Dynamic stability refers to the ability of a magnetic actuation system to maintain equilibrium by damping oscillations. It is typically quantified by physical scalars that serve as critical indicators of both safety and effectiveness in real-world applications. Traditional real-time assessment methods often require measuring and calibrating task-specific parameters. While feasible in principle, these approaches are hindered in practice by procedural complexity, time consumption, measurement difficulty, and uncertainties inherent to the non-contact, non-rigid nature of magnetic actuation. In this work, we eliminate the need for parameter assumptions and direct measurements, enabling a more efficient and generalizable evaluation of dynamic stability. Our approach implicitly incorporates uncertain physical properties into a learning-based framework. Specifically, we propose a temporal difference policy that predicts dynamic stability by comparing multiple time-varying sequences, thereby reducing the influence of task-specific parameters. The robustness and effectiveness are validated through extensive experiments, including baseline comparisons and online implementations across diverse magnetically actuated objects. Our findings highlight its practical advantages and pave the way for innovative control strategies in precise magnetic actuation applications.

Learning transferable data representations from abundant unlabeled data remains a central challenge in machine learning. Although numerous self-supervised learning methods have been proposed to address this challenge, a significant class of these approaches aligns the covariance or correlation matrix with the identity matrix. Despite impressive performance across various downstream tasks, these methods often suffer from biased sample risk, leading to substantial optimization shifts in mini-batch settings and complicating theoretical analysis. In this paper, we introduce a novel \underline{\bf Adv}ersarial \underline{\bf S}elf-\underline{\bf S}upervised Representation \underline{\bf L}earning (Adv-SSL) for unbiased transfer learning with no additional cost compared to its biased counterparts. Our approach not only outperforms the existing methods across multiple benchmark datasets but is also supported by comprehensive end-to-end theoretical guarantees. Our analysis reveals that the minimax optimization in Adv-SSL encourages representations to form well-separated clusters in the embedding space, provided there is sufficient upstream unlabeled data. As a result, our method achieves strong classification performance even with limited downstream labels, shedding new light on few-shot learning.

It is widely known that the error analysis for deep learning involves approximation, statistical, and optimization errors. However, it is challenging to combine them together due to overparameterization. In this paper, we address this gap by providing a comprehensive error analysis of the Deep Ritz Method (DRM). Specifically, we investigate a foundational question in the theoretical analysis of DRM under the overparameterized regime: given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision?

We propose SDORE, asemi-superviseddeep Sobolevregressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep ReQU neural networks to minimize the empirical risk with gradient norm regularization, allowing the approximation of the regularization term by unlabeled data. Our study includes a thorough analysis of the convergence rates of SDORE in$L^{2}$-norm, achieving the minimax optimality. Further, we establish a convergence rate for the associated plug-in gradient estimator, even in the presence of significant domain shift. These theoretical findings offer valuable insights for selecting regularization parameters and determining the size of the neural network, while showcasing the provable advantage of leveraging unlabeled data in semi-supervised learning. To the best of our knowledge, SDORE is the first provable neural network-based approach that simultaneously estimates the regression function and its gradient, with diverse applications such as nonparametric variable selection. The effectiveness of SDORE is validated through an extensive range of numerical simulations.

K-plane clustering (KPC), hyperplane clustering, and mixture regression all essentially fall within the same class of problems. This problem can be conceptualized as clustering in relatively high-dimensional K subspaces or K linear manifolds. Traditional KPC or fuzzy KPC models demonstrate a pronounced susceptibility to outliers, as they presuppose that the projection distance between data points and the plane normal vector adheres to the$L_{2}$distance. Meanwhile, the assumption of infinitely extending clusters adversely affects clustering performance. To solve these problems, this paper proposed a new robust fuzzy local k-plane clustering (RFLkPC) method that combines the mixture distance of hinge loss and$L_{1}$norm. The RFLkPC model assumes that each plane cluster is bounded to a finite area, which can flexibly and robustly handle plane clustering tasks with outliers or not. The corresponding model and optimization algorithms of RFLkPC were provided. Compared to other related models on this topic, a large number of experiments verify the efficiency of RFLkPC on simulated data and real data.

In this work, we investigate the utilization of deep approximate policy iteration (DAPI) in estimating the optimal action-value function within the context of reinforcement learning, employing rectified linear unit (ReLU) ResNet as the underlying framework. The iterative process of DAPI incorporates the minimax average Bellman error minimization principle. It employs ReLU ResNet to estimate the fixed point of the Bellman equation, which is aligned with the estimated greedy policy. Through error propagation, we derive nonasymptotic error bounds between and the estimated function induced by the output greedy policy in DAPI. To effectively control the Bellman residual error, we address both the statistical and approximation errors associated with the -mixing dependent data derived from Markov decision processes, using the techniques of empirical process and deep approximation theory, respectively. Furthermore, we present a novel generalization bound for ReLU ResNet in the presence of dependent data, as well as an approximation bound for ReLU ResNet within the Hölder class. Notably, this approximation bound contributes to a significant improvement in the dependence on the ambient dimension, transitioning from an exponential relationship to a polynomial one. The derived nonasymptotic error bounds explicitly depend on factors such as the sample size, the ambient dimension (in polynomial terms), and the width and depth of the neural networks. Consequently, these bounds serve as valuable theoretical guidelines for appropriately setting the hyperparameters, thereby enabling the achievement of the desired convergence rate during the training process of DAPI.

Understanding the power of parameterized quantum circuits (PQCs) in accomplishing machine learning tasks is one of the most important questions in quantum machine learning. In this paper, we focus on the PQC expressivity for general multivariate function classes. Previously established Universal Approximation Theorems for PQCs are either nonconstructive or assisted with parameterized classical data processing, making it hard to justify whether the expressive power comes from the classical or quantum parts. We explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions and establish the first non-asymptotic approximation error bounds for such functions in terms of the number of qubits, the quantum circuit depth and the number of trainable parameters of the PQCs. Notably, we show that for multivariate polynomials and multivariate smooth functions, the quantum circuit size and the number of trainable parameters of our proposed PQCs can be smaller than the deep ReLU neural networks. We further demonstrate the approximation capability of PQCs via numerical experiments. Our results pave the way for designing practical PQCs that can be implemented on near-term quantum devices with limited resources.

Internet of Medical Things (IoMT) technology has significantly helped surgeons perform complex clinical procedures, including interventional and endoscopic surgeries. However, surgeons face challenges in quickly becoming proficient with some IoMT devices. This difficulty stems from the fact that IoMT devices are not commonly used or familiar in their daily work and lives. To address this issue, we propose a novel interactive framework for IoMT, named freehand interaction, which includes visual control and haptic feedback. Our idea is to allow surgeons to operate surgical instruments, such as needles, capsules, and catheters with their bare hands and regular experience. At the same time, identical instruments in the surgical environment mirror the surgeon’s actions through visual control. The interactive forces encountered in the surgical environment are quantitatively communicated to the surgeon through the hand-held instruments. Our IoMT framework achieves both visual control and haptic feedback using electromagnetic mechanisms, ensuring mid-air freehand manipulation and contactless remote actuation. We perform different tasks in suspended, liquid, and in-vitro environments. The hand-held and mirroring instruments show high similarity and correlation, even within different electromagnetic systems and confined workspaces. Tracking accuracy, response time, and haptic forces quantified by a mechanical gauge are satisfactory. Our algorithm processes raw video streams and maintains efficiency even in scenarios with partial hand occlusion and various types of image noise. In summary, this work contributes to improving visual intuition and haptic immersion in IoMT applications.

The membership matrix is a key element in fuzzy clustering, enabling novel data representation in multiple clusters. The row vectors of the membership matrix represent each sample's degree of membership to different clusters. Notably, researchers have confirmed the presence of the local affinity among these row vectors, effectively preserving the local structure of the original data distribution. However, in this work, we consider that most sample points have insignificant fuzziness, with fuzziness found primarily in a few clusters, resulting in most membership vectors being sparse. To tackle this issue, we present the sparse, membership-affinity fuzzy clustering model, which leverages the sparsity of the row vectors and its affinity to establish a more appropriate representation, along with an optimization algorithm. Our experimental results on both simulated and real datasets demonstrate that the combination of sparsity and affinity can significantly enhance fuzzy clustering performance over other models.

Based on the offset Rademacher complexity, this work outlines a systematical framework for deriving sharp excess risk bounds in statistical learning without Bernstein condition. In addition to recovering fast rates in a unified way for some parametric and nonparametric supervised learning models with minimum identifiability assumptions, we also obtain new and improved results for LAD (sparse) linear regression and deep logistic regression with deep ReLU neural networks, respectively.