Search Results (37)

This paper investigates pseudo-symmetric space–times within two interrelated frameworks: vacuum $f\left(R\right)$-gravity and Gray’s seven canonical decomposition subspaces. First, it is established that any conformally flat pseudo-symmetric space–time satisfying the vacuum field equations of $f\left(R\right)$-gravity necessarily corresponds to a perfect fluid. Subsequently, a detailed analysis of Gray’s subspaces reveals the following structural results: In the trivial and $\mathsf{𝒜}$ subspaces, pseudo-symmetric space–times are Ricci-simple and Weyl-harmonic, and thus are necessarily generalized Robertson–Walker space–times. In the $\mathcal{B}$ and $\mathsf{𝒜}\oplus \mathcal{B}$ subspaces, the associated time-like vector field ${\xi }^l$ is shown to be an eigenvector of the Ricci tensor with the eigenvalue $-R/2$. Furthermore, for a perfect fluid pseudo-symmetric space–time obeying $f\left(R\right)$-gravity and belonging to the trivial, $\mathsf{𝒜}$, $\mathcal{B}$, or $\mathsf{𝒜}\oplus \mathcal{B}$ subspaces, the isotropic pressure p and energy density $\sigma$ are proven to be constants. Additionally, it is demonstrated that Gray’s $\mathcal{I}$ subspace reduces to the $\mathcal{B}$ subspace in the pseudo-symmetric setting. Finally, under specific geometric conditions, pseudo-symmetric space–times in the $\mathcal{I}\oplus \mathsf{𝒜}$ and $\mathcal{I}\oplus \mathcal{B}$ subspaces are also shown to admit perfect fluid representations. These results collectively clarify the geometric and physical constraints imposed by pseudo-symmetry within $f\left(R\right)$-gravity and Gray’s classification scheme. Full article

Hyperspectral images present significant challenges for conventional dimensionality reduction methods due to their high dimensionality, spectral redundancy, and complex spatial–spatial dependencies. While kernel-based sparse representation methods have shown promise in handling spectral non-linearities, they often fail to preserve spatial consistency and semantic discriminability during feature transformation. To address these limitations, we propose a novel semantic-guided kernel low-rank sparse preserving projection (SKLSPP) framework. Unlike previous approaches that primarily focus on spectral information, our method introduces three key innovations: a semantic-aware kernel representation that maintains discriminability through label constraints, a spatially adaptive manifold regularization term that preserves local pixel affinities in the reduced subspace, and an efficient optimization framework that jointly learns sparse codes and projection matrices. Extensive experiments on benchmark datasets demonstrate that SKLSPP achieves superior performance compared to state-of-the-art methods, showing enhanced feature discrimination, reduced redundancy, and improved robustness to noise while maintaining spatial coherence in the dimensionality-reduced features. Full article

We propose a unified mathematical framework showing that the representational universality of modern foundational models arises from a shared finite latent domain. Building on the Finite Ring Continuum (FRC) framework, we model all modalities as epistemic projections of a common latent set $\mathcal{Z}\subset {\mathcal{U}}_t$, where ${\mathcal{U}}_t$ is a symmetry-complete finite-field shell. Using the uniqueness of minimal adequate representations, we prove the Universal Subspace Theorem, establishing that independently trained embeddings coincide, up to bijection, as coordinate charts on the same latent structure. This result explains cross-modal alignment, transferability, and semantic coherence as consequences of finite relational geometry rather than architectural similarity. The framework links representation learning, sufficiency theory, and FRC algebra, providing a principled foundation for universal latent structure in multimodal models. Full article

Pre-trained visual language models have become excellent basic models for many downstream tasks in transfer learning. However, due to the serious gap between the data scale of downstream tasks and the large-scale data used by pre-trained models, migration to downstream tasks will face the dilemma of discriminability and generalization. Therefore, it is necessary to learn task-specific knowledge while retaining general knowledge. How to accurately identify and distinguish these two types of representations remains a challenge. This paper proposes a dual-subspace driven cross-modal semantic interaction and dynamic feature fusion framework, which uses a decentralized covariance dual-subspace decomposition method to decouple visual and text features by constructing task subspaces and general knowledge subspaces, and performs refined modal interactions on the decoupled general features and task features through a cross-modal semantic interaction adapter module. Finally, a cross-level semantic fusion module based on a gating mechanism is used to achieve dynamic fusion of different semantics from shallow to deep. We verify the effectiveness of this method on three tasks: generalization to novel classes, novel target datasets, and domain generalization. Compared with a variety of advanced methods, the proposed method has achieved excellent performance in all evaluation tasks. Full article

Aiming at the problems of high complexity in source domain data, inaccessibility of target domain data, and unknown fault patterns in real-world industrial scenarios for mechanical fault diagnosis, this paper proposes a Feature Decomposition-based Source-Free Universal Domain Adaptation (FD-SFUniDA) framework for mechanical equipment fault diagnosis. First, the CBAM attention module is incorporated to enhance the ResNet-50 convolutional network for extracting feature information from source domain data. During the target domain adaptation phase, singular value decomposition is applied to the weights of the pre-trained model’s classification layer, orthogonally decoupling the feature space into a source-known subspace and a target-private subspace. Then, based on the magnitude of feature projections, a dynamic decision boundary is constructed and combined with an entropy threshold mechanism to accurately distinguish between known and unknown class samples. Furthermore, intra-class feature consistency is strengthened through neighborhood-expanded contrastive learning, and semantic weight calibration is employed to reconstruct the feature space, thereby suppressing the negative transfer effect. Finally, extensive experiments under multiple operating conditions on rolling bearing and reciprocating mechanism datasets demonstrate that the proposed method excels in addressing source-free fault diagnosis problems for mechanical equipment and shows promising potential for practical engineering applications in fault classification tasks. Full article

Some large language models (LLMs) are open source and are therefore fully open for scientific study. However, many LLMs are proprietary, and their internals are hidden, which hinders the ability of the research community to study their behavior under controlled conditions. For instance, the token input embedding specifies an internal vector representation of each token used by the model. If the token input embedding is hidden, latent semantic information about the set of tokens is unavailable to researchers. This article presents a general and flexible method for prompting an LLM to reveal its token input embedding, even if this information is not published with the model. Moreover, this article provides strong theoretical justification—a mathematical proof for generic LLMs—for why this method should be expected to work. If the LLM can be prompted systematically and certain benign conditions about the quantity of data collected from the responses are met, the topology of the token embedding is recovered. With this method in hand, we demonstrate its effectiveness by recovering the token subspace of the Llemma-7BLLM. We demonstrate the flexibility of this method by performing the recovery at three different times, each using the same algorithm applied to different information collected from the responses. While the prompting can be a performance bottleneck depending on the size and complexity of the LLM, the recovery runs within a few hours on a typical workstation. The results of this paper apply not only to LLMs but also to general nonlinear autoregressive processes. Full article

This paper addresses the challenge of segmenting consumer behavior in contexts characterized by both numerical regularities and semantic variability. Traditional models, such as RFM-based segmentation, capture the transactional dimension but neglect the implicit meanings expressed through product descriptions, reviews, and linguistic diversity. To overcome this gap, we propose a hybrid clustering algorithm that integrates numerical and semantic distances within a unified scalar framework. The central element is a scalar objective function that combines Euclidean distance in the RFM space with cosine dissimilarity in the semantic embedding space. A continuous parameter λ regulates the relative influence of each component, allowing the model to adapt granularity and balance interpretability across heterogeneous data. Optimization is performed through a dual strategy: gradient descent ensures convergence in the numerical subspace, while genetic operators enable a broader exploration of semantic structures. This combination supports both computational stability and semantic coherence. The method is validated on a large-scale multilingual dataset of transactional records, covering five culturally distinct markets. Results indicate systematic improvements over classical approaches, with higher Silhouette scores, lower Davies–Bouldin values, and stronger intra-cluster semantic consistency. Beyond numerical performance, the proposed framework produces intelligible and culturally adaptable clusters, confirming its relevance for personalized decision-making. The contribution lies in advancing a scalarized formulation and hybrid optimization strategy with wide applicability in scenarios where numerical and textual signals must be analyzed jointly. Full article

Unsupervised representation learning has emerged as a promising paradigm in machine learning, owing to its capacity to extract semantically meaningful features from unlabeled data. Despite recent progress, however, such methods remain vulnerable to collapse phenomena, wherein the expressiveness and diversity of learned representations are severely degraded. This phenomenon poses significant challenges to both model performance and generalizability. This paper presents a systematic investigation into two distinct forms of collapse: complete collapse and dimensional collapse. Complete collapse typically arises in non-contrastive frameworks, where all learned representations converge to trivial constants, thereby rendering the learned feature space non-informative. While contrastive learning has been introduced as a principled remedy, recent empirical findings indicate that it falls to prevent collapse entirely. In particular, contrastive methods are still susceptible to dimensional collapse, where representations are confined to a narrow subspace, thus restricting both the information content and effective dimensionality. To address these concerns, we conduct a comprehensive literature analysis encompassing theoretical definitions, underlying causes, and mitigation strategies for each collapse type. We further categorize recent approaches to collapse prevention, including feature decorrelation techniques, eigenvalue distribution regularization, and batch-level statistical constraints, and assess their effectiveness through a comparative framework. This work aims to establish a unified conceptual foundation for understanding collapse in unsupervised learning and to guide the design of more robust representation learning algorithms. Full article

Graph convolutional networks (GCNs) have demonstrated remarkable effectiveness in processing graph-structured data and have been widely adopted across various domains. Existing methods mitigate over-smoothing through selective aggregation strategies such as attention mechanisms, edge dropout, and neighbor sampling. While some approaches incorporate global structural context, they often underexplore category-aware representations and inter-category differences, which are crucial for enhancing node discriminability. To address these limitations, a novel framework, CA-NodeNet, is proposed for semi-supervised node classification. CA-NodeNet comprises three key components: (1) coarse-grained node feature learning, (2) category-decoupled multi-branch attention, and (3) inter-category difference feature learning. Initially, a GCN-based encoder is employed to aggregate neighborhood information and learn coarse-grained representations. Subsequently, the category-decoupled multi-branch attention module employs a hierarchical multi-branch architecture, in which each branch incorporates category-specific attention mechanisms to project coarse-grained features into disentangled semantic subspaces. Furthermore, a layer-wise intermediate supervision strategy is adopted to facilitate the learning of discriminative category-specific features within each branch. To further enhance node feature discriminability, we introduce an inter-category difference feature learning module. This module first encodes pairwise differences between the category-specific features obtained from the previous stage and then integrates complementary information across multiple feature pairs to refine node representations. Finally, we design a dual-component optimization function that synergistically combines intermediate supervision loss with the final classification objective, encouraging the network to learn robust and fine-grained node representations. Extensive experiments on multiple real-world benchmark datasets demonstrate the superior performance of CA-NodeNet over existing state-of-the-art methods. Ablation studies further validate the effectiveness of each module in contributing to overall performance gains. Full article

Semantic change detection technology based on remote sensing data holds significant importance for urban and rural planning decisions and the monitoring of ground objects. However, simple convolutional networks are limited by the receptive field, cannot fully capture detailed semantic information, and cannot effectively perceive subtle changes and constrain edge information. Therefore, a dynamic graph reasoning network with layer-by-layer semantic decomposition for semantic change detection in remote sensing data is developed in response to these limitations. This network aims to understand and perceive subtle changes in the semantic content of remote sensing data from the image pixel level. On the one hand, low-level semantic information and cross-scale spatial local feature details are obtained by dividing subspaces and decomposing convolutional layers with significant kernel expansion. Semantic selection aggregation is used to enhance the characterization of global and contextual semantics. Meanwhile, the initial multi-scale local spatial semantics are screened and re-aggregated to improve the characterization of significant features. On the other hand, at the encoding stage, the weight-sharing approach is employed to align the positions of ground objects in the change area and generate more comprehensive encoding information. Meanwhile, the dynamic graph reasoning module is used to decode the encoded semantics layer by layer to investigate the hidden associations between pixels in the neighborhood. In addition, the edge constraint module is used to constrain boundary pixels and reduce semantic ambiguity. The weighted loss function supervises and optimizes each module separately to enable the network to acquire the optimal feature representation. Finally, experimental results on three open-source datasets, such as SECOND, HIUSD, and Landsat-SCD, show that the proposed method achieves good performance, with an SCD score reaching 35.65%, 98.33%, and 67.29%, respectively. Full article

Gait recognition, as a non-contact biometric technology, offers unique advantages in scenarios requiring long-distance identification without active cooperation from subjects. However, existing gait recognition methods predominantly rely on single-modal data, which demonstrates insufficient feature expression capabilities when confronted with complex factors in real-world environments, including viewpoint variations, clothing differences, occlusion problems, and illumination changes. This paper addresses these challenges by introducing a multi-modal gait recognition network based on channel shuffle regulation and spatial-frequency joint learning, which integrates two complementary modalities (silhouette data and heatmap data) to construct a more comprehensive gait representation. The channel shuffle-based feature selective regulation module achieves cross-channel information interaction and feature enhancement through channel grouping and feature shuffling strategies. This module divides input features along the channel dimension into multiple subspaces, which undergo channel-aware and spatial-aware processing to capture dependency relationships across different dimensions. Subsequently, channel shuffling operations facilitate information exchange between different semantic groups, achieving adaptive enhancement and optimization of features with relatively low parameter overhead. The spatial-frequency joint learning module maps spatiotemporal features to the spectral domain through fast Fourier transform, effectively capturing inherent periodic patterns and long-range dependencies in gait sequences. The global receptive field advantage of frequency domain processing enables the model to transcend local spatiotemporal constraints and capture global motion patterns. Concurrently, the spatial domain processing branch balances the contributions of frequency and spatial domain information through an adaptive weighting mechanism, maintaining computational efficiency while enhancing features. Experimental results demonstrate that the proposed GaitCSF model achieves significant performance improvements on mainstream datasets including GREW, Gait3D, and SUSTech1k, breaking through the performance bottlenecks of traditional methods. The implications of this research are significant for improving the performance and robustness of gait recognition systems when implemented in practical application scenarios. Full article

Currently, deep learning networks based on architectures such as CNN and Transformer have achieved significant advances in remote sensing image change detection, effectively addressing the issue of false changes due to spectral and radiometric discrepancies. However, when handling remote sensing image data from multiple sensors, different viewing angles, and extended periods, these models show limitations in modelling dynamic interactions and feature representations in change regions, restricting their ability to model the integrity and precision of irregular change areas. We propose the Context-Aware Global-Local Subspace Attention Change Detection Network (CGLCS-Net) to resolve these issues and introduce the Global-Local Context-Aware Selector (GLCAS) and the Subspace-based Self-Attention Fusion (SSAF) module. GLCAS dynamically selects receptive fields at different feature extraction stages through a joint pooling attention mechanism and depthwise separable convolution, enhancing global context and local feature extraction capabilities and improving feature representation for multi-scale and irregular change regions. The SSAF module establishes dynamic interactions between dual-temporal features via feature decomposition and self-attention mechanisms, focusing on semantic change areas to address challenges such as sensor viewpoint variations and the texture and spectral inconsistencies caused by long periods. Compared to ChangeFormer, CGLCS-Net achieved improvements in the IoU metric of 0.95%, 9.23%, and 13.16% on the three public datasets, i.e., LEVIR-CD, SYSU-CD, and S2Looking, respectively. Additionally, it reduced model parameters by 70.05%, floating-point operations by 7.5%, and inference time by 11.5%. These improvements enhance its applicability for continuous land use and land cover change monitoring. Full article

Travel mode identification (TMI) plays a crucial role in intelligent transportation systems by accurately identifying travel modes from Global Positioning System (GPS) trajectory data. Given that trajectory data inherently exhibit spatial and kinematic patterns that complement each other, recent TMI methods generally combine these characteristics through image-based projections or direct concatenation. However, such approaches achieve only shallow fusion of these two types of features and cannot effectively align them into a shared latent space. To overcome this limitation, we introduce multi-view contrastive fusion (MVCF)-TMI, a novel TMI framework that enhances identification accuracy and model generalizability by aligning spatial and kinematic views through multi-view contrastive learning. Our framework employs multi-view learning to separately extract spatial and kinematic features, followed by an inter-view contrastive loss to optimize feature alignment in a shared subspace. This approach enables cross-view semantic understanding and better captures complementary information across different trajectory representations. Extensive experiments show that MVCF-TMI outperforms baseline methods, achieving 86.45% accuracy on the GeoLife dataset. The model also demonstrates strong generalization by transferring knowledge from pretraining on the large-scale GeoLife dataset to the smaller SHL dataset. Full article

Assume that A, $A_1$, and $A_2$ are three selfadjoint linear relations (multi-valued linear operators) in a certain complex Hilbert space. In this study, conditions are presented for the multi-valued operator equality $A=A_1{A}_2$ to hold when the inclusion $A\subset A_1{A}_2$ is assumed to be satisfied. The present study is strongly motivated by the invalidity of a classical result from A. Devinatz, A. E. Nussbaum, and J. von Neumann in the general case of selfadjoint linear relations. Two types of conditions for the aforementioned equality to hold are presented. Firstly, a condition is given in terms of the resolvent sets of the involved objects, which does not depend on the product structure of the right-hand side, $A_1{A}_2$. Secondly, a condition is also presented where the structure of the right-hand side is taken into account. This one is based on the notion of the $\mathfrak{L}$-stability of a linear operator under linear subspaces. It should be mentioned that the classical Devinatz–Nussbaum–von Neumann theorem is obtained as a particular case of one of the main results. Full article

Non-negative Matrix Factorization (NMF) has gained popularity due to its effectiveness in clustering and feature selection tasks. It is particularly valuable for managing high-dimensional data by reducing dimensionality and providing meaningful semantic representations. However, traditional NMF methods may encounter challenges when dealing with noisy data, outliers, or when the underlying manifold structure of the data is overlooked. This paper introduces an innovative approach called SGRiT, which employs Stiefel manifold optimization to enhance the extraction of latent features. These learned features have been shown to be highly informative for clustering tasks. The method leverages a spectral decomposition criterion to obtain a low-dimensional embedding that captures the intrinsic geometric structure of the data. Additionally, this paper presents a solution for addressing the Stiefel manifold problem and utilizes a Riemannian-based trust region algorithm to optimize the loss function. The outcome of this optimization process is a new representation of the data in a transformed space, which can subsequently serve as input for the NMF algorithm. Furthermore, this paper incorporates a novel subspace graph regularization term that considers high-order geometric information and introduces a sparsity term for the factor matrices. These enhancements significantly improve the discrimination capabilities of the learning process. This paper conducts an impartial analysis of several essential NMF algorithms. To demonstrate that the proposed approach consistently outperforms other benchmark algorithms, four clustering evaluation indices are employed. Full article