Time series forecasting relies on predicting future values from historical data, yet most state-of-the-art approaches—including transformer and multilayer perceptron-based models—optimize using Mean Squared Error (MSE), which has two fundamental weaknesses: its point-wise error computation fails to capture temporal relationships, and it does not account for inherent noise in the data. To overcome these limitations, we introduce the Residual-Informed Loss (RI-Loss), a novel objective function based on the Hilbert-Schmidt Independence Criterion (HSIC). RI-Loss explicitly models noise structure by enforcing dependence between the residual sequence and a random time series, enabling more robust, noise-aware representations. Theoretically, we derive the first non-asymptotic HSIC bound with explicit double-sample complexity terms, achieving optimal convergence rates through Bernstein-type concentration inequalities and Rademacher complexity analysis. This provides rigorous guarantees for RI-Loss optimization while precisely quantifying kernel space interactions. Empirically, experiments across eight real-world benchmarks and five leading forecasting models demonstrate improvements in predictive performance, validating the effectiveness of our approach.

Most deep learning-based time series clustering models concentrate on data representation in a separate process from clustering. This leads to that clustering loss cannot guide feature extraction. Moreover, most methods solely analyze data from the temporal domain, disregarding the potential within the frequency domain. To address these challenges, we introduce a novel end-to-end Cross-Domain Contrastive learning model for time series Clustering (CDCC). Firstly, it integrates the clustering process and feature extraction using contrastive constraints at both cluster-level and instance-level. Secondly, the data is encoded simultaneously in both temporal and frequency domains, leveraging contrastive learning to enhance within-domain representation. Thirdly, cross-domain constraints are proposed to align the latent representations and category distribution across domains. With the above strategies, CDCC not only achieves end-to-end output but also effectively integrates frequency domains. Extensive experiments and visualization analysis are conducted on 40 time series datasets from UCR, demonstrating the superior performance of the proposed model.

Graph Convolutional Neural Network (GCN), a widely adopted method for analyzing relational data, enhances node discriminability through the aggregation of neighboring information. Usually, stacking multiple layers can improve the performance of GCN by leveraging information from high-order neighbors. However, the increase of the network depth will induce the over-smoothing problem, which can be attributed to the quality and quantity of neighbors changing: (a) neighbor quality, node's neighbors become overlapping in high order, leading to aggregated information becoming indistinguishable, (b) neighbor quantity, the exponentially growing aggregated neighbors submerges the node's initial feature by recursively aggregating operations. Current solutions mainly focus on one of the above causes and seldom consider both at once. Aiming at tackling both causes of over-smoothing in one shot, we introduce a simple Two-Sided Constraint (TSC) for GCNs, comprising two straightforward yet potent techniques: random masking and contrastive constraint. The random masking acts on the representation matrix's columns to regulate the degree of information aggregation from neighbors, thus preventing the convergence of node representations. Meanwhile, the contrastive constraint, applied to the representation matrix's rows, enhances the discriminability of the nodes. Designed as a plug-in module, TSC can be easily coupled with GCN or SGC architectures. Experimental analyses on diverse real-world graph datasets verify that our approach markedly reduces the convergence of node's representation and the performance degradation in deeper GCN.

Neural Collapse (NC) was a recently discovered phenomenon that the output features and the classifier weights of the neural network converge to optimal geometric structures at the Terminal Phase of Training (TPT) under various losses. However, the relationship between these optimal structures at TPT and the classification performance remains elusive, especially in imbalanced learning. Even though it is noticed that fixing the classifier to an optimal structure can mitigate the minority collapse problem, the performance is still not comparable to the classical imbalanced learning methods with a learnable classifier. In this work, we find that the optimal structure can be designed to represent a better classification rule, and thus achieve better performance. In particular, we justify that, to achieve better classification, the features from the minor classes should align with more directions. This justification then yields a decision rule called the Generalized Classification Rule (GCR) and we also term these directions as the centers of the classes. Then we study the NC under an MSE-type loss via the Unconstrained Features Model (UFM) framework where (1) the features from a class tend to collapse to the mean of the corresponding centers of that class (named Neural Collapse to Multiple Centers (NCMC)) at the global optimum, and (2) the original classifier approximates a surrogate to GCR when NCMC occurs. Based on the analysis, we develop a strategy for determining the number of centers and propose a Cosine Loss function for the fixed classifier that induces NCMC. Our experiments have shown that the Cosine Loss can induce NCMC and has performance on long-tail classification comparable to the classical imbalanced learning methods.

Hashing technique has become an effective method for information retrieval due to the fast calculation of the Hamming distance. However, with the continuous growth of data coming from the Internet, the online update of hashing on the massive social data becomes very time-consuming. To alleviate this issue, in this paper, we propose a novel updating technique for hashing methods, namely Hamming Subspace Learning (HSL). The motivation of HSL is to generate a low-dimensional Hamming subspace from a high-dimensional Hamming space by selecting representative hash functions. Through HSL, we aim to improve the speed of updating binary codes for all samples. We present a method for Hamming subspace learning based on greedy selection strategy and the Distribution Preserving Hamming Subspace learning (DHSL) algorithm by designing a novel loss function. The experimental results demonstrate that the HSL is effective to improve the speed of online updating and the performance of hashing algorithm.

Object registration has been widely discussed with the development of various range sensing technologies. In most work, however, the point clouds of reference and target are generated by the same technology, such as a Kinect range camera, LiDAR sensor, or Structure from Motion technique. Cases in which reference and target point clouds are generated by different technologies are rarely discussed. Due to the significant differences across various point cloud data in terms of point cloud density, sensing noise, scale, occlusion etc., object registration between such different point clouds becomes extremely difficult. In this study, we address for the first time an even more challenging case in which the differently-sourced point clouds are acquired from a real street view. One is generated on the basis of an image sequence through the SfM process, and the other is produced directly by the LiDAR system. We propose a two-stage matching and registration algorithm to achieve object registration between these two different point clouds. The experiments are based on real building object point cloud data and demonstrate the effectiveness and efficiency of the proposed solution. The newly proposed solution can be further developed to contribute to several related applications, such as Location Based Service.