augmentation technique that produces synthetic graph data by linearly mixing a pair of graph data and their labels, has been widely adopted. However, the performance of Manifold-Mixup can be highly affected by graph pooling operators, and there have not been many studies that are dedicated to uncovering such affection. To bridge this gap, we take an early step to explore how graph pooling operators affect the performance of Mixup-based graph learning. To that end, we conduct a comprehensive empirical study by applying Manifold-Mixup to a formal characterization of graph pooling based on 11 graph pooling operations (9 hybrid pooling operators, 2 non-hybrid pooling operators). The experimental results on both natural language datasets (Gossipcop, Politifact) and programming language datasets (JAVA250, Python800) demonstrate that hybrid pooling operators are more effective for Manifold-Mixup than the standard Max-pooling and the state-of-the-art graph multiset transformer (GMT) pooling, in terms of producing more accurate and robust GNN models.
Graph Neural Networks (GNNs) have recently been applied to graph learning tasks and achieved state-of-the-art (SOTA) results. However, many competitive methods run GNNs multiple times with subgraph extraction and customized labeling to capture information that is hard for normal GNNs to learn. Such operations are time-consuming and do not scale to large graphs. In this paper, we propose an efficient GNN framework called Geodesic GNN (GDGNN) that requires only one GNN run and injects conditional relationships between nodes into the model without labeling. This strategy effectively reduces the runtime of subgraph methods. Specifically, we view the shortest paths between two nodes as the spatial graph context of the neighborhood around them. The GNN embeddings of nodes on the shortest paths are used to generate geodesic representations. Conditioned on the geodesic representations, GDGNN can generate node, link, and graph representations that carry much richer structural information than plain GNNs. We theoretically prove that GDGNN is more powerful than plain GNNs. We present experimental results to show that GDGNN achieves highly competitive performance with SOTA GNN models on various graph learning tasks while taking significantly less time.
Leveraging artificial intelligence for automatic retrosynthesis speeds up organic pathway planning in digital laboratories. However, existing deep learning approaches are unexplainable, like "black box" with few insights, notably limiting their applications in real retrosynthesis scenarios. Here, we propose MechRetro, a chemical-mechanism-driven graph learning framework for interpretable retrosynthetic prediction and pathway planning, which learns several retrosynthetic actions to simulate a reverse reaction via elaborate self-adaptive joint learning. By integrating chemical knowledge as prior information, we design a novel Graph Transformer architecture to adaptively learn discriminative and chemically meaningful molecule representations, highlighting the strong capacity in molecule feature representation learning. We demonstrate that MechRetro outperforms the state-of-the-art approaches for retrosynthetic prediction with a large margin on large-scale benchmark datasets. Extending MechRetro to the multi-step retrosynthesis analysis, we identify efficient synthetic routes via an interpretable reasoning mechanism, leading to a better understanding in the realm of knowledgeable synthetic chemists. We also showcase that MechRetro discovers a novel pathway for protokylol, along with energy scores for uncertainty assessment, broadening the applicability for practical scenarios. Overall, we expect MechRetro to provide meaningful insights for high-throughput automated organic synthesis in drug discovery.
Recently there has been increasing interest in developing and deploying deep graph learning algorithms for many tasks, such as fraud detection and recommender systems. Albeit, there is a limited number of publicly available graph-structured datasets, most of which are tiny compared to production-sized applications or are limited in their application domain. This work tackles this shortcoming by proposing a scalable synthetic graph generation tool to scale the datasets to production-size graphs with trillions of edges and billions of nodes. The tool learns a series of parametric models from proprietary datasets that can be released to researchers to study various graph methods on the synthetic data increasing prototype development and novel applications. We demonstrate the generalizability of the framework across a series of datasets, mimicking structural and feature distributions as well as the ability to scale them across varying sizes demonstrating their usefulness for benchmarking and model development. Code can be found on https://github.com/NVIDIA/DeepLearningExamples/tree/master/Tools/DGLPyTorch/SyntheticGraphGeneration.
Prevailing deep graph learning models often suffer from label sparsity issue. Although many graph few-shot learning (GFL) methods have been developed to avoid performance degradation in face of limited annotated data, they excessively rely on labeled data, where the distribution shift in the test phase might result in impaired generalization ability. Additionally, they lack a general purpose as their designs are coupled with task or data-specific characteristics. To this end, we propose a general and effective Contrastive Graph Few-shot Learning framework (CGFL). CGFL leverages a self-distilled contrastive learning procedure to boost GFL. Specifically, our model firstly pre-trains a graph encoder with contrastive learning using unlabeled data. Later, the trained encoder is frozen as a teacher model to distill a student model with a contrastive loss. The distilled model is finally fed to GFL. CGFL learns data representation in a self-supervised manner, thus mitigating the distribution shift impact for better generalization and making model task and data-independent for a general graph mining purpose. Furthermore, we introduce an information-based method to quantitatively measure the capability of CGFL. Comprehensive experiments demonstrate that CGFL outperforms state-of-the-art baselines on several graph mining tasks in the few-shot scenario. We also provide quantitative measurement of CGFL's success.
We present Gradient Gating (G$^2$), a novel framework for improving the performance of Graph Neural Networks (GNNs). Our framework is based on gating the output of GNN layers with a mechanism for multi-rate flow of message passing information across nodes of the underlying graph. Local gradients are harnessed to further modulate message passing updates. Our framework flexibly allows one to use any basic GNN layer as a wrapper around which the multi-rate gradient gating mechanism is built. We rigorously prove that G$^2$ alleviates the oversmoothing problem and allows the design of deep GNNs. Empirical results are presented to demonstrate that the proposed framework achieves state-of-the-art performance on a variety of graph learning tasks, including on large-scale heterophilic graphs.
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties of the originally given graph. Graph data consist of node features and graph matrix (e.g., adjacency and Laplacian). The existing graph coarsening methods ignore the node features and rely solely on a graph matrix to simplify graphs. In this paper, we introduce a novel optimization-based framework for graph dimensionality reduction. The proposed framework lies in the unification of graph learning and dimensionality reduction. It takes both the graph matrix and the node features as the input and learns the coarsen graph matrix and the coarsen feature matrix jointly while ensuring desired properties. The proposed optimization formulation is a multi-block non-convex optimization problem, which is solved efficiently by leveraging block majorization-minimization, $\log$ determinant, Dirichlet energy, and regularization frameworks. The proposed algorithms are provably convergent and practically amenable to numerous tasks. It is also established that the learned coarsened graph is $\epsilon\in(0,1)$ similar to the original graph. Extensive experiments elucidate the efficacy of the proposed framework for real-world applications.
Network analysis has been a powerful tool to unveil relationships and interactions among a large number of objects. Yet its effectiveness in accurately identifying important node-node interactions is challenged by the rapidly growing network size, with data being collected at an unprecedented granularity and scale. Common wisdom to overcome such high dimensionality is collapsing nodes into smaller groups and conducting connectivity analysis on the group level. Dividing efforts into two phases inevitably opens a gap in consistency and drives down efficiency. Consensus learning emerges as a new normal for common knowledge discovery with multiple data sources available. In this paper, we propose a unified multi-view sparse low-rank block model (msLBM) framework, which enables simultaneous grouping and connectivity analysis by combining multiple data sources. The msLBM framework efficiently represents overlapping information across large scale concepts and accommodates different types of heterogeneity across sources. Both features are desirable when analyzing high dimensional electronic health record (EHR) datasets from multiple health systems. An estimating procedure based on the alternating minimization algorithm is proposed. Our theoretical results demonstrate that a consensus knowledge graph can be more accurately learned by leveraging multi-source datasets, and statistically optimal rates can be achieved under mild conditions. Applications to the real world EHR data suggest that our proposed msLBM algorithm can more reliably reveal network structure among clinical concepts by effectively combining summary level EHR data from multiple health systems.
Graph Neural Networks (GNNs) have been generalized to process the heterogeneous graphs by various approaches. Unfortunately, these approaches usually model the heterogeneity via various complicated modules. This paper aims to propose a simple yet effective framework to assign adequate ability to the homogeneous GNNs to handle the heterogeneous graphs. Specifically, we propose Relation Embedding based Graph Neural Network (RE-GNN), which employs only one parameter per relation to embed the importance of distinct types of relations and node-type-specific self-loop connections. To optimize these relation embeddings and the model parameters simultaneously, a gradient scaling factor is proposed to constrain the embeddings to converge to suitable values. Besides, we interpret the proposed RE-GNN from two perspectives, and theoretically demonstrate that our RE-GCN possesses more expressive power than GTN (which is a typical heterogeneous GNN, and it can generate meta-paths adaptively). Extensive experiments demonstrate that our RE-GNN can effectively and efficiently handle the heterogeneous graphs and can be applied to various homogeneous GNNs.
Link prediction (LP) has been recognized as an important task in graph learning with its broad practical applications. A typical application of LP is to retrieve the top scoring neighbors for a given source node, such as the friend recommendation. These services desire the high inference scalability to find the top scoring neighbors from many candidate nodes at low latencies. There are two popular decoders that the recent LP models mainly use to compute the edge scores from node embeddings: the HadamardMLP and Dot Product decoders. After theoretical and empirical analysis, we find that the HadamardMLP decoders are generally more effective for LP. However, HadamardMLP lacks the scalability for retrieving top scoring neighbors on large graphs, since to the best of our knowledge, there does not exist an algorithm to retrieve the top scoring neighbors for HadamardMLP decoders in sublinear complexity. To make HadamardMLP scalable, we propose the Flashlight algorithm to accelerate the top scoring neighbor retrievals for HadamardMLP: a sublinear algorithm that progressively applies approximate maximum inner product search (MIPS) techniques with adaptively adjusted query embeddings. Empirical results show that Flashlight improves the inference speed of LP by more than 100 times on the large OGBL-CITATION2 dataset without sacrificing effectiveness. Our work paves the way for large-scale LP applications with the effective HadamardMLP decoders by greatly accelerating their inference.
As a tool for estimating networks in high dimensions, graphical models are commonly applied to calcium imaging data to estimate functional neuronal connectivity, i.e. relationships between the activities of neurons. However, in many calcium imaging data sets, the full population of neurons is not recorded simultaneously, but instead in partially overlapping blocks. This leads to the Graph Quilting problem, as first introduced by (Vinci et.al. 2019), in which the goal is to infer the structure of the full graph when only subsets of features are jointly observed. In this paper, we study a novel two-step approach to Graph Quilting, which first imputes the complete covariance matrix using low-rank covariance completion techniques before estimating the graph structure. We introduce three approaches to solve this problem: block singular value decomposition, nuclear norm penalization, and non-convex low-rank factorization. While prior works have studied low-rank matrix completion, we address the challenges brought by the block-wise missingness and are the first to investigate the problem in the context of graph learning. We discuss theoretical properties of the two-step procedure, showing graph selection consistency of one proposed approach by proving novel L infinity-norm error bounds for matrix completion with block-missingness. We then investigate the empirical performance of the proposed methods on simulations and on real-world data examples, through which we show the efficacy of these methods for estimating functional connectivity from calcium imaging data.
The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many datasets, the stable coloring is reached after a few iterations and the optimal number of iterations for machine learning tasks is typically even lower. This suggests that the colors diverge too fast, defining a similarity that is too coarse. We generalize the concept of color refinement and propose a framework for gradual neighborhood refinement, which allows a slower convergence to the stable coloring and thus provides a more fine-grained refinement hierarchy and vertex similarity. We assign new colors by clustering vertex neighborhoods, replacing the original injective color assignment function. Our approach is used to derive new variants of existing graph kernels and to approximate the graph edit distance via optimal assignments regarding vertex similarity. We show that in both tasks, our method outperforms the original color refinement with only a moderate increase in running time advancing the state of the art.
While graph neural networks (GNNs) have been successful for node classification tasks and link prediction tasks in graph, learning graph-level representations still remains a challenge. For the graph-level representation, it is important to learn both representation of neighboring nodes, i.e., aggregation, and graph structural information. A number of graph pooling methods have been developed for this goal. However, most of the existing pooling methods utilize k-hop neighborhood without considering explicit structural information in a graph. In this paper, we propose Structure Prototype Guided Pooling (SPGP) that utilizes prior graph structures to overcome the limitation. SPGP formulates graph structures as learnable prototype vectors and computes the affinity between nodes and prototype vectors. This leads to a novel node scoring scheme that prioritizes informative nodes while encapsulating the useful structures of the graph. Our experimental results show that SPGP outperforms state-of-the-art graph pooling methods on graph classification benchmark datasets in both accuracy and scalability.
Among different existing graph self-supervised learning strategies, graph contrastive learning (GCL) has been one of the most prevalent approaches to this problem. Despite the remarkable performance those GCL methods have achieved, existing GCL methods that heavily depend on various manually designed augmentation techniques still struggle to alleviate the feature suppression issue without risking losing task-relevant information. Consequently, the learned representation is either brittle or unilluminating. In light of this, we introduce the Graph Contrastive Learning with Cross-View Reconstruction (GraphCV), which follows the information bottleneck principle to learn minimal yet sufficient representation from graph data. Specifically, GraphCV aims to elicit the predictive (useful for downstream instance discrimination) and other non-predictive features separately. Except for the conventional contrastive loss which guarantees the consistency and sufficiency of the representation across different augmentation views, we introduce a cross-view reconstruction mechanism to pursue the disentanglement of the two learned representations. Besides, an adversarial view perturbed from the original view is added as the third view for the contrastive loss to guarantee the intactness of the global semantics and improve the representation robustness. We empirically demonstrate that our proposed model outperforms the state-of-the-art on graph classification task over multiple benchmark datasets.
Existing deepfake detectors face several challenges in achieving robustness and generalization. One of the primary reasons is their limited ability to extract relevant information from forgery videos, especially in the presence of various artifacts such as spatial, frequency, temporal, and landmark mismatches. Current detectors rely on pixel-level features that are easily affected by unknown disturbances or facial landmarks that do not provide sufficient information. Furthermore, most detectors cannot utilize information from multiple domains for detection, leading to limited effectiveness in identifying deepfake videos. To address these limitations, we propose a novel framework, namely Multimodal Graph Learning (MGL) that leverages information from multiple modalities using two GNNs and several multimodal fusion modules. At the frame level, we employ a bi-directional cross-modal transformer and an adaptive gating mechanism to combine the features from the spatial and frequency domains with the geometric-enhanced landmark features captured by a GNN. At the video level, we use a Graph Attention Network (GAT) to represent each frame in a video as a node in a graph and encode temporal information into the edges of the graph to extract temporal inconsistency between frames. Our proposed method aims to effectively identify and utilize distinguishing features for deepfake detection. We evaluate the effectiveness of our method through extensive experiments on widely-used benchmarks and demonstrate that our method outperforms the state-of-the-art detectors in terms of generalization ability and robustness against unknown disturbances.
Network flow problems, which involve distributing traffic such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics. Among them, the general Multi-Commodity Network Flow (MCNF) problem concerns the distribution of multiple flows of different sizes between several sources and sinks, while achieving effective utilization of the links. Due to the appeal of data-driven optimization, these problems have increasingly been approached using graph learning methods. In this paper, we propose a novel graph learning architecture for network flow problems called Per-Edge Weights (PEW). This method builds on a Graph Attention Network and uses distinctly parametrized message functions along each link. We extensively evaluate the proposed solution through an Internet flow routing case study using $17$ Service Provider topologies and $2$ routing schemes. We show that PEW yields substantial gains over architectures whose global message function constrains the routing unnecessarily. We also find that an MLP is competitive with other standard architectures. Furthermore, we analyze the relationship between graph structure and predictive performance for data-driven routing of flows, an aspect that has not been considered by existing work in the area.
Although previous graph-based multi-view clustering algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view-consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the k-means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this paper presents an efficient multi-view clustering approach via unified and discrete bipartite graph learning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view-consensus bipartite graph with adaptive weight learning. Further, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view-consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.
Artificial intelligence for graphs has achieved remarkable success in modeling complex systems, ranging from dynamic networks in biology to interacting particle systems in physics. However, the increasingly heterogeneous graph datasets call for multimodal methods that can combine different inductive biases: the set of assumptions that algorithms use to make predictions for inputs they have not encountered during training. Learning on multimodal datasets presents fundamental challenges because the inductive biases can vary by data modality and graphs might not be explicitly given in the input. To address these challenges, multimodal graph AI methods combine different modalities while leveraging cross-modal dependencies using graphs. Diverse datasets are combined using graphs and fed into sophisticated multimodal architectures, specified as image-intensive, knowledge-grounded and language-intensive models. Using this categorization, we introduce a blueprint for multimodal graph learning, use it to study existing methods and provide guidelines to design new models.
Representation learning on temporal graphs has drawn considerable research attention owing to its fundamental importance in a wide spectrum of real-world applications. Though a number of studies succeed in obtaining time-dependent representations, it still faces significant challenges. On the one hand, most of the existing methods restrict the embedding space with a certain curvature. However, the underlying geometry in fact shifts among the positive curvature hyperspherical, zero curvature Euclidean and negative curvature hyperbolic spaces in the evolvement over time. On the other hand, these methods usually require abundant labels to learn temporal representations, and thereby notably limit their wide use in the unlabeled graphs of the real applications. To bridge this gap, we make the first attempt to study the problem of self-supervised temporal graph representation learning in the general Riemannian space, supporting the time-varying curvature to shift among hyperspherical, Euclidean and hyperbolic spaces. In this paper, we present a novel self-supervised Riemannian graph neural network (SelfRGNN). Specifically, we design a curvature-varying Riemannian GNN with a theoretically grounded time encoding, and formulate a functional curvature over time to model the evolvement shifting among the positive, zero and negative curvature spaces. To enable the self-supervised learning, we propose a novel reweighting self-contrastive approach, exploring the Riemannian space itself without augmentation, and propose an edge-based self-supervised curvature learning with the Ricci curvature. Extensive experiments show the superiority of SelfRGNN, and moreover, the case study shows the time-varying curvature of temporal graph in reality.