We study the convergence rate of first-order methods for rectangular matrix factorization, which is a canonical nonconvex optimization problem. Specifically, given a rank-$r$ matrix $\mathbf{A}\in\mathbb{R}^{m\times n}$, we prove that gradient descent (GD) can find a pair of $\epsilon$-optimal solutions $\mathbf{X}_T\in\mathbb{R}^{m\times d}$ and $\mathbf{Y}_T\in\mathbb{R}^{n\times d}$, where $d\geq r$, satisfying $\lVert\mathbf{X}_T\mathbf{Y}_T^\top-\mathbf{A}\rVert_\mathrm{F}\leq\epsilon\lVert\mathbf{A}\rVert_\mathrm{F}$ in $T=O(\kappa^2\log\frac{1}{\epsilon})$ iterations with high probability, where $\kappa$ denotes the condition number of $\mathbf{A}$. Furthermore, we prove that Nesterov's accelerated gradient (NAG) attains an iteration complexity of $O(\kappa\log\frac{1}{\epsilon})$, which is the best-known bound of first-order methods for rectangular matrix factorization. Different from small balanced random initialization in the existing literature, we adopt an unbalanced initialization, where $\mathbf{X}_0$ is large and $\mathbf{Y}_0$ is $0$. Moreover, our initialization and analysis can be further extended to linear neural networks, where we prove that NAG can also attain an accelerated linear convergence rate. In particular, we only require the width of the network to be greater than or equal to the rank of the output label matrix. In contrast, previous results achieving the same rate require excessive widths that additionally depend on the condition number and the rank of the input data matrix.

In the field of autonomous driving or robotics, simultaneous localization and mapping (SLAM) and multi-object tracking (MOT) are two fundamental problems and are generally applied separately. Solutions to SLAM and MOT usually rely on certain assumptions, such as the static environment assumption for SLAM and the accurate ego-vehicle pose assumption for MOT. But in complex dynamic environments, it is difficult or even impossible to meet these assumptions. Therefore, the SLAMMOT, i.e., simultaneous localization, mapping, and moving object tracking, integrated system of SLAM and object tracking, has emerged for autonomous vehicles in dynamic environments. However, many conventional SLAMMOT solutions directly perform data association on the predictions and detections for object tracking, but ignore their quality. In practice, inaccurate predictions caused by continuous multi-frame missed detections in temporary occlusion scenarios, may degrade the performance of tracking, thereby affecting SLAMMOT. To address this challenge, this paper presents a LiDAR SLAMMOT based on confidence-guided data association (Conf SLAMMOT) method, which tightly couples the LiDAR SLAM and the confidence-guided data association based multi-object tracking into a graph optimization backend for estimating the state of the ego-vehicle and objects simultaneously. The confidence of prediction and detection are applied in the factor graph-based multi-object tracking for its data association, which not only avoids the performance degradation caused by incorrect initial assignments in some filter-based methods but also handles issues such as continuous missed detection in tracking while also improving the overall performance of SLAMMOT. Various comparative experiments demonstrate the superior advantages of Conf SLAMMOT, especially in scenes with some missed detections.

Full waveform inversion (FWI) is able to construct high-resolution subsurface models by iteratively minimizing discrepancies between observed and simulated seismic data. However, its implementation can be rather involved for complex wave equations, objective functions, or regularization. Recently, automatic differentiation (AD) has proven to be effective in simplifying solutions of various inverse problems, including FWI. In this study, we present an open-source AD-based FWI framework (ADFWI), which is designed to simplify the design, development, and evaluation of novel approaches in FWI with flexibility. The AD-based framework not only includes forword modeling and associated gradient computations for wave equations in various types of media from isotropic acoustic to vertically or horizontally transverse isotropic elastic, but also incorporates a suite of objective functions, regularization techniques, and optimization algorithms. By leveraging state-of-the-art AD, objective functions such as soft dynamic time warping and Wasserstein distance, which are difficult to apply in traditional FWI are also easily integrated into ADFWI. In addition, ADFWI is integrated with deep learning for implicit model reparameterization via neural networks, which not only introduces learned regularization but also allows rapid estimation of uncertainty through dropout. To manage high memory demands in large-scale inversion associated with AD, the proposed framework adopts strategies such as mini-batch and checkpointing. Through comprehensive evaluations, we demonstrate the novelty, practicality and robustness of ADFWI, which can be used to address challenges in FWI and as a workbench for prompt experiments and the development of new inversion strategies.

High-dimensional vectors have been proposed as a neural method for representing information in the brain using Vector Symbolic Algebras (VSAs). While previous work has explored decoding and cleaning up these vectors under the noise that arises during computation, existing methods are limited. Cleanup methods are essential for robust computation within a VSA. However, cleanup methods for continuous-value encodings are not as effective. In this paper, we present an iterative optimization method to decode and clean up Fourier Holographic Reduced Representation (FHRR) vectors that are encoding continuous values. We combine composite likelihood estimation (CLE) and maximum likelihood estimation (MLE) to ensure convergence to the global optimum. We also demonstrate that this method can effectively decode FHRR vectors under different noise conditions, and show that it outperforms existing methods.

Skin cancer (SC) stands out as one of the most life-threatening forms of cancer, with its danger amplified if not diagnosed and treated promptly. Early intervention is critical, as it allows for more effective treatment approaches. In recent years, Deep Learning (DL) has emerged as a powerful tool in the early detection and skin cancer diagnosis (SCD). Although the DL seems promising for the diagnosis of skin cancer, still ample scope exists for improving model efficiency and accuracy. This paper proposes a novel approach to skin cancer detection, utilizing optimization techniques in conjunction with pre-trained networks and wavelet transformations. First, normalized images will undergo pre-trained networks such as Densenet-121, Inception, Xception, and MobileNet to extract hierarchical features from input images. After feature extraction, the feature maps are passed through a Discrete Wavelet Transform (DWT) layer to capture low and high-frequency components. Then the self-attention module is integrated to learn global dependencies between features and focus on the most relevant parts of the feature maps. The number of neurons and optimization of the weight vectors are performed using three new swarm-based optimization techniques, such as Modified Gorilla Troops Optimizer (MGTO), Improved Gray Wolf Optimization (IGWO), and Fox optimization algorithm. Evaluation results demonstrate that optimizing weight vectors using optimization algorithms can enhance diagnostic accuracy and make it a highly effective approach for SCD. The proposed method demonstrates substantial improvements in accuracy, achieving top rates of 98.11% with the MobileNet + Wavelet + FOX and DenseNet + Wavelet + Fox combination on the ISIC-2016 dataset and 97.95% with the Inception + Wavelet + MGTO combination on the ISIC-2017 dataset, which improves accuracy by at least 1% compared to other methods.

Unmanned Aerial Vehicles (UAVs) are increasingly utilized in wireless communication, yet accurate channel loss prediction remains a significant challenge, limiting resource optimization performance. To address this issue, this paper leverages Artificial Intelligence Generated Content (AIGC) for the efficient construction of Channel Knowledge Maps (CKM) and UAV trajectory design. Given the time-consuming nature of channel data collection, AI techniques are employed in a Wasserstein Generative Adversarial Network (WGAN) to extract environmental features and augment the data. Experiment results demonstrate the effectiveness of the proposed framework in improving CKM construction accuracy. Moreover, integrating CKM into UAV trajectory planning reduces channel gain uncertainty, demonstrating its potential to enhance wireless communication efficiency.

Industrial networks are undergoing rapid transformation driven by the convergence of emerging technologies that are revolutionizing conventional workflows, enhancing operational efficiency, and fundamentally redefining the industrial landscape across diverse sectors. Amidst this revolution, Digital Twin (DT) emerges as a transformative innovation that seamlessly integrates real-world systems with their virtual counterparts, bridging the physical and digital realms. In this article, we present a comprehensive survey of the emerging DT-enabled services and applications across industries, beginning with an overview of DT fundamentals and its components to a discussion of key enabling technologies for DT. Different from literature works, we investigate and analyze the capabilities of DT across a wide range of industrial services, including data sharing, data offloading, integrated sensing and communication, content caching, resource allocation, wireless networking, and metaverse. In particular, we present an in-depth technical discussion of the roles of DT in industrial applications across various domains, including manufacturing, healthcare, transportation, energy, agriculture, space, oil and gas, as well as robotics. Throughout the technical analysis, we delve into real-time data communications between physical and virtual platforms to enable industrial DT networking. Subsequently, we extensively explore and analyze a wide range of major privacy and security issues in DT-based industry. Taxonomy tables and the key research findings from the survey are also given, emphasizing important insights into the significance of DT in industries. Finally, we point out future research directions to spur further research in this promising area.

Recent advances in dataset distillation have led to solutions in two main directions. The conventional batch-to-batch matching mechanism is ideal for small-scale datasets and includes bi-level optimization methods on models and syntheses, such as FRePo, RCIG, and RaT-BPTT, as well as other methods like distribution matching, gradient matching, and weight trajectory matching. Conversely, batch-to-global matching typifies decoupled methods, which are particularly advantageous for large-scale datasets. This approach has garnered substantial interest within the community, as seen in SRe$^2$L, G-VBSM, WMDD, and CDA. A primary challenge with the second approach is the lack of diversity among syntheses within each class since samples are optimized independently and the same global supervision signals are reused across different synthetic images. In this study, we propose a new Diversity-driven EarlyLate Training (DELT) scheme to enhance the diversity of images in batch-to-global matching with less computation. Our approach is conceptually simple yet effective, it partitions predefined IPC samples into smaller subtasks and employs local optimizations to distill each subset into distributions from distinct phases, reducing the uniformity induced by the unified optimization process. These distilled images from the subtasks demonstrate effective generalization when applied to the entire task. We conduct extensive experiments on CIFAR, Tiny-ImageNet, ImageNet-1K, and its sub-datasets. Our approach outperforms the previous state-of-the-art by 2$\sim$5% on average across different datasets and IPCs (images per class), increasing diversity per class by more than 5% while reducing synthesis time by up to 39.3% for enhancing the training efficiency. Code is available at: https://github.com/VILA-Lab/DELT.

A popular approach of automated mechanism design is to formulate a linear program (LP) whose solution gives a mechanism with desired properties. We analytically derive a class of optimal solutions for such an LP that gives mechanisms achieving standard properties of efficiency, incentive compatibility, strong budget balance (SBB), and individual rationality (IR), where SBB and IR are satisfied in expectation. Notably, our solutions are represented by an exponentially smaller number of essential variables than the original variables of LP. Our solutions, however, involve a term whose exact evaluation requires solving a certain optimization problem exponentially many times as the number of players, $N$, grows. We thus evaluate this term by modeling it as the problem of estimating the mean reward of the best arm in multi-armed bandit (MAB), propose a Probably and Approximately Correct estimator, and prove its asymptotic optimality by establishing a lower bound on its sample complexity. This MAB approach reduces the number of times the optimization problem is solved from exponential to $O(N\,\log N)$. Numerical experiments show that the proposed approach finds mechanisms that are guaranteed to achieve desired properties with high probability for environments with up to 128 players, which substantially improves upon the prior work.

Over the past few years, the federated learning ($\texttt{FL}$) community has witnessed a proliferation of new $\texttt{FL}$ algorithms. However, our understating of the theory of $\texttt{FL}$ is still fragmented, and a thorough, formal comparison of these algorithms remains elusive. Motivated by this gap, we show that many of the existing $\texttt{FL}$ algorithms can be understood from an operator splitting point of view. This unification allows us to compare different algorithms with ease, to refine previous convergence results and to uncover new algorithmic variants. In particular, our analysis reveals the vital role played by the step size in $\texttt{FL}$ algorithms. The unification also leads to a streamlined and economic way to accelerate $\texttt{FL}$ algorithms, without incurring any communication overhead. We perform numerical experiments on both convex and nonconvex models to validate our findings.