Contrastive learning (CL) continuously achieves significant breakthroughs across multiple domains. However, the most common InfoNCE-based methods suffer from some dilemmas, such as \textit{uniformity-tolerance dilemma} (UTD) and \textit{gradient reduction}, both of which are related to a $\mathcal{P}_{ij}$ term. It has been identified that UTD can lead to unexpected performance degradation. We argue that the fixity of temperature is to blame for UTD. To tackle this challenge, we enrich the CL loss family by presenting a Model-Aware Contrastive Learning (MACL) strategy, whose temperature is adaptive to the magnitude of alignment that reflects the basic confidence of the instance discrimination task, then enables CL loss to adjust the penalty strength for hard negatives adaptively. Regarding another dilemma, the gradient reduction issue, we derive the limits of an involved gradient scaling factor, which allows us to explain from a unified perspective why some recent approaches are effective with fewer negative samples, and summarily present a gradient reweighting to escape this dilemma. Extensive remarkable empirical results in vision, sentence, and graph modality validate our approach's general improvement for representation learning and downstream tasks.
Self-Supervised learning aims to eliminate the need for expensive annotation in graph representation learning, where graph contrastive learning (GCL) is trained with the self-supervision signals containing data-data pairs. These data-data pairs are generated with augmentation employing stochastic functions on the original graph. We argue that some features can be more critical than others depending on the downstream task, and applying stochastic function uniformly, will vandalize the influential features, leading to diminished accuracy. To fix this issue, we introduce a Feature Based Adaptive Augmentation (FebAA) approach, which identifies and preserves potentially influential features and corrupts the remaining ones. We implement FebAA as plug and play layer and use it with state-of-the-art Deep Graph Contrastive Learning (GRACE) and Bootstrapped Graph Latents (BGRL). We successfully improved the accuracy of GRACE and BGRL on eight graph representation learning's benchmark datasets.
Traffic demand forecasting by deep neural networks has attracted widespread interest in both academia and industry society. Among them, the pairwise Origin-Destination (OD) demand prediction is a valuable but challenging problem due to several factors: (i) the large number of possible OD pairs, (ii) implicitness of spatial dependence, and (iii) complexity of traffic states. To address the above issues, this paper proposes a Continuous-time and Multi-level dynamic graph representation learning method for Origin-Destination demand prediction (CMOD). Firstly, a continuous-time dynamic graph representation learning framework is constructed, which maintains a dynamic state vector for each traffic node (metro stations or taxi zones). The state vectors keep historical transaction information and are continuously updated according to the most recently happened transactions. Secondly, a multi-level structure learning module is proposed to model the spatial dependency of station-level nodes. It can not only exploit relations between nodes adaptively from data, but also share messages and representations via cluster-level and area-level virtual nodes. Lastly, a cross-level fusion module is designed to integrate multi-level memories and generate comprehensive node representations for the final prediction. Extensive experiments are conducted on two real-world datasets from Beijing Subway and New York Taxi, and the results demonstrate the superiority of our model against the state-of-the-art approaches.
Brain graph representation learning serves as the fundamental technique for brain diseases diagnosis. Great efforts from both the academic and industrial communities have been devoted to brain graph representation learning in recent years. The isomorphic neural network (IsoNN) introduced recently can automatically learn the existence of sub-graph patterns in brain graphs, which is also the state-of-the-art brain graph representation learning method by this context so far. However, IsoNN fails to capture the orientations of sub-graph patterns, which may render the learned representations to be useless for many cases. In this paper, we propose a new Iso-CapsNet (Isomorphic Capsule Net) model by introducing the graph isomorphic capsules for effective brain graph representation learning. Based on the capsule dynamic routing, besides the subgraph pattern existence confidence scores, Iso-CapsNet can also learn other sub-graph rich properties, including position, size and orientation, for calculating the class-wise digit capsules. We have compared Iso-CapsNet with both classic and state-of-the-art brain graph representation approaches with extensive experiments on four brain graph benchmark datasets. The experimental results also demonstrate the effectiveness of Iso-CapsNet, which can out-perform the baseline methods with significant improvements.
Representation learning on graphs, also called graph embedding, has demonstrated its significant impact on a series of machine learning applications such as classification, prediction and recommendation. However, existing work has largely ignored the rich information contained in the properties (or attributes) of both nodes and edges of graphs in modern applications, e.g., those represented by property graphs. To date, most existing graph embedding methods either focus on plain graphs with only the graph topology, or consider properties on nodes only. We propose PGE, a graph representation learning framework that incorporates both node and edge properties into the graph embedding procedure. PGE uses node clustering to assign biases to differentiate neighbors of a node and leverages multiple data-driven matrices to aggregate the property information of neighbors sampled based on a biased strategy. PGE adopts the popular inductive model for neighborhood aggregation. We provide detailed analyses on the efficacy of our method and validate the performance of PGE by showing how PGE achieves better embedding results than the state-of-the-art graph embedding methods on benchmark applications such as node classification and link prediction over real-world datasets.
Negative sampling (NS) loss plays an important role in learning knowledge graph embedding (KGE) to handle a huge number of entities. However, the performance of KGE degrades without hyperparameters such as the margin term and number of negative samples in NS loss being appropriately selected. Currently, empirical hyperparameter tuning addresses this problem at the cost of computational time. To solve this problem, we theoretically analyzed NS loss to assist hyperparameter tuning and understand the better use of the NS loss in KGE learning. Our theoretical analysis showed that scoring methods with restricted value ranges, such as TransE and RotatE, require appropriate adjustment of the margin term or the number of negative samples different from those without restricted value ranges, such as RESCAL, ComplEx, and DistMult. We also propose subsampling methods specialized for the NS loss in KGE studied from a theoretical aspect. Our empirical analysis on the FB15k-237, WN18RR, and YAGO3-10 datasets showed that the results of actually trained models agree with our theoretical findings.
Recently, graph neural networks (GNNs) have shown prominent performance in graph representation learning by leveraging knowledge from both graph structure and node features. However, most of them have two major limitations. First, GNNs can learn higher-order structural information by stacking more layers but can not deal with large depth due to the over-smoothing issue. Second, it is not easy to apply these methods on large graphs due to the expensive computation cost and high memory usage. In this paper, we present node-adaptive feature smoothing (NAFS), a simple non-parametric method that constructs node representations without parameter learning. NAFS first extracts the features of each node with its neighbors of different hops by feature smoothing, and then adaptively combines the smoothed features. Besides, the constructed node representation can further be enhanced by the ensemble of smoothed features extracted via different smoothing strategies. We conduct experiments on four benchmark datasets on two different application scenarios: node clustering and link prediction. Remarkably, NAFS with feature ensemble outperforms the state-of-the-art GNNs on these tasks and mitigates the aforementioned two limitations of most learning-based GNN counterparts.
With the development of graph kernels and graph representation learning, many superior methods have been proposed to handle scalability and oversmoothing issues on graph structure learning. However, most of those strategies are designed based on practical experience rather than theoretical analysis. In this paper, we use a particular dummy node connecting to all existing vertices without affecting original vertex and edge properties. We further prove that such the dummy node can help build an efficient monomorphic edge-to-vertex transform and an epimorphic inverse to recover the original graph back. It also indicates that adding dummy nodes can preserve local and global structures for better graph representation learning. We extend graph kernels and graph neural networks with dummy nodes and conduct experiments on graph classification and subgraph isomorphism matching tasks. Empirical results demonstrate that taking graphs with dummy nodes as input significantly boosts graph structure learning, and using their edge-to-vertex graphs can also achieve similar results. We also discuss the gain of expressive power from the dummy in neural networks.
Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry. While extensive research has been done on developing GNN models with superior performance according to a collection of graph representation learning benchmarks, it is currently not well understood what aspects of a given model are probed by them. For example, to what extent do they test the ability of a model to leverage graph structure vs. node features? Here, we develop a principled approach to taxonomize benchmarking datasets according to a $\textit{sensitivity profile}$ that is based on how much GNN performance changes due to a collection of graph perturbations. Our data-driven analysis provides a deeper understanding of which benchmarking data characteristics are leveraged by GNNs. Consequently, our taxonomy can aid in selection and development of adequate graph benchmarks, and better informed evaluation of future GNN methods. Finally, our approach and implementation in $\texttt{GTaxoGym}$ package are extendable to multiple graph prediction task types and future datasets.
Graph contrastive learning (GCL) improves graph representation learning, leading to SOTA on various downstream tasks. The graph augmentation step is a vital but scarcely studied step of GCL. In this paper, we show that the node embedding obtained via the graph augmentations is highly biased, somewhat limiting contrastive models from learning discriminative features for downstream tasks. Thus, instead of investigating graph augmentation in the input space, we alternatively propose to perform augmentations on the hidden features (feature augmentation). Inspired by so-called matrix sketching, we propose COSTA, a novel COvariance-preServing feaTure space Augmentation framework for GCL, which generates augmented features by maintaining a "good sketch" of original features. To highlight the superiority of feature augmentation with COSTA, we investigate a single-view setting (in addition to multi-view one) which conserves memory and computations. We show that the feature augmentation with COSTA achieves comparable/better results than graph augmentation based models.
Many modern deep-learning techniques do not work without enormous datasets. At the same time, several fields demand methods working in scarcity of data. This problem is even more complex when the samples have varying structures, as in the case of graphs. Graph representation learning techniques have recently proven successful in a variety of domains. Nevertheless, the employed architectures perform miserably when faced with data scarcity. On the other hand, few-shot learning allows employing modern deep learning models in scarce data regimes without waiving their effectiveness. In this work, we tackle the problem of few-shot graph classification, showing that equipping a simple distance metric learning baseline with a state-of-the-art graph embedder allows to obtain competitive results on the task. While the simplicity of the architecture is enough to outperform more complex ones, it also allows straightforward additions. To this end, we show that additional improvements may be obtained by encouraging a task-conditioned embedding space. Finally, we propose a MixUp-based online data augmentation technique acting in the latent space and show its effectiveness on the task.
Designing accurate deep learning models for molecular property prediction plays an increasingly essential role in drug and material discovery. Recently, due to the scarcity of labeled molecules, self-supervised learning methods for learning generalizable and transferable representations of molecular graphs have attracted lots of attention. In this paper, we argue that there exist two major issues hindering current self-supervised learning methods from obtaining desired performance on molecular property prediction, that is, the ill-defined pre-training tasks and the limited model capacity. To this end, we introduce Knowledge-guided Pre-training of Graph Transformer (KPGT), a novel self-supervised learning framework for molecular graph representation learning, to alleviate the aforementioned issues and improve the performance on the downstream molecular property prediction tasks. More specifically, we first introduce a high-capacity model, named Line Graph Transformer (LiGhT), which emphasizes the importance of chemical bonds and is mainly designed to model the structural information of molecular graphs. Then, a knowledge-guided pre-training strategy is proposed to exploit the additional knowledge of molecules to guide the model to capture the abundant structural and semantic information from large-scale unlabeled molecular graphs. Extensive computational tests demonstrated that KPGT can offer superior performance over current state-of-the-art methods on several molecular property prediction tasks.
The human proteome contains a vast network of interacting kinases and substrates. Even though some kinases have proven to be immensely useful as therapeutic targets, a majority are still understudied. In this work, we present a novel knowledge graph representation learning approach to predict novel interaction partners for understudied kinases. Our approach uses a phosphoproteomic knowledge graph constructed by integrating data from iPTMnet, Protein Ontology, Gene Ontology and BioKG. The representation of kinases and substrates in this knowledge graph are learned by performing directed random walks on triples coupled with a modified SkipGram or CBOW model. These representations are then used as an input to a supervised classification model to predict novel interactions for understudied kinases. We also present a post-predictive analysis of the predicted interactions and an ablation study of the phosphoproteomic knowledge graph to gain an insight into the biology of the understudied kinases.
Graph contrastive learning (GCL) alleviates the heavy reliance on label information for graph representation learning (GRL) via self-supervised learning schemes. The core idea is to learn by maximising mutual information for similar instances, which requires similarity computation between two node instances. However, GCL is inefficient in both time and memory consumption. In addition, GCL normally requires a large number of training epochs to be well-trained on large-scale datasets. Inspired by an observation of a technical defect (i.e., inappropriate usage of Sigmoid function) commonly used in two representative GCL works, DGI and MVGRL, we revisit GCL and introduce a new learning paradigm for self-supervised graph representation learning, namely, Group Discrimination (GD), and propose a novel GD-based method called Graph Group Discrimination (GGD). Instead of similarity computation, GGD directly discriminates two groups of node samples with a very simple binary cross-entropy loss. In addition, GGD requires much fewer training epochs to obtain competitive performance compared with GCL methods on large-scale datasets. These two advantages endow GGD with very efficient property. Extensive experiments show that GGD outperforms state-of-the-art self-supervised methods on eight datasets. In particular, GGD can be trained in 0.18 seconds (6.44 seconds including data preprocessing) on ogbn-arxiv, which is orders of magnitude (10,000+) faster than GCL baselines while consuming much less memory. Trained with 9 hours on ogbn-papers100M with billion edges, GGD outperforms its GCL counterparts in both accuracy and efficiency.
Graph Neural Networks (GNNs) are effective tools for graph representation learning. Most GNNs rely on a recursive neighborhood aggregation scheme, named message passing, thereby their theoretical expressive power is limited to the first-order Weisfeiler-Lehman test (1-WL). An effective approach to this challenge is to explicitly retrieve some annotated examples used to enhance GNN models. While retrieval-enhanced models have been proved to be effective in many language and vision domains, it remains an open question how effective retrieval-enhanced GNNs are when applied to graph datasets. Motivated by this, we want to explore how the retrieval idea can help augment the useful information learned in the graph neural networks, and we design a retrieval-enhanced scheme called GRAPHRETRIEVAL, which is agnostic to the choice of graph neural network models. In GRAPHRETRIEVAL, for each input graph, similar graphs together with their ground-true labels are retrieved from an existing database. Thus they can act as a potential enhancement to complete various graph property predictive tasks. We conduct comprehensive experiments over 13 datasets, and we observe that GRAPHRETRIEVAL is able to reach substantial improvements over existing GNNs. Moreover, our empirical study also illustrates that retrieval enhancement is a promising remedy for alleviating the long-tailed label distribution problem.
Recent years have witnessed a rapid growth of applying deep spatiotemporal methods in traffic forecasting. However, the prediction of origin-destination (OD) demands is still a challenging problem since the number of OD pairs is usually quadratic to the number of stations. In this case, most of the existing spatiotemporal methods fail to handle spatial relations on such a large scale. To address this problem, this paper provides a dynamic graph representation learning framework for OD demands prediction. In particular, a hierarchical memory updater is first proposed to maintain a time-aware representation for each node, and the representations are updated according to the most recently observed OD trips in continuous-time and multiple discrete-time ways. Second, a spatiotemporal propagation mechanism is provided to aggregate representations of neighbor nodes along a random spatiotemporal route which treats origin and destination as two different semantic entities. Last, an objective function is designed to derive the future OD demands according to the most recent node representations, and also to tackle the data sparsity problem in OD prediction. Extensive experiments have been conducted on two real-world datasets, and the experimental results demonstrate the superiority of the proposed method. The code and data are available at https://github.com/Rising0321/HMOD.
Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's similarity relationship in the embedded space needs specific tools and a similarity metric. This paper develops a new graph representation learning scheme, namely EGG, which embeds approximated second-order graph characteristics into a Grassmann manifold. The proposed strategy leverages graph convolutions to learn hidden representations of the corresponding subspace of the graph, which is then mapped to a Grassmann point of a low dimensional manifold through truncated singular value decomposition (SVD). The established graph embedding approximates denoised correlationship of node attributes, as implemented in the form of a symmetric matrix space for Euclidean calculation. The effectiveness of EGG is demonstrated using both clustering and classification tasks at the node level and graph level. It outperforms baseline models on various benchmarks.
We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of graph representation learning with a variety of recent publications but they lack a common foundation about what constitutes a good positional or structural encoding, and what differentiates them. In this paper, we summarize the different types of encodings with a clearer definition and categorize them as being $\textit{local}$, $\textit{global}$ or $\textit{relative}$. The prior GTs are constrained to small graphs with a few hundred nodes, here we propose the first architecture with a complexity linear in the number of nodes and edges $O(N+E)$ by decoupling the local real-edge aggregation from the fully-connected Transformer. We argue that this decoupling does not negatively affect the expressivity, with our architecture being a universal function approximator on graphs. Our GPS recipe consists of choosing 3 main ingredients: (i) positional/structural encoding, (ii) local message-passing mechanism, and (iii) global attention mechanism. We provide a modular framework $\textit{GraphGPS}$ that supports multiple types of encodings and that provides efficiency and scalability both in small and large graphs. We test our architecture on 16 benchmarks and show highly competitive results in all of them, show-casing the empirical benefits gained by the modularity and the combination of different strategies.
Transformers have achieved remarkable performance in widespread fields, including natural language processing, computer vision and graph mining. However, vanilla Transformer architectures have not yielded promising improvements in the Knowledge Graph (KG) representations, where the translational distance paradigm dominates this area. Note that vanilla Transformer architectures struggle to capture the intrinsically heterogeneous structural and semantic information of knowledge graphs. To this end, we propose a new variant of Transformer for knowledge graph representations dubbed Relphormer. Specifically, we introduce Triple2Seq which can dynamically sample contextualized sub-graph sequences as the input to alleviate the heterogeneity issue. We propose a novel structure-enhanced self-attention mechanism to encode the relational information and keep the semantic information within entities and relations. Moreover, we utilize masked knowledge modeling for general knowledge graph representation learning, which can be applied to various KG-based tasks including knowledge graph completion, question answering, and recommendation. Experimental results on six datasets show that Relphormer can obtain better performance compared with baselines. Code is available in https://github.com/zjunlp/Relphormer.
The real-time transient stability assessment (TSA) plays a critical role in the secure operation of the power system. Although the classic numerical integration method, \textit{i.e.} time-domain simulation (TDS), has been widely used in industry practice, it is inevitably trapped in a high computational complexity due to the high latitude sophistication of the power system. In this work, a data-driven power system estimation method is proposed to quickly predict the stability of the power system before TDS reaches the end of simulating time windows, which can reduce the average simulation time of stability assessment without loss of accuracy. As the topology of the power system is in the form of graph structure, graph neural network based representation learning is naturally suitable for learning the status of the power system. Motivated by observing the distribution information of crucial active power and reactive power on the power system's bus nodes, we thus propose a distribution-aware learning~(DAL) module to explore an informative graph representation vector for describing the status of a power system. Then, TSA is re-defined as a binary classification task, and the stability of the system is determined directly from the resulting graph representation without numerical integration. Finally, we apply our method to the online TSA task. The case studies on the IEEE 39-bus system and Polish 2383-bus system demonstrate the effectiveness of our proposed method.