Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data

Graph neural networks (GNNs) have proven effective in capturing relationships among nodes in a graph. This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and $k$-simplices, enabling the definition of graph-structured data on any $k$-simplices. Our contribution is the Hodge-Laplacian heterogeneous graph attention network (HL-HGAT), designed to learn heterogeneous signal representations across $k$-simplices. The HL-HGAT incorporates three key components: HL convolutional filters (HL-filters), simplicial projection (SP), and simplicial attention pooling (SAP) operators, applied to $k$-simplices. HL-filters leverage the unique topology of $k$-simplices encoded by the Hodge-Laplacian (HL) operator, operating within the spectral domain of the $k$-th HL operator. To address computation challenges, we introduce a polynomial approximation for HL-filters, exhibiting spatial localization properties. Additionally, we propose a pooling operator to coarsen $k$-simplices, combining features through simplicial attention mechanisms of self-attention and cross-attention via transformers and SP operators, capturing topological interconnections across multiple dimensions of simplices. The HL-HGAT is comprehensively evaluated across diverse graph applications, including NP-hard problems, graph multi-label and classification challenges, and graph regression tasks in logistics, computer vision, biology, chemistry, and neuroscience. The results demonstrate the model's efficacy and versatility in handling a wide range of graph-based scenarios.

Increasing Fairness in Compromise on Accuracy via Weighted Vote with Learning Guarantees

As the bias issue is being taken more and more seriously in widely applied machine learning systems, the decrease in accuracy in most cases deeply disturbs researchers when increasing fairness. To address this problem, we present a novel analysis of the expected fairness quality via weighted vote, suitable for both binary and multi-class classification. The analysis takes the correction of biased predictions by ensemble members into account and provides learning bounds that are amenable to efficient minimisation. We further propose a pruning method based on this analysis and the concepts of domination and Pareto optimality, which is able to increase fairness under a prerequisite of little or even no accuracy decline. The experimental results indicate that the proposed learning bounds are faithful and that the proposed pruning method can indeed increase ensemble fairness without much accuracy degradation.

Adversarial Patch Attacks and Defences in Vision-Based Tasks: A Survey

Adversarial attacks in deep learning models, especially for safety-critical systems, are gaining more and more attention in recent years, due to the lack of trust in the security and robustness of AI models. Yet the more primitive adversarial attacks might be physically infeasible or require some resources that are hard to access like the training data, which motivated the emergence of patch attacks. In this survey, we provide a comprehensive overview to cover existing techniques of adversarial patch attacks, aiming to help interested researchers quickly catch up with the progress in this field. We also discuss existing techniques for developing detection and defences against adversarial patches, aiming to help the community better understand this field and its applications in the real world.

When does Diversity Help Generalization in Classification Ensembles?

Ensembles, as a widely used and effective technique in the machine learning community, succeed within a key element--"diversity." The relationship between diversity and generalization, unfortunately, is not entirely understood and remains an open research issue. To reveal the effect of diversity on the generalization of classification ensembles, we investigate three issues on diversity, i.e., the measurement of diversity, the relationship between the proposed diversity and generalization error, and the utilization of this relationship for ensemble pruning. In the diversity measurement, we measure diversity by error decomposition inspired by regression ensembles, which decomposes the error of classification ensembles into accuracy and diversity. Then we formulate the relationship between the measured diversity and ensemble performance through the theorem of margin and generalization, and observe that the generalization error is reduced effectively only when the measured diversity is increased in a few specific ranges, while in other ranges larger diversity is less beneficial to increase generalization of an ensemble. Besides, we propose a pruning method based on diversity management to utilize this relationship, which could increase diversity appropriately and shrink the size of the ensemble with non-decreasing performance. The experiments validate the effectiveness of this proposed relationship between the proposed diversity and the ensemble generalization error.

Sub-Architecture Ensemble Pruning in Neural Architecture Search

Neural architecture search (NAS) is gaining more and more attention in recent years due to its flexibility and the remarkable capability of reducing the burden of neural network design. To achieve better performance, however, the searching process usually costs massive computation, which might not be affordable to researchers and practitioners. While recent attempts have employed ensemble learning methods to mitigate the enormous computation, an essential characteristic of diversity in ensemble methods is missed out, causing more similar sub-architectures to be gathered and potential redundancy in the final ensemble architecture. To bridge this gap, we propose a pruning method for NAS ensembles, named as ''Sub-Architecture Ensemble Pruning in Neural Architecture Search (SAEP).'' It targets to utilize diversity and achieve sub-ensemble architectures in a smaller size with comparable performance to the unpruned ensemble architectures. Three possible solutions are proposed to decide which subarchitectures should be pruned during the searching process. Experimental results demonstrate the effectiveness of the proposed method in largely reducing the size of ensemble architectures while maintaining the final performance. Moreover, distinct deeper architectures could be discovered if the searched sub-architectures are not diverse enough.

Ensemble Pruning based on Objection Maximization with a General Distributed Framework

Ensemble pruning, selecting a subset of individual learners from an original ensemble, alleviates the deficiencies of ensemble learning on the cost of time and space. Accuracy and diversity serve as two crucial factors while they usually conflict with each other. To balance both of them, we formalize the ensemble pruning problem as an objection maximization problem based on information entropy. Then we propose an ensemble pruning method including a centralized version and a distributed version, in which the latter is to speed up the former's execution. At last, we extract a general distributed framework for ensemble pruning, which can be widely suitable for most of existing ensemble pruning methods and achieve less time consuming without much accuracy decline. Experimental results validate the efficiency of our framework and methods, particularly with regard to a remarkable improvement of the execution speed, accompanied by gratifying accuracy performance.