Curvature graph neural network

A universal strategy for smoothing deceleration in deep graph neural networks

Graph neural networks (GNNs) have shown great promise in modeling graph-structured data, but the over-smoothing problem restricts their effectiveness in deep layers. Two key weaknesses of existing research on deep GNN models are: (1) ignoring the beneficial aspects of intra-class smoothing while focusing solely on reducing inter-class smoothing, and (2) inefficient computation of residual weights that neglect the influence of neighboring nodes' distributions. To address these weaknesses, we propose a novel Smoothing Deceleration (SD) strategy to reduce the smoothing speed rate of nodes as information propagates between layers, thereby mitigating over-smoothing. Firstly, we analyze the smoothing speed rate of node representations between layers by differential operations. Subsequently, based on this analysis, we introduce two innovative modules: Class-Related Smoothing Deceleration (CR-SD) loss and Smooth Deceleration Residual (NAR). CR-SD loss first takes into account the duality of smoothing, reducing inter-class smoothing while preserving the benefits of intra-class smoothing, thus reducing over-smoothing while maintaining model performance. NAR is specifically designed for graph-structured data, integrating the distribution of neighboring nodes, and is a novel method for computing residual weights. Finally, the comparative experimental results demonstrate that our SD strategy can extend existing shallow GNNs to deeper and delivers superior performance compared to both vanilla models and existing deep GNNs. And, a series of analytical experiments be conducted to prove that our proposed SD strategy effectively mitigates over-smoothing in deep GNNs. The source code for this work is available at https://github.com/cheng-qi/sd.

Motif-aware curriculum learning for node classification

Node classification, seeking to predict the categories of unlabeled nodes, is a crucial task in graph learning. One of the most popular methods for node classification is currently Graph Neural Networks (GNNs). However, conventional GNNs assign equal importance to all training nodes, which can lead to a reduction in accuracy and robustness due to the influence of complex nodes information. In light of the potential benefits of curriculum learning, some studies have proposed to incorporate curriculum learning into GNNs , where the node information can be acquired in an orderly manner. Nevertheless, the existing curriculum learning-based node classification methods fail to consider the subgraph structural information. To address this issue, we propose a novel approach, Motif-aware Curriculum Learning for Node Classification (MACL). It emphasizes the role of motif structures within graphs to fully utilize subgraph information and measure the quality of nodes, supporting an organized learning process for GNNs. Specifically, we design a motif-aware difficulty measurer to evaluate the difficulty of training nodes from different perspectives. Furthermore, we have implemented a training scheduler to introduce appropriate training nodes to the GNNs at suitable times. We conduct extensive experiments on five representative datasets. The results show that incorporating MACL into GNNs can improve the accuracy.

Curvature-enhanced graph convolutional network for biomolecular interaction prediction

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction. Our CGCN employs Ollivier-Ricci curvature (ORC) to characterize network local geometric properties and enhance the learning capability of GCNs. More specifically, ORCs are evaluated based on the local topology from node neighborhoods, and further incorporated into the weight function for the feature aggregation in message-passing procedure. Our CGCN model is extensively validated on fourteen real-world bimolecular interaction networks and analyzed in details using a series of well-designed simulated data. It has been found that our CGCN can achieve the state-of-the-art results. It outperforms all existing models, as far as we know, in thirteen out of the fourteen real-world datasets and ranks as the second in the rest one. The results from the simulated data show that our CGCN model is superior to the traditional GCN models regardless of the positive-to-negative-curvature ratios, network densities, and network sizes (when larger than 500).

Signed Curvature Graph Representation Learning of Brain Networks for Brain Age Estimation

Graph Neural Networks (GNNs) play a pivotal role in learning representations of brain networks for estimating brain age. However, the over-squashing impedes interactions between long-range nodes, hindering the ability of message-passing mechanism-based GNNs to learn the topological structure of brain networks. Graph rewiring methods and curvature GNNs have been proposed to alleviate over-squashing. However, most graph rewiring methods overlook node features and curvature GNNs neglect the geometric properties of signed curvature. In this study, a Signed Curvature GNN (SCGNN) was proposed to rewire the graph based on node features and curvature, and learn the representation of signed curvature. First, a Mutual Information Ollivier-Ricci Flow (MORF) was proposed to add connections in the neighborhood of edge with the minimal negative curvature based on the maximum mutual information between node features, improving the efficiency of information interaction between nodes. Then, a Signed Curvature Convolution (SCC) was proposed to aggregate node features based on positive and negative curvature, facilitating the model's ability to capture the complex topological structures of brain networks. Additionally, an Ollivier-Ricci Gradient Pooling (ORG-Pooling) was proposed to select the key nodes and topology structures by curvature gradient and attention mechanism, accurately obtaining the global representation for brain age estimation. Experiments conducted on six public datasets with structural magnetic resonance imaging (sMRI), spanning ages from 18 to 91 years, validate that our method achieves promising performance compared with existing methods. Furthermore, we employed the gaps between brain age and chronological age for identifying Alzheimer's Disease (AD), yielding the best classification performance.

CurvAGN: Curvature-based Adaptive Graph Neural Networks for Predicting Protein-Ligand Binding Affinity

Accurately predicting the binding affinity between proteins and ligands is crucial for drug discovery. Recent advances in graph neural networks (GNNs) have made significant progress in learning representations of protein-ligand complexes to estimate binding affinities. To improve the performance of GNNs, there frequently needs to look into protein-ligand complexes from geometric perspectives. While the "off-the-shelf" GNNs could incorporate some basic geometric structures of molecules, such as distances and angles, through modeling the complexes as homophilic graphs, these solutions seldom take into account the higher-level geometric attributes like curvatures and homology, and also heterophilic interactions.To address these limitations, we introduce the Curvature-based Adaptive Graph Neural Network (CurvAGN). This GNN comprises two components: a curvature block and an adaptive attention guided neural block (AGN). The curvature block encodes multiscale curvature informaton, then the AGN, based on an adaptive graph attention mechanism, incorporates geometry structure including angle, distance, and multiscale curvature, long-range molecular interactions, and heterophily of the graph into the protein-ligand complex representation. We demonstrate the superiority of our proposed model through experiments conducted on the PDBbind-V2016 core dataset.

Deeper Exploiting Graph Structure Information by Discrete Ricci Curvature in a Graph Transformer

Graph-structured data, operating as an abstraction of data containing nodes and interactions between nodes, is pervasive in the real world. There are numerous ways dedicated to extract graph structure information explicitly or implicitly, but whether it has been adequately exploited remains an unanswered question. This work goes deeper by heuristically incorporating a geometric descriptor, the discrete Ricci curvature (DRC), in order to uncover more graph structure information. We present a curvature-based topology-aware graph transformer, termed Curvphormer. This work expands the expressiveness by using a more illuminating geometric descriptor to quantify the connections within graphs in modern models and to extract the desired structure information, such as the inherent community structure in graphs with homogeneous information. We conduct extensive experiments on a variety of scaled datasets, including PCQM4M-LSC, ZINC, and MolHIV, and obtain a remarkable performance gain on various graph-level tasks and fine-tuned tasks.

An Adaptive Data Traffic Control Scheme with Load Balancing in a Wireless Network

The symmetric wireless network has been expected to be a revolutionary technology for mobile communications. Due to the limited resources of the microbase stations in the wireless network, the way to jointly optimize resource allocation, traffic throughput, latency, and other key performances is a hot research issue. In this paper, we introduce a joint optimization algorithm for improving the performance and balancing the traffic load of the wireless network. For the optimal traffic routing scheme, we transfer the problem to a mixed mathematical programming model. The model contains multiple traffic constraints and a single joint objective; the objective of the joint optimization are data transmission latency, energy consumption of wireless microbase stations, and throughput of links. Moreover, in order to approximately solve the optimization problem, we propose an efficient heuristic traffic transmission and migration scheme with load balancing, called an adaptive data traffic control scheme. The main idea of the proposed scheme is to split the traffic of overloaded microbase stations and links in the symmetric wireless network, so as to achieve load balancing and reduce the energy consumption of microbase stations. At last, the evaluations and simulations verify the proposed algorithm can efficiently optimize the energy allocation of microbase stations, and the network lifetime is increased to 210 rounds. Meanwhile, the network latency is reduced to 2–3 ms, and the network throughput is increased to 1000 Mb in our simulation environment. The constructed traffic control system for the traffic engineering-based wireless network in this paper can serve the intelligent system in the future.

RAISE: Rank-Aware Incremental Learning for Remote Sensing Object Detection

The deep learning method is widely used in remote sensing object detection on the premise that the training data have complete features. However, when data with a fixed class are added continuously, the trained detector is less able to adapt to new instances, impelling it to carry out incremental learning (IL). IL has two tasks with knowledge-related symmetry: continuing to learn unknown knowledge and maintaining existing knowledge. Unknown knowledge is more likely to exist in these new instances, which have features dissimilar from those of the old instances and cannot be well adapted by the detector before IL. Discarding all the old instances leads to the catastrophic forgetting of existing knowledge, which can be alleviated by relearning old instances, while different subsets represent different existing knowledge ranges and have different memory-retention effects on IL. Due to the different IL values of the data, the existing methods without appropriate distinguishing treatment preclude the efficient absorption of useful knowledge. Therefore, a rank-aware instance-incremental learning (RAIIL) method is proposed in this article, which pays attention to the difference in learning values from the aspects of the data-learning order and training loss weight. Specifically, RAIIL first designs the rank-score according to inference results and the true labels to determine the learning order and then weights the training loss according to the rank-score to balance the learning contribution. Comparative and analytical experiments conducted on two public remote sensing datasets for object detection, DOTA and DIOR, verified the superiority and effectiveness of the proposed method.

Comprehensive Geographic Networks Analysis: Statistical, Geometric and Algebraic Perspectives

Using complex network analysis methods to analyze the internal structure of geographic networks is a popular topic in urban geography research. Statistical analysis occupies a dominant position in the current research on geographic networks. This perspective mainly focuses on node connectivity, while other perspectives, such as geometric and algebraic perspectives, can provide additional insights into network structure. Using 11 different real-world geographic networks as examples, this study examines geographic networks from statistical, geometric, and algebraic perspectives. The following are some of the paper’s new findings: (1) When viewed statistically, geometrically, and algebraically, geographic networks have completely different properties. The statistical perspective describes both local and global connectivity; the Ricci curvature in the geometric perspective can assess the network’s development potential as well as describe its transmission capability, and the algebraic perspective can capture the global network topology other than connectivity; (2) Networks are qualitatively and quantitatively classified from three perspectives. The classification results are in accordance with the topological robustness experiment results, which indicate that an analysis from many angles has a lot of practical relevance; (3) Statistical indicators are better than Ricci curvature in identifying essential nodes in networks from a geometric standpoint, whereas the latter is better at detecting significant edges. Overall, studying geographic networks from various perspectives may provide new insights into their understanding.