Recent text-to-image (T2I) diffusion models have demonstrated remarkable capabilities in visual synthesis, yet their performance heavily relies on the quality of input prompts. However, optimizing discrete prompts remains challenging because the discrete nature of tokens prevents the direct application of the gradient descent method and the vast search space of possible token combinations. As a result, existing approaches either suffer from quantization errors when employing continuous optimization techniques or be- come trapped in local optima due to coordinate-wise greedy search. In this paper, we propose STEPS, a novel Sequential probability Tensor Estimation approach for hard Prompt Search. Our method reformulates discrete prompt optimization as a sequential probability tensor estimation problem, leveraging the inherent low-rank characteristics to address the curse of dimensionality. To further improve the computational efficiency, we develop a memory-bounded sampling approach that shrinks the prompt space without the iteration step dependency while preserving sequential optimization dynamics. Extensive experiments on various public datasets demonstrate that our method consistently outperforms existing approaches in T2I generation, cross-model prompt transferability, and harmful prompt optimization, validating the effectiveness of the proposed framework.

Class-Incremental Learning (CIL) has gained considerable attention due to its capacity to accommodate new classes during learning. Replay-based methods demonstrate state-of-the-art performance in CIL but suffer from high memory consumption to save a set of old exemplars for revisiting. To address this challenge, many memory-efficient replay methods have been developed by exploiting image compression techniques. However, the gains are often bittersweet when pixel-level compression methods are used. Here, we present a simple yet efficient approach that employs tensor decomposition to address these limitations. This method fully exploits the low intrinsic dimensionality and pixel correlation of images to achieve high compression efficiency while preserving sufficient discriminative information, significantly enhancing performance. We also introduce a hybrid exemplar selection strategy to improve the representativeness and diversity of stored exemplars. Extensive experiments across datasets with varying resolutions consistently demonstrate that our approach substantially boosts the performance of baseline methods, showcasing strong generalization and robustness.

Tensor regression is a powerful tool for analyzing complex multi-dimensional data in fields such as neuroimaging and spatiotemporal analysis, but its effectiveness is often hindered by insufficient sample sizes. To overcome this limitation, we adopt a transfer learning strategy that leverages knowledge from related source tasks to improve performance in data-scarce target tasks. This approach, however, introduces additional challenges including model shifts, covariate shifts, and decentralized data management. We propose the Low-Rank Tensor Transitions (LoRT) framework, which incorporates a novel fusion regularizer and a two-step refinement to enable robust adaptation while preserving low-tubal-rank structure. To support decentralized scenarios, we extend LoRT to D-LoRT, a distributed variant that maintains statistical efficiency with minimal communication overhead. Theoretical analysis and experiments on tensor regression tasks, including compressed sensing and completion, validate the robustness and versatility of the proposed methods. These findings indicate the potential of LoRT as a robust method for tensor regression in settings with limited data and complex distributional structures.

As the length of input text increases, the key-value (KV) cache in LLMs imposes prohibitive GPU memory costs and limits long-context inference on resource constrained devices. Existing approaches, such as KV quantization and pruning, reduce memory usage but suffer from numerical precision loss or suboptimal retention of key-value pairs. In this work, Low Rank Query and Key attention (LRQK) is introduced, a two-stage framework that jointly decomposes full-precision query and key matrices into compact rank-\(r\) factors during the prefill stage, and then employs these low-dimensional projections to compute proxy attention scores in \(\mathcal{O}(lr)\) time at each decode step. By selecting only the top-\(k\) tokens and a small fixed set of recent tokens, LRQK employs a mixed GPU-CPU cache with a hit-and-miss mechanism where only missing full-precision KV pairs are transferred, thereby preserving exact attention outputs while reducing CPU-GPU data movement. Extensive experiments on the RULER and LongBench benchmarks with LLaMA-3-8B and Qwen2.5-7B demonstrate that LRQK matches or surpasses leading sparse-attention methods in long context settings, while delivering significant memory savings with minimal accuracy loss. Our code is available at \url{https://github.com/tenghuilee/LRQK}.

Despite the growing success of transform-based tensor models such as the t-product, their underlying geometric principles remain poorly understood. Classical differential geometry, built on real-valued function spaces, is not well suited to capture the algebraic and spectral structure induced by transform-based tensor operations. In this work, we take an initial step toward a geometric framework for tensors equipped with tube-wise multiplication via orthogonal transforms. We introduce the notion of smooth t-manifolds, defined as topological spaces locally modeled on structured tensor modules over a commutative t-scalar ring. This formulation enables transform-consistent definitions of geometric objects, including metrics, gradients, Laplacians, and geodesics, thereby bridging discrete and continuous tensor settings within a unified algebraic-geometric perspective. On this basis, we develop a statistical procedure for testing whether tensor data lie near a low-dimensional t-manifold, and provide nonasymptotic guarantees for manifold fitting under noise. We further establish approximation bounds for tensor neural networks that learn smooth functions over t-manifolds, with generalization rates determined by intrinsic geometric complexity. This framework offers a theoretical foundation for geometry-aware learning in structured tensor spaces and supports the development of models that align with transform-based tensor representations.

Giant AI models, typically trained and deployed centrally in the cloud, demand significant computational resources, posing privacy risks for the Internet of Things (IoT), particularly in the era of 6G-driven connectivity. federated learning (FL) mitigates this by enabling local training and server-side aggregation, fostering 6G Symbiotic IoT while preserving privacy in 6G networks. However, data heterogeneity (DH) in multimodal settings remains a formidable challenge, degrading model performance. While prior studies attribute DH to uneven data distributions, our empirical analysis reveals that hard samples also drive DH, manifesting across both local and global models. To address this, we propose MCMFL, a multimodal FL framework leveraging Monte Carlo dropout to quantify sample uncertainty and identify hard samples. Exploiting 6G’s excellent capabilities, MCMFL optimizes the local loss function and introduces MC dropout-based aggregation, a robust aggregation algorithm, enhancing the model’s resilience to hard samples. Extensive experiments show that MCMFL demonstrates superior performance, outperforming baseline aggregation methods by up to 5.38% on CIFAR-100, leading local enhancement baselines by 3.14% on TinyImageNet-200 and achieving the highest score of 4.79 in MTBenchmark for large language model. By shifting the focus from data distribution to sample-level uncertainty, MCMFL provides a novel framework for deploying large AI models via FL in IoT scenarios, mitigating the critical challenge of DH and enhancing model robustness.

Amid a rapidly evolving information era, large-scale multimodal knowledge discovery in computational social systems emerges as a key research domain. Large language models (LLMs) play a crucial role in this field, providing contextual understanding and task adaptability. Yet, centralized training of LLM raises privacy concerns. Federated learning (FL) offers a distributed alternative, but it struggles with data heterogeneity and security issues related to model parameters. To this end, we propose a robust aggregation method that leverages the relative total distance of models to improve global model performance in heterogeneous settings, complemented by Cheon-Kim-Kim-Song (CKKS) encryption to secure parameters against parameter stealing without performance loss. Extensive numeric results show our approach excels in LLM testing, scoring 3.74 on MTBenchmark and 8.17 on Vicuna, outperforming state-of-the-art FL methods against data heterogeneity challenges. It also achieves consistent gains on image datasets such as SVHN, CIFAR10, MNIST, TinyImageNet200, and CIFAR100, TinyImageNet200. In summary, our method offers an effective solution for secure multimodal data analysis in computational social systems.

The recently proposed tensor tubal rank has been witnessed to obtain extraordinary success in real-world tensor data completion. However, existing works usually fix the transform orientation along the third mode and may fail to turn multidimensional low-tubal-rank structure into account. To alleviate these bottlenecks, we introduce two unfolding induced tensor nuclear norms (TNNs) for the tensor completion (TC) problem, which naturally extends tensor tubal rank to high-order data. Specifically, we show how multidimensional low-tubal-rank structure can be captured by utilizing a novel balanced unfolding strategy, upon which two TNNs, namely, overlapped TNN (OTNN) and latent TNN (LTNN), are developed. We also show the immediate relationship between the tubal rank of unfolding tensor and the existing tensor network (TN) rank, e.g., CANDECOMP/PARAFAC (CP) rank, Tucker rank, and tensor ring (TR) rank, to demonstrate its efficiency and practicality. Two efficient TC models are then proposed with theoretical guarantees by analyzing a unified nonasymptotic upper bound. To solve optimization problems, we develop two alternating direction methods of multipliers (ADMM) based algorithms. The proposed models have been demonstrated to exhibit superior performance based on experimental findings involving synthetic and real-world tensors, including facial images, light field images, and video sequences.

Conventional Outlier Robust Tensor Decomposition (ORTD) approaches generally represent sparse outlier corruption within a specific mode. However, such an assumption, which may hold for matrices, proves inadequate when applied to high-order tensors. In the tensor domain, the outliers are prone to be corrupted in multiple modes simultaneously. Addressing this limitation, this study proposes a novel ORTD approach by recovering low-rank tensors contaminated by outliers spanning multiple modes. In particular, we conceptualize outliers within high-order tensors as latent tensor group sparsity by decomposing the corrupted tensor into a sum of multiple latent components, where each latent component is exclusive to outliers within a particular direction. Thus, it can effectively mitigate the outlier corruptions prevalent in high-order tensors across multiple modes. To theoretically guarantee recovery performance, we rigorously analyze a non-asymptotic upper bound of the estimation error for the proposed ORTD approach. In the optimization process, we develop an efficient alternate direction method of multipliers (ADMM) algorithm. Empirical validation of the approach's efficacy is undertaken through comprehensive experimentation.

Deep Multi-view Clustering (DMVC) stands out as a widely adopted technique aiming at enhanced clustering performance by leveraging diverse data sources. However, the critical issue of vulnerability to adversarial attacks is unexplored due to the lack of well-defined attack objectives. To fill this crucial gap, this paper is the first work to investigate the possibility of adversarial attacks on DMVC models. Specifically, we introduce an adversarial attack with Generative Adversarial Networks (GANs) with the aim to maximally change the complementarity and consistency of multiple views, thus leading to wrong clustering. Building upon this adversarial context, in the realm of defense, we propose a novel Adversarially Robust Deep Multi-View Clustering by leveraging adversarial training. Based on the analysis from an information-theoretic perspective, we design an Attack Mitigator that provides a foundation to guarantee the adversarial robustness of our DMVC models. Experiments conducted on multi-view datasets confirmed that our attack framework effectively reduces the clustering performance of the target model. Furthermore, our proposed adversarially robust method is also demonstrated to be an effective defense against such attacks. This work is a pioneer in exploring adversarial threats and advancing both theoretical understanding and practical strategies for robust multi-view clustering. Code is available at https://github.com/libertyhhn/AR-DMVC.

In multi-output regression, we identify a previously neglected challenge that arises from the inability of training distribution to cover all combinations of input features, leading to combinatorial distribution shift (CDS). To the best of our knowledge, this is the first work to formally define and address this problem. We tackle it through a novel tensor decomposition perspective, proposing the Functional t-Singular Value Decomposition (Ft-SVD) theorem which extends the classical tensor SVD to infinite and continuous feature domains, providing a natural tool for representing and analyzing multi-output functions. Within the Ft-SVD framework, we formulate the multi-output regression problem under CDS as a low-rank tensor estimation problem under the missing not at random (MNAR) setting, and introduce a series of assumptions about the true functions, training and testing distributions, and spectral properties of the ground-truth embeddings, making the problem more tractable. To address the challenges posed by CDS in multi-output regression, we develop a tailored Double-Stage Empirical Risk Minimization (ERM-DS) algorithm that leverages the spectral properties of the embeddings and uses specific hypothesis classes in each frequency component to better capture the varying spectral decay patterns. We provide rigorous theoretical analyses that establish performance guarantees for the ERM-DS algorithm. This work lays a preliminary theoretical foundation for multi-output regression under CDS.

Recently, fusing low-resolution hyperspectral images (LR-HSIs) with high-resolution multispectral images (HR-MSIs) to obtain high-resolution HSI (HR-HSI) has become an emerging study. In this letter, Bayesian nonlocal canonical polyadic (CP) factorization (BNCPF) is proposed for fusing LR-HSI with HR-MSI, which applies CP factorization on the nonlocal tensors of HR-HSI. Compared with the vanilla scheme of applying CP factorization on HR-HSI, the nonlocal tensors reveal balanced low-rank properties along different modes, and thus CP factorization can better capture their intrinsic low-rankness. To avoid the immense CP-ranks selection on the nonlocal tensors, we develop a sparse Bayesian framework for automatic rank determination. For parameters estimation, we adopt the alternating direction method of multipliers (ADMMs) for the maximum a posteriori (MAP) estimator optimization. Experimental results verify the superiority and rank-robustness of the proposed method.

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries are noise-free to provide a theoretical guarantee of exact recovery of missing entries, which is quite restrictive in practice. To remedy such drawback, this article proposes a novel noisy tensor completion model, which complements the incompetence of existing works in handling the degeneration of high-order and noisy observations. Specifically, the tensor ring nuclear norm (TRNN) and least-squares estimator are adopted to regularize the underlying tensor and the observed entries, respectively. In addition, a nonasymptotic upper bound of estimation error is provided to depict the statistical performance of the proposed estimator. Two efficient algorithms are developed to solve the optimization problem with convergence guarantee, one of which is specially tailored to handle large-scale tensors by replacing the minimization of TRNN of the original tensor equivalently with that of a much smaller one in a heterogeneous tensor decomposition framework. Experimental results on both synthetic and real-world data demonstrate the effectiveness and efficiency of the proposed model in recovering noisy incomplete tensor data compared with state-of-the-art tensor completion models.

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observations with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the methods using the TR model either require a preassigned TR rank or aggressively pursue the minimum TR rank, where the latter often leads to biased solutions in the presence of noise. To tackle these bottlenecks, a Bayesian robust TR decomposition (BRTR) method is proposed to give a more accurate solution for the RTC problem, which can avoid exquisite selection of the TR rank and penalty parameters. A variational Bayesian (VB) algorithm is developed to infer the probability distribution of posteriors. During the learning process, BRTR can prune off zero components of core tensors, resulting in automatic TR rank determination. Extensive experiments show that BRTR can achieve significantly improved performance than other state-of-the-art methods.

Driving anomaly detection is important for advanced driver assistance systems (ADAS) to increase driving safety and avoid traffic accidents. However, driving anomaly detection faces many challenges such as numerous and uncertain abnormal patterns observed on the road, sparsity of real anomaly cases documented with accurate labels, and rigid existing systems that rely on manually set thresholds and rules. Previous studies have proposed unsupervised methods for driving anomaly detection in the driver’s behaviors or the road condition by identifying deviations from normal driving conditions. A challenge with unsupervised models is the lack of interpretability, where the cause of the anomaly is not always clear. We address this problem with an example-based query method that combines unsupervised anomaly detection methods with the multi-label k-nearest neighbors (ML-KNN) algorithm to interpret the detected driving anomalies by identifying their possible causes (e.g., surrounding objects or driver’s errors). Our approach relies on a few manually labeled driving segments that are efficiently used as anchors to retrieve the causes of driving anomalies in a given driving segment. These anchors are projected into the embedding created by unsupervised driving anomaly detection systems. The experimental results show that this method can effectively identify the causes of driving anomalies, even for abnormal driving segments triggered by multiple causes. The evaluation shows the flexibility of our proposed solution, where we successfully implement the ML-KNN approach with three alternative feature representations.

Tensor-ring (TR) decomposition is a powerful tool for exploiting the low-rank property of multiway data and has been demonstrated great potential in a variety of important applications. In this article, non-negative TR (NTR) decomposition and graph-regularized NTR (GNTR) decomposition are proposed. The former equips TR decomposition with the ability to learn the parts-based representation by imposing non-negativity on the core tensors, and the latter additionally introduces a graph regularization to the NTR model to capture manifold geometry information from tensor data. Both of the proposed models extend TR decomposition and can be served as powerful representation learning tools for non-negative multiway data. The optimization algorithms based on an accelerated proximal gradient are derived for NTR and GNTR. We also empirically justified that the proposed methods can provide more interpretable and physically meaningful representations. For example, they are able to extract parts-based components with meaningful color and line patterns from objects. Extensive experimental results demonstrated that the proposed methods have better performance than state-of-the-art tensor-based methods in clustering and classification tasks.

Despite the recent advancement in driver assistance systems, most existing solutions and partial automation systems such as SAE Level 2 driving automation systems assume that the driver is in the loop; the human driver must continuously monitor the driving environment. Frequent transition of maneuver control is expected between the driver and the car while using such automation in difficult traffic conditions. In this work, we aim to predict driver takeover timing in order for the system to prepare transition from automation to driver control. While previous studies indicated that eye gaze is an important cue to predict driver takeover, we hypothesize that traffic condition as well as the reliability of the driving automation also have a strong impact. Therefore, we propose an algorithm that jointly consider the driver’s gaze information and contextual driving environment, which is complemented with the vehicle operational and driver physiological signals. Specifically, we consider joint embedding of traffic scene information and gaze behavior using 3DConvolutional Neural Network (3D-CNN). We demonstrate that our algorithm is successfully able to predict driver takeover intent, using user study data from 28 participants collected in simulated driving environments.

Modern advanced driver assistant systems (ADAS) rely on various types of sensors to monitor the vehicle status, driver's behaviors and road condition. The multimodal systems in the vehicle include sensors, such as accelerometers, pressure sensors, cameras, lidar and radars. When looking at a given scene with multiple modalities, there should be congruent in-formation among different modalities. Exploring the congruent information across modalities can lead to appealing solutions to create robust multimodal representations. This work proposes an unsupervised approach based on contrastive multiview coding (CMC) to capture the correlations in representations extracted from different modalities, learning a more discriminative rep-resentation space for unsupervised anomaly driving detection. We use CMC to train our model to extract view-invariant factors by maximizing the mutual information between mul-tiple representations from a given view, and increasing the distance of views from unrelated segments. We consider the vehicle driving data, driver's physiological data, and external environment data consisting of distances to nearby pedestrians, bicycles, and vehicles. The experimental results on the driving anomaly dataset (DAD) indicate that the CMC representation is effective for driving anomaly detection. The approach is efficient, scalable and interpretable, where the distances in the contrastive embedding for each view can be used to understand potential causes of the detected anomalies.

We make an attempt to understand convolutional neural network by exploring the relationship between (deep) convolutional neural networks and Volterra convolutions. We propose a novel approach to explain and study the overall characteristics of neural networks without being disturbed by the horribly complex architectures. Specifically, we attempt to convert the basic structures of a convolutional neural network (CNN) and their combinations to the form of Volterra convolutions. The results show that most of convolutional neural networks can be approximated in the form of Volterra convolution, where the approximated proxy kernels preserve the characteristics of the original network. Analyzing these proxy kernels may give valuable insight about the original network. Based on this setup, we present methods to approximate the order-zero and order-one proxy kernels, and verify the correctness and effectiveness of our results.

As the volume of real-world data with numerous missing entries continues to grow rapidly, tensor completion has been a powerful tool to enhance such flawed data analysis. While existing methods mainly consider static data, there is a great need to deal with streaming data. In this letter, a multi-aspect streaming tensor ring completion (MASTR) method is proposed, where the low-rank tensor ring (TR) model is exploited to capture subspace information and transfer high-order correlations between multiple sub-tensors. Experimental results on synthetic data, hyperspectral data and video data demonstrate superior recovery performance compared to state-of-the-art methods.

Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor recovery tasks. However, due to the large-scale tensor data in real-world applications, existing TRPCA models often suffer from high computational complexity. In this letter, we propose an efficient TRPCA under hybrid model of Tucker and TT. Specifically, in theory we reveal that TT nuclear norm (TTNN) of the original big tensor can be equivalently converted to that of a much smaller tensor via a Tucker compression format, thereby significantly reducing the computational cost of singular value decomposition (SVD). Numerical experiments on both synthetic and real-world tensor data verify the superiority of the proposed model.

Non-negative Tucker decomposition (NTD) is one of the most popular techniques for tensor data representation. To enhance the representation ability of NTD by multiple intrinsic cues, that is, manifold structure and supervisory information, in this article, we propose a generalized graph regularized NTD (GNTD) framework for tensor data representation. We first develop the unsupervised GNTD (UGNTD) method by constructing the nearest neighbor graph to maintain the intrinsic manifold structure of tensor data. Then, when limited must-link and cannot-link constraints are given, unlike most existing semisupervised learning methods that only use the pregiven supervisory information, we propagate the constraints through the entire dataset and then build a semisupervised graph weight matrix by which we can formulate the semisupervised GNTD (SGNTD). Moreover, we develop a fast and efficient alternating proximal gradient-based algorithm to solve the optimization problem and show its convergence and correctness. The experimental results on unsupervised and semisupervised clustering tasks using four image datasets demonstrate the effectiveness and high efficiency of the proposed methods.

Nonnegative Tucker Decomposition (NTD) is one of the most popular technique for feature extraction and representation from nonnegative tensor data with preserving internal structure information. From the perspective of geometry, highdimensional data are usually drawn in low-dimensional submanifold of the ambient space. In this paper, we propose a novel Graph reguralized Nonnegative Tucker Decomposition (GNTD) method which is able to extract the low-dimensional parts-based representation and preserve the geometrical information simultaneously from high-dimensional tensor data. We also present an effictive algorithm to solve the proposed GNTD model. Experimental results demonstrate the effectiveness and high efficiency of the proposed GNTD method.

New developments in advanced driver assistance systems (ADAS) can help drivers deal with risky driving maneuvers, preventing potential hazard scenarios. A key challenge in these systems is to determine when to intervene. While there are situations where the needs for intervention or feedback is clear (e.g., lane departure), it is often difficult to determine scenarios that deviate from normal driving conditions. These scenarios can appear due to errors by the drivers, presence of pedestrian or bicycles, or maneuvers from other vehicles. We formulate this problem as a driving anomaly detection, where the goal is to automatically identify cases that require intervention. Towards addressing this challenging but important goal, we propose a multimodal system that considers (1) physiological signals from the driver, and (2) vehicle information obtained from the controller area network (CAN) bus sensor. The system relies on conditional generative adversarial networks (GAN) where the models are constrained by the signals previously observed. The difference of the scores in the discriminator between the predicted and actual signals is used as a metric for detecting driving anomalies. We collected and annotated a novel dataset for driving anomaly detection tasks, which is used to validate our proposed models. We present the analysis of the results, and perceptual evaluations which demonstrate the discriminative power of this unsupervised approach for detecting driving anomalies.