Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects' representation. More important, we lack an effective approach to capture such evolution from streaming data, which is common in real-world applications. To address these issues, we propose Streaming Factor Trajectory Learning (SFTL) for temporal tensor decomposition. We use Gaussian processes (GPs) to model the trajectory of factors so as to flexibly estimate their temporal evolution.

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems. In this work, we generalize optimized Schwarz domain decomposition methods to unstructured-grid problems, using Graph Convolutional Neural Networks (GCNNs) and unsupervised learning to learn optimal modifications at subdomain interfaces. A key ingredient in our approach is an improved loss function, enabling effective training on relatively small problems, but robust performance on arbitrarily large problems, with computational cost linear in problem size. The performance of the learned linear solvers is compared with both classical and optimized domain decomposition algorithms, for both structured-and unstructured-grid problems.

Thispaperproposes animplicit model-based multi-agent reinforcement learning method based onvalue decomposition methods. Under this method, agents can interact with thelearned virtual environment and evaluate thecurrent state value according to imagined future states in the latent space, making agents have the foresight. Our approach can be applied toanymulti-agent value decomposition method.

Value decomposition methods have gained popularity in the field of cooperative multi-agent reinforcement learning. However, almost all existing methods follow the principle of Individual Global Max (IGM) or its variants, which limits their problem-solving capabilities. To address this, we propose a dual self-awareness value decomposition framework, inspired by the notion of dual self-awareness in psychology, that entirely rejects the IGM premise. Each agent consists of an ego policy for action selection and an alter ego value function to solve the credit assignment problem. The value function factorization can ignore the IGM assumption by utilizing an explicit search procedure. On the basis of the above, we also suggest a novel anti-ego exploration mechanism to avoid the algorithm becoming stuck in a local optimum. As the first fully IGM-free value decomposition method, our proposed framework achieves desirable performance in various cooperative tasks.

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the \textit{optimal} construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems. In this work, we generalize optimized Schwarz domain decomposition methods to unstructured-grid problems, using Graph Convolutional Neural Networks (GCNNs) and unsupervised learning to learn optimal modifications at subdomain interfaces. A key ingredient in our approach is an improved loss function, enabling effective training on relatively small problems, but robust performance on arbitrarily large problems, with computational cost linear in problem size. The performance of the learned linear solvers is compared with both classical and optimized domain decomposition algorithms, for both structured-and unstructured-grid problems.

Abstract--The integration of advanced technologies, such as Artificial Intelligence (AI), into manufacturing processes is attracting significant attention, paving the way for the development of intelligent systems that enhance efficiency and automation. This paper uses the term "Gentelligent system" to refer to systems that incorporate inherent component information (akin to genes in bioinformatics--where manufacturing operations are likened to chromosomes in this study) and automated mechanisms. By implementing reliable fault detection methods, manufacturers can achieve several benefits, including improved product quality, increased yield, and reduced production costs. T o support these objectives, we propose a hybrid framework with a dominance-based multi-objective evolutionary algorithm. This mechanism enables simultaneous optimization of feature selection and classification performance by exploring Pareto-optimal solutions in a single run. This solution helps monitor various manufacturing operations, addressing a range of conflicting objectives that need to be minimized together . Manufacturers can leverage such predictive methods and better adapt to emerging trends. T o strengthen the validation of our model, we incorporate two real-world datasets from different industrial domains. The results on both datasets demonstrate the generalizability and effectiveness of our approach. ORE recently, manufacturing has embraced the Industrial Internet of Things (IIoT), where digital sensors, network technologies, and gentelligent components are integrated into manufacturing processes. A gentelligent component, as defined in the Collaborative Research Centre 653 project [1], refers to components that intrinsically store information. The focus of that work is on encoding and preserving data within physical parts throughout the product lifecycle. Inspired by this concept, we extend the notion into what we define as a "gentelligent system."

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an input tensor. We empirically show that Legendre decomposition can more accurately reconstruct tensors than other nonnegative tensor decomposition methods.

Tensor decomposition faces fundamental challenges in analyzing high-dimensional data, where traditional methods based on reconstruction and fixed-rank constraints often fail to capture semantically meaningful structures. This paper introduces a no-rank tensor decomposition framework grounded in metric learning, which replaces reconstruction objectives with a discriminative, similarity-based optimization. The proposed approach learns data-driven embeddings by optimizing a triplet loss with diversity and uniformity regularization, creating a feature space where distance directly reflects semantic similarity. We provide theoretical guarantees for the framework's convergence and establish bounds on its metric properties. Evaluations across diverse domains -- including face recognition (LFW, Olivetti), brain connectivity analysis (ABIDE), and simulated data (galaxy morphology, crystal structures) -- demonstrate that our method outperforms baseline techniques, including PCA, t-SNE, UMAP, and tensor decomposition baselines (CP and Tucker). Results show substantial improvements in clustering metrics (Silhouette Score, Davies-Bouldin Index, Calinski-Harabasz Index, Separation Ratio, Adjusted Rand Index, Normalized Mutual Information) and reveal a fundamental trade-off: while metric learning optimizes global class separation, it deliberately transforms local geometry to align with semantic relationships. Crucially, our approach achieves superior performance with smaller training datasets compared to transformer-based methods, offering an efficient alternative for domains with limited labeled data. This work establishes metric learning as a paradigm for tensor-based analysis, prioritizing semantic relevance over pixel-level fidelity while providing computational advantages in data-scarce scenarios.

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor decomposition methods require predefined ranks and iterative optimization, resulting in high computational costs and dependence on analyst expertise. This study proposes a novel tensor low-rank approximation method that eliminates both prior rank specification and iterative optimization. The method applies statistical singular value hard thresholding to each mode-wise unfolded matrix to automatically extract statistically significant components, effectively reducing noise while preserving the intrinsic structure. Theoretically, the optimal thresholds for each mode are derived from the asymptotic properties of the Marcenko-Pastur distribution. Simulation experiments demonstrate that the proposed method outperforms conventional approaches (HOSVD, HOOI, and Tucker-L2E) in both estimation accuracy and computational efficiency. These results indicate that the proposed approach provides a theoretically grounded, fully automatic, and non-iterative framework for tensor decomposition.