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Homophily principle, \ie{} nodes with the same labels or similar attributes are more likely to be connected, has been commonly believed to be the main reason for the superiority of Graph Neural Networks (GNNs) over traditional Neural Networks (NNs) on graph-structured data, especially on node-level tasks. However, recent work has identified a non-trivial set of datasets where GNN's performance compared to the NN's is not satisfactory. Heterophily, i.e. low homophily, has been considered the main cause of this empirical observation. People have begun to revisit and re-evaluate most existing graph models, including graph transformer and its variants, in the heterophily scenario across various kinds of graphs, e.g. heterogeneous graphs, temporal graphs and hypergraphs. Moreover, numerous graph-related applications are found to be closely related to the heterophily problem. In the past few years, considerable effort has been devoted to studying and addressing the heterophily issue. In this survey, we provide a comprehensive review of the latest progress on heterophilic graph learning, including an extensive summary of benchmark datasets and evaluation of homophily metrics on synthetic graphs, meticulous classification of the most updated supervised and unsupervised learning methods, thorough digestion of the theoretical analysis on homophily/heterophily, and broad exploration of the heterophily-related applications. Notably, through detailed experiments, we are the first to categorize benchmark heterophilic datasets into three sub-categories: malignant, benign and ambiguous heterophily. Malignant and ambiguous datasets are identified as the real challenging datasets to test the effectiveness of new models on the heterophily challenge. Finally, we propose several challenges and future directions for heterophilic graph representation learning., Comment: Suggestions and comments are welcomed at sitao.luan@mail.mcgill.ca!

Massive MIMO (multiple-input multiple-output) detection is an important topic in wireless communication and various machine learning based methods have been developed recently for this task. Expectation Propagation (EP) and its variants are widely used for MIMO detection and have achieved the best performance. However, EP-based solvers fail to capture the correlation between unknown variables, leading to a loss of information, and in addition, they are computationally expensive. In this paper, we show that the real-valued system can be modeled as spectral signal convolution on graph, through which the correlation between unknown variables can be captured. Based on such analysis, we propose graph convolution-enhanced expectation propagation (GCEPNet). GCEPNet incorporates data-dependent attention scores into Chebyshev polynomial for powerful graph convolution with better generalization capacity. It enables a better estimation of the cavity distribution for EP and empirically achieves the state-of-the-art (SOTA) MIMO detection performance with much faster inference speed. To our knowledge, we are the first to shed light on the connection between the system model and graph convolution, and the first to design the data-dependent coefficients for graph convolution., Comment: In IEEE GLOBECOM 2024 Conference Proceedings

Graph Attention Network (GAT) is one of the most popular Graph Neural Network (GNN) architecture, which employs the attention mechanism to learn edge weights and has demonstrated promising performance in various applications. However, since it only incorporates information from immediate neighborhood, it lacks the ability to capture long-range and global graph information, leading to unsatisfactory performance on some datasets, particularly on heterophilic graphs. To address this limitation, we propose the Directional Graph Attention Network (DGAT) in this paper. DGAT is able to combine the feature-based attention with the global directional information extracted from the graph topology. To this end, a new class of Laplacian matrices is proposed which can provably reduce the diffusion distance between nodes. Based on the new Laplacian, topology-guided neighbour pruning and edge adding mechanisms are proposed to remove the noisy and capture the helpful long-range neighborhood information. Besides, a global directional attention is designed to enable a topological-aware information propagation. The superiority of the proposed DGAT over the baseline GAT has also been verified through experiments on real-world benchmarks and synthetic data sets. It also outperforms the state-of-the-art (SOTA) models on 6 out of 7 real-world benchmark datasets.

Learning time-series representations for discriminative tasks, such as classification and regression, has been a long-standing challenge in the healthcare domain. Current pre-training methods are limited in either unidirectional next-token prediction or randomly masked token prediction. We propose a novel architecture called Bidirectional Timely Generative Pre-trained Transformer (BiTimelyGPT), which pre-trains on biosignals and longitudinal clinical records by both next-token and previous-token prediction in alternating transformer layers. This pre-training task preserves original distribution and data shapes of the time-series. Additionally, the full-rank forward and backward attention matrices exhibit more expressive representation capabilities. Using biosignals and longitudinal clinical records, BiTimelyGPT demonstrates superior performance in predicting neurological functionality, disease diagnosis, and physiological signs. By visualizing the attention heatmap, we observe that the pre-trained BiTimelyGPT can identify discriminative segments from biosignal time-series sequences, even more so after fine-tuning on the task.

Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success in Natural Language Processing and Computer Vision domains. However, the development of PTMs on time-series data is lagging behind. This underscores the limitations of the existing transformer-based architectures, particularly their scalability to handle large-scale data and ability to capture long-term temporal dependencies. In this study, we present Timely Generative Pre-trained Transformer (TimelyGPT). TimelyGPT employs an extrapolatable position (xPos) embedding to encode trend and periodic patterns into time-series representations. It also integrates recurrent attention and temporal convolution modules to effectively capture global-local temporal dependencies. Our experiments show that TimelyGPT excels in modeling continuously monitored biosignals and irregularly-sampled time series data commonly observed in longitudinal electronic health records (EHRs). In ultra-long-term forecasting experiment, TimelyGPT achieves accurate extrapolation up to 6,000 timesteps of body temperature during the sleep stage transition given a short look-up window (i.e., prompt) containing only 2,000 timesteps. We further demonstrated TimelyGPT's forecasting capabilities on a preprocessed longitudinal healthcare administrative database called PopHR consisting of 489,000 patients randomly sampled from Montreal population. Together, we envision TimelyGPT to be useful in a broad spectrum of health domains including long-term patient health state forecasting and patient risk trajectory prediction.

Homophily principle, i.e., nodes with the same labels are more likely to be connected, has been believed to be the main reason for the performance superiority of Graph Neural Networks (GNNs) over Neural Networks on node classification tasks. Recent research suggests that, even in the absence of homophily, the advantage of GNNs still exists as long as nodes from the same class share similar neighborhood patterns. However, this argument only considers intra-class Node Distinguishability (ND) but neglects inter-class ND, which provides incomplete understanding of homophily on GNNs. In this paper, we first demonstrate such deficiency with examples and argue that an ideal situation for ND is to have smaller intra-class ND than inter-class ND. To formulate this idea and study ND deeply, we propose Contextual Stochastic Block Model for Homophily (CSBM-H) and define two metrics, Probabilistic Bayes Error (PBE) and negative generalized Jeffreys divergence, to quantify ND. With the metrics, we visualize and analyze how graph filters, node degree distributions and class variances influence ND, and investigate the combined effect of intra- and inter-class ND. Besides, we discovered the mid-homophily pitfall, which occurs widely in graph datasets. Furthermore, we verified that, in real-work tasks, the superiority of GNNs is indeed closely related to both intra- and inter-class ND regardless of homophily levels. Grounded in this observation, we propose a new hypothesis-testing based performance metric beyond homophily, which is non-linear, feature-based and can provide statistical threshold value for GNNs' the superiority. Experiments indicate that it is significantly more effective than the existing homophily metrics on revealing the advantage and disadvantage of graph-aware modes on both synthetic and benchmark real-world datasets., Comment: Accepted by 37th Conference on Neural Information Processing Systems (NeurIPS 2023)

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically distributed (i.i.d.) samples. Though GNNs are believed to outperform basic NNs in real-world tasks, it is found that in some cases, GNNs have little performance gain or even underperform graph-agnostic NNs. To identify these cases, based on graph signal processing and statistical hypothesis testing, we propose two measures which analyze the cases in which the edge bias in features and labels does not provide advantages. Based on the measures, a threshold value can be given to predict the potential performance advantages of graph-aware models over graph-agnostic models., Comment: Accepted by 12th International Conference on Complex Networks and Their Applications

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels node-wisely to extract richer localized information for diverse node heterophily situations. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs and is easy to be implemented in baseline GNN layers. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-the-art GNNs on most tasks without incurring significant computational burden., Comment: Published at 36th Conference on Neural Information Processing Systems (NeurIPS 2022). arXiv admin note: substantial text overlap with arXiv:2109.05641

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the graph structures based on the relational inductive bias (homophily assumption). Though GNNs are believed to outperform NNs in real-world tasks, performance advantages of GNNs over graph-agnostic NNs seem not generally satisfactory. Heterophily has been considered as a main cause and numerous works have been put forward to address it. In this paper, we first show that not all cases of heterophily are harmful for GNNs with aggregation operation. Then, we propose new metrics based on a similarity matrix which considers the influence of both graph structure and input features on GNNs. The metrics demonstrate advantages over the commonly used homophily metrics by tests on synthetic graphs. From the metrics and the observations, we find some cases of harmful heterophily can be addressed by diversification operation. With this fact and knowledge of filterbanks, we propose the Adaptive Channel Mixing (ACM) framework to adaptively exploit aggregation, diversification and identity channels in each GNN layer to address harmful heterophily. We validate the ACM-augmented baselines with 10 real-world node classification tasks. They consistently achieve significant performance gain and exceed the state-of-the-art GNNs on most of the tasks without incurring significant computational burden.