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Time series data in real-world scenarios contain a substantial amount of nonlinear information, which significantly interferes with the training process of models, leading to decreased prediction performance. Therefore, during the time series forecasting process, extracting the local and global time series patterns and understanding the potential nonlinear features among different time observations are highly significant. To address this challenge, we introduce multi-resolution convolution and deformable convolution operations. By enlarging the receptive field using convolution kernels with different dilation factors to capture temporal correlation information at different resolutions, and adaptively adjusting the sampling positions through additional offset vectors, we enhance the network's ability to capture potential nonlinear features among time observations. Building upon this, we propose ACNet, an adaptive convolutional network designed to effectively model the local and global temporal dependencies and the nonlinear features between observations in multivariate time series. Specifically, by extracting and fusing time series features at different resolutions, we capture both local contextual information and global patterns in the time series. The designed nonlinear feature adaptive extraction module captures the nonlinear features among different time observations in the time series. We evaluated the performance of ACNet across twelve real-world datasets. The results indicate that ACNet consistently achieves state-of-the-art performance in both short-term and long-term forecasting tasks with favorable runtime efficiency.

This study, we introduce a novel Topological Cycle Graph Attention Network (CycGAT), designed to delineate a functional backbone within brain functional graph--key pathways essential for signal transmissio--from non-essential, redundant connections that form cycles around this core structure. We first introduce a cycle incidence matrix that establishes an independent cycle basis within a graph, mapping its relationship with edges. We propose a cycle graph convolution that leverages a cycle adjacency matrix, derived from the cycle incidence matrix, to specifically filter edge signals in a domain of cycles. Additionally, we strengthen the representation power of the cycle graph convolution by adding an attention mechanism, which is further augmented by the introduction of edge positional encodings in cycles, to enhance the topological awareness of CycGAT. We demonstrate CycGAT's localization through simulation and its efficacy on an ABCD study's fMRI data (n=8765), comparing it with baseline models. CycGAT outperforms these models, identifying a functional backbone with significantly fewer cycles, crucial for understanding neural circuits related to general intelligence. Our code will be released once accepted.

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.

The concern about underlying discrimination hidden in machine learning (ML) models is increasing, as ML systems have been widely applied in more and more real-world scenarios and any discrimination hidden in them will directly affect human life. Many techniques have been developed to enhance fairness including commonly-used group fairness measures and several fairness-aware methods combining ensemble learning. However, existing fairness measures can only focus on one aspect -- either group or individual fairness, and the hard compatibility among them indicates a possibility of remaining biases even if one of them is satisfied. Moreover, existing mechanisms to boost fairness usually present empirical results to show validity, yet few of them discuss whether fairness can be boosted with certain theoretical guarantees. To address these issues, we propose a fairness quality measure named discriminative risk to reflect both individual and group fairness aspects. Furthermore, we investigate the properties of the proposed measure and propose first- and second-order oracle bounds to show that fairness can be boosted via ensemble combination with theoretical learning guarantees. The analysis is suitable for both binary and multi-class classification. A pruning method is also proposed to utilise our proposed measure and comprehensive experiments are conducted to evaluate the effectiveness of the proposed methods., Comment: 18 pages, 13 figures, and 8 tables