CLDG: Contrastive Learning on Dynamic Graphs

The graph with complex annotations is the most potent data type, whose constantly evolving motivates further exploration of the unsupervised dynamic graph representation. One of the representative paradigms is graph contrastive learning. It constructs self-supervised signals by maximizing the mutual information between the statistic graph's augmentation views. However, the semantics and labels may change within the augmentation process, causing a significant performance drop in downstream tasks. This drawback becomes greatly magnified on dynamic graphs. To address this problem, we designed a simple yet effective framework named CLDG. Firstly, we elaborate that dynamic graphs have temporal translation invariance at different levels. Then, we proposed a sampling layer to extract the temporally-persistent signals. It will encourage the node to maintain consistent local and global representations, i.e., temporal translation invariance under the timespan views. The extensive experiments demonstrate the effectiveness and efficiency of the method on seven datasets by outperforming eight unsupervised state-of-the-art baselines and showing competitiveness against four semi-supervised methods. Compared with the existing dynamic graph method, the number of model parameters and training time is reduced by an average of 2,001.86 times and 130.31 times on seven datasets, respectively.

Lyapunov Analysis For Monotonically Forward-Backward Accelerated Algorithms

In the realm of gradient-based optimization, Nesterov's accelerated gradient method (NAG) is a landmark advancement, achieving an accelerated convergence rate that outperforms the vanilla gradient descent method for convex function. However, for strongly convex functions, whether NAG converges linearly remains an open question, as noted in the comprehensive review by Chambolle and Pock [2016]. This issue, aside from the critical step size, was addressed by Li et al. [2024a] using a high-resolution differential equation framework. Furthermore, Beck [2017, Section 10.7.4] introduced a monotonically convergent variant of NAG, referred to as M-NAG. Despite these developments, the Lyapunov analysis presented in [Li et al., 2024a] cannot be directly extended to M-NAG. In this paper, we propose a modification to the iterative relation by introducing a gradient term, leading to a new gradient-based iterative relation. This adjustment allows for the construction of a novel Lyapunov function that excludes kinetic energy. The linear convergence derived from this Lyapunov function is independent of both the parameters of the strongly convex functions and the step size, yielding a more general and robust result. Notably, we observe that the gradient iterative relation derived from M-NAG is equivalent to that from NAG when the position-velocity relation is applied. However, the Lyapunov analysis does not rely on the position-velocity relation, allowing us to extend the linear convergence to M-NAG. Finally, by utilizing two proximal inequalities, which serve as the proximal counterparts of strongly convex inequalities, we extend the linear convergence to both the fast iterative shrinkage-thresholding algorithm (FISTA) and its monotonic counterpart (M-FISTA).

Training a Label-Noise-Resistant GNN with Reduced Complexity

Graph Neural Networks (GNNs) have been widely employed for semi-supervised node classification tasks on graphs. However, the performance of GNNs is significantly affected by label noise, that is, a small amount of incorrectly labeled nodes can substantially misguide model training. Mainstream solutions define node classification with label noise (NCLN) as a reliable labeling task, often introducing node similarity with quadratic computational complexity to more accurately assess label reliability. To this end, in this paper, we introduce the Label Ensemble Graph Neural Network (LEGNN), a lower complexity method for robust GNNs training against label noise. LEGNN reframes NCLN as a label ensemble task, gathering informative multiple labels instead of constructing a single reliable label, avoiding high-complexity computations for reliability assessment. Specifically, LEGNN conducts a two-step process: bootstrapping neighboring contexts and robust learning with gathered multiple labels. In the former step, we apply random neighbor masks for each node and gather the predicted labels as a high-probability label set. This mitigates the impact of inaccurately labeled neighbors and diversifies the label set. In the latter step, we utilize a partial label learning based strategy to aggregate the high-probability label information for model training. Additionally, we symmetrically gather a low-probability label set to counteract potential noise from the bootstrapped high-probability label set. Extensive experiments on six datasets demonstrate that LEGNN achieves outstanding performance while ensuring efficiency. Moreover, it exhibits good scalability on dataset with over one hundred thousand nodes and one million edges.

Estimating Noisy Class Posterior with Part-level Labels for Noisy Label Learning

In noisy label learning, estimating noisy class posteriors plays a fundamental role for developing consistent classifiers, as it forms the basis for estimating clean class posteriors and the transition matrix. Existing methods typically learn noisy class posteriors by training a classification model with noisy labels. However, when labels are incorrect, these models may be misled to overemphasize the feature parts that do not reflect the instance characteristics, resulting in significant errors in estimating noisy class posteriors. To address this issue, this paper proposes to augment the supervised information with part-level labels, encouraging the model to focus on and integrate richer information from various parts. Specifically, our method first partitions features into distinct parts by cropping instances, yielding part-level labels associated with these various parts. Subsequently, we introduce a novel single-to-multiple transition matrix to model the relationship between the noisy and part-level labels, which incorporates part-level labels into a classifier-consistent framework. Utilizing this framework with part-level labels, we can learn the noisy class posteriors more precisely by guiding the model to integrate information from various parts, ultimately improving the classification performance. Our method is theoretically sound, while experiments show that it is empirically effective in synthetic and real-world noisy benchmarks.

GraphPub: Generation of Differential Privacy Graph with High Availability

In recent years, with the rapid development of graph neural networks (GNN), more and more graph datasets have been published for GNN tasks. However, when an upstream data owner publishes graph data, there are often many privacy concerns, because many real-world graph data contain sensitive information like person's friend list. Differential privacy (DP) is a common method to protect privacy, but due to the complex topological structure of graph data, applying DP on graphs often affects the message passing and aggregation of GNN models, leading to a decrease in model accuracy. In this paper, we propose a novel graph edge protection framework, graph publisher (GraphPub), which can protect graph topology while ensuring that the availability of data is basically unchanged. Through reverse learning and the encoder-decoder mechanism, we search for some false edges that do not have a large negative impact on the aggregation of node features, and use them to replace some real edges. The modified graph will be published, which is difficult to distinguish between real and false data. Sufficient experiments prove that our framework achieves model accuracy close to the original graph with an extremely low privacy budget.

Teaching MLP More Graph Information: A Three-stage Multitask Knowledge Distillation Framework

We study the challenging problem for inference tasks on large-scale graph datasets of Graph Neural Networks: huge time and memory consumption, and try to overcome it by reducing reliance on graph structure. Even though distilling graph knowledge to student MLP is an excellent idea, it faces two major problems of positional information loss and low generalization. To solve the problems, we propose a new three-stage multitask distillation framework. In detail, we use Positional Encoding to capture positional information. Also, we introduce Neural Heat Kernels responsible for graph data processing in GNN and utilize hidden layer outputs matching for better performance of student MLP's hidden layers. To the best of our knowledge, it is the first work to include hidden layer distillation for student MLP on graphs and to combine graph Positional Encoding with MLP. We test its performance and robustness with several settings and draw the conclusion that our work can outperform well with good stability.

Interpretable Geoscience Artificial Intelligence (XGeoS-AI): Application to Demystify Image Recognition

As Earth science enters the era of big data, artificial intelligence (AI) not only offers great potential for solving geoscience problems, but also plays a critical role in accelerating the understanding of the complex, interactive, and multiscale processes of Earth's behavior. As geoscience AI models are progressively utilized for significant predictions in crucial situations, geoscience researchers are increasingly demanding their interpretability and versatility. This study proposes an interpretable geoscience artificial intelligence (XGeoS-AI) framework to unravel the mystery of image recognition in the Earth sciences, and its effectiveness and versatility is demonstrated by taking computed tomography (CT) image recognition as an example. Inspired by the mechanism of human vision, the proposed XGeoS-AI framework generates a threshold value from a local region within the whole image to complete the recognition. Different kinds of artificial intelligence (AI) methods, such as Support Vector Regression (SVR), Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), can be adopted as the AI engines of the proposed XGeoS-AI framework to efficiently complete geoscience image recognition tasks. Experimental results demonstrate that the effectiveness, versatility, and heuristics of the proposed framework have great potential in solving geoscience image recognition problems. Interpretable AI should receive more and more attention in the field of the Earth sciences, which is the key to promoting more rational and wider applications of AI in the field of Earth sciences. In addition, the proposed interpretable framework may be the forerunner of technological innovation in the Earth sciences.

Uncertainty-aware Traffic Prediction under Missing Data

Traffic prediction is a crucial topic because of its broad scope of applications in the transportation domain. Recently, various studies have achieved promising results. However, most studies assume the prediction locations have complete or at least partial historical records and cannot be extended to non-historical recorded locations. In real-life scenarios, the deployment of sensors could be limited due to budget limitations and installation availability, which makes most current models not applicable. Though few pieces of literature tried to impute traffic states at the missing locations, these methods need the data simultaneously observed at the locations with sensors, making them not applicable to prediction tasks. Another drawback is the lack of measurement of uncertainty in prediction, making prior works unsuitable for risk-sensitive tasks or involving decision-making. To fill the gap, inspired by the previous inductive graph neural network, this work proposed an uncertainty-aware framework with the ability to 1) extend prediction to missing locations with no historical records and significantly extend spatial coverage of prediction locations while reducing deployment of sensors and 2) generate probabilistic prediction with uncertainty quantification to help the management of risk and decision making in the down-stream tasks. Through extensive experiments on real-life datasets, the result shows our method achieved promising results on prediction tasks, and the uncertainty quantification gives consistent results which highly correlated with the locations with and without historical data. We also show that our model could help support sensor deployment tasks in the transportation field to achieve higher accuracy with a limited sensor deployment budget.

Linear convergence of Nesterov-1983 with the strong convexity

For modern gradient-based optimization, a developmental landmark is Nesterov's accelerated gradient descent method, which is proposed in [Nesterov, 1983], so shorten as Nesterov-1983. Afterward, one of the important progresses is its proximal generalization, named the fast iterative shrinkage-thresholding algorithm (FISTA), which is widely used in image science and engineering. However, it is unknown whether both Nesterov-1983 and FISTA converge linearly on the strongly convex function, which has been listed as the open problem in the comprehensive review [Chambolle and Pock, 2016, Appendix B]. In this paper, we answer this question by the use of the high-resolution differential equation framework. Along with the phase-space representation previously adopted, the key difference here in constructing the Lyapunov function is that the coefficient of the kinetic energy varies with the iteration. Furthermore, we point out that the linear convergence of both the two algorithms above has no dependence on the parameter $r$ on the strongly convex function. Meanwhile, it is also obtained that the proximal subgradient norm converges linearly.

On Underdamped Nesterov's Acceleration

The high-resolution differential equation framework has been proven to be tailor-made for Nesterov's accelerated gradient descent method~(\texttt{NAG}) and its proximal correspondence -- the class of faster iterative shrinkage thresholding algorithms (FISTA). However, the systems of theories is not still complete, since the underdamped case ($r < 2$) has not been included. In this paper, based on the high-resolution differential equation framework, we construct the new Lyapunov functions for the underdamped case, which is motivated by the power of the time $t^{\gamma}$ or the iteration $k^{\gamma}$ in the mixed term. When the momentum parameter $r$ is $2$, the new Lyapunov functions are identical to the previous ones. These new proofs do not only include the convergence rate of the objective value previously obtained according to the low-resolution differential equation framework but also characterize the convergence rate of the minimal gradient norm square. All the convergence rates obtained for the underdamped case are continuously dependent on the parameter $r$. In addition, it is observed that the high-resolution differential equation approximately simulates the convergence behavior of~\texttt{NAG} for the critical case $r=-1$, while the low-resolution differential equation degenerates to the conservative Newton's equation. The high-resolution differential equation framework also theoretically characterizes the convergence rates, which are consistent with that obtained for the underdamped case with $r=-1$.