Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often overlook the over-smoothing issue caused by traditional GNN models, as well as the gradient explosion or vanishing problems in deep GNNs. (2) Most models operate on first-order information, neglecting that the real world often consists of second-order systems, which further limits the model’s representation capabilities. To address these issues, we propose the Dual Second-order Equivariant Graph Ordinary (DuSEGO) Differential Equation for equivariant representation. Specifically, DuSEGO applies the dual second-order equivariant graph ordinary differential equations (Graph ODEs) to both graph embeddings and node coordinates simultaneously. Theoretically, we first prove that DuSEGO maintains the equivariant property. Furthermore, we provide theoretical insights showing that DuSEGO effectively alleviates the over-smoothing problem in both feature representation and coordinate update. Additionally, we demonstrate that the proposed DuSEGO mitigates the exploding and vanishing gradients problem, facilitating the training of deep multi-layer GNNs. Extensive experiments on benchmark datasets validate the superiority of the proposed DuSEGO compared to baselines.

Graph neural networks (GNNs) have gained significant attention for their impressive results on different graph-based tasks. The essential mechanism of GNNs is the message-passing framework, whereby node representations are aggregated from local neighborhoods. Recently, Transformer-based GNNs have been introduced to learn the long-range dependencies, enhancing performance. However, their quadratic computational complexity, due to the attention computation, has constrained their applicability on large-scale graphs. To address this issue, we propose MGIGNN ( M emorized G lobal I nformation G raph N eural N etwork), an innovative approach that leverages memorized global information to enhance existing GNNs in both transductive and inductive scenarios. Specifically, MGIGNN captures long-range dependencies by identifying and incorporating global similar nodes, which are defined as nodes exhibiting similar features, structural patterns and label information within a graph. To alleviate the computational overhead associated with computing embeddings for all nodes, we introduce an external memory module to facilitate the retrieval of embeddings and optimize performance on large graphs. To enhance the memory-efficiency, MGIGNN selectively retrieves global similar nodes from a small set of candidate nodes. These candidate nodes are selected from the training nodes based on a sparse node selection distribution with a Dirichlet prior. This selecting approach not only reduces the memory size required but also ensures efficient utilization of computational resources. Through comprehensive experiments conducted on ten widely-used and real-world datasets, including seven homogeneous datasets and three heterogeneous datasets, we demonstrate that our MGIGNN can generally improve the performance of existing GNNs on node classification tasks under both inductive and transductive settings.

Traditional methods of pre-training, fine-tuning, and ensembling often overlook essential relational data and task interconnections. To address this gap, our study presents a novel approach to harnessing this relational information via a relational graph-based model. We introduce Relational grAph Model ensemBLE model, abbreviated as RAMBLE. This model distinguishes itself by performing class label inference simultaneously across all data nodes and task nodes, employing the relational graph in a transductive manner. This fine-grained approach allows us to better comprehend and model the intricate interplay between data and tasks. Furthermore, we incorporate a novel variational information bottleneck-guided scheme for embedding fusion and aggregation. This innovative technique facilitates the creation of an informative fusion embedding, honing in on embeddings beneficial for the intended task while simultaneously filtering out potential noise-laden embeddings. Our theoretical analysis, grounded in information theory, confirms that the use of relational information for embedding fusion allows us to achieve higher upper and lower bounds on our target task's accuracy. We thoroughly assess our proposed model across eight diverse datasets, and the experimental results demonstrate the model's effective utilization of relational knowledge derived from all pre-trained models, thereby enhancing its performance on our target tasks.

Leveraging the side information associated with entities (i.e., users and items) to enhance recommendation systems has been widely recognized as an essential modeling dimension. Most of the existing approaches address this task by theintegration-based scheme, which incorporates the entity side information by combining the recommendation objective with an extra side information-aware objective. Despite the growing progress made by the existing integration-based approaches, they are largely limited by the potential conflicts between the two objectives. Moreover, the heterogeneous side information among entities is still under-explored in these systems. In this article, we propose a novelpre-training schemeto leverage the entity side information by pre-training entity embeddings using the multi-graph neural network. Instead of jointly training with two objectives, ourpre-training schemefirst pre-trains two representation models under the entity multi/single relational graphs constructed by their side information and then fine-tunes their embeddings under an existing general representation-based recommendation model. Our proposed multi-graph and single-graph neural networks can generate within-entity knowledge-encapsulated embeddings, while capturing the heterogeneity from the entity side information simultaneously, thereby improving the performance of the underlying recommendation model. An extensive evaluation of our pre-training scheme fine-tuned under four general representation-based recommender models, namely, MF, NCF, NGCF, and LightGCN, shows that effectively pre-training embeddings with both the user’s and item’s side information can significantly improve these original models in terms of both effectiveness and stability.

Graph-based recommender systems (GBRSs) have achieved promising performance by incorporating the user-item bipartite graph using the Graph Neural Network (GNN). Among GBRSs, the information from each user and item's multi-hop neighbours is effectively conveyed between nodes through neighbourhood aggregation and message passing. Although effective, existing neighbourhood information aggregation and passing functions are usually computationally expensive. Motivated by the emerging contrastive learning technique, we design a simple neighbourhood construction method in conjunction with the contrastive objective function to simulate the neighbourhood information processing of GNN. In addition, we propose a simple algorithm based on Multilayer Perceptron (MLP) for learning users and items' representations with extra non-linearity while lowering computational burden compared with multi-layers GNNs. Our extensive empirical experiments on three public datasets demonstrate that our proposed model, i.e. MLP-CGRec, can reduce the GPU memory consumption and training time by up to 24.0% and 33.1%, respectively, without significantly degenerating the recommendation accuracy in comparison with competitive baselines.

The field of recommender systems has rapidly evolved over the last few years, with significant advances made due to the in-flux of deep learning techniques. However, as a result of this rapid progress, escalating barriers-to-entry for new researchers is emerging. In particular, state-of-the-art approaches have fragmented into a large number of code-bases, often requiring different input formats, pre-processing stages and evaluating with different metric packages. Hence, it is time-consuming for new researchers to reach the point of having both an effective baseline set and a sound comparative environment. As a step towards elevating this problem, we have developed BETA-Rec, an open source project for Building, Evaluating and Tuning Automated Recommender Systems. BETA-Rec aims to provide a practical data toolkit for building end-to-end recommendation systems in a standardized way. It provides means for dataset preparation and splitting using common strategies, a generalized model engine for implementing recommender models using Pytorch with 9 models available out-of-the-box, as well as a unified training, validation, tuning and testing pipeline. Furthermore, BETA-Rec is designed to be both modular and extensible, enabling new models to be quickly added to the framework. It is deployable in a wide range of environments via pre-built docker containers and supports distributed parameter tuning using Ray. In this demo, we will illustrate the deployment and use of BETA-Rec for researchers and practitioners on a number of standard recommendation datasets. The source code of the project is available at github: https://github.com/beta-team/beta-recsys.

Recommender systems lie at the heart of many online services such as E-commerce, social media platforms and advertising. To keep users engaged and satisfied with the displayed items, recommender systems usually use the users' historical interactions containing their interests and purchase habits to make personalised recommendations. Recently, Graph Neural Networks (GNNs) have emerged as a technique that can effectively learn representations from structured graph data. By treating the traditional user-item interaction matrix as a bipartite graph, many existing graph-based recommender systems (GBRS) have been shown to achieve state-of-the-art performance when employing GNNs. However, the existing GBRS approaches still have several limitations, which prevent the GNNs from achieving their full potential. In this work, we propose to enhance the performance of the GBRS approaches along several research directions, namely leveraging additional items and users' side information, extending the existing undirected graphs to account for social influence among users, and enhancing their underlying optimisation criterion. In the following, we describe these proposed research directions.

The users' historical interactions usually contain their interests and purchase habits based on which personalised recommendations can be made. However, such user interactions are often sparse, leading to the well-known cold-start problem when a user has no or very few interactions. In this paper, we propose a new recommendation model, named Heterogeneous Graph Neural Recommender (HGNR), to tackle the cold-start problem while ensuring effective recommendations for all users. Our HGNR model learns users and items' embeddings by using the Graph Convolutional Network based on a heterogeneous graph, which is constructed from user-item interactions, social links and semantic links predicted from the social network and textual reviews. Our extensive empirical experiments on three public datasets demonstrate that HGNR significantly outperforms competitive baselines in terms of the Normalised Discounted Cumulative Gain and Hit Ratio measures.