Point cloud bundle adjustment is critical in large-scale point cloud mapping. However, it is both computationally and memory intensive, with its complexity growing cubically as the number of scan poses increases. This paper presents BALM3.0, an efficient and distributed large-scale point cloud bundle adjustment method. The proposed method employs the majorization-minimization algorithm to decouple the scan poses in the bundle adjustment process, thus performing the point cloud bundle adjustment on large-scale data with improved computational efficiency. The key difficulty of applying majorization-minimization on bundle adjustment is to identify the proper surrogate cost function. In this paper, the proposed surrogate cost function is based on the point-to-plane distance. The primary advantages of decoupling the scan poses via a majorization-minimization algorithm stem from two key aspects. First, the decoupling of scan poses reduces the optimization time complexity from cubic to linear, significantly enhancing the computational efficiency of the bundle adjustment process in large-scale environments. Second, it lays the theoretical foundation for distributed bundle adjustment. By distributing both data and computation across multiple devices, this approach helps overcome the limitations posed by large memory and computational requirements, which may be difficult for a single device to handle. The proposed method is extensively evaluated in both simulated and real-world environments. The results demonstrate that the proposed method achieves the same optimal residual with comparable accuracy while offering up to 704 times faster optimization speed and reducing memory usage to 1/8. Furthermore, this paper also presented and implemented a distributed bundle adjustment framework and successfully optimized large-scale data (21,436 poses with 70 GB point clouds) with four consumer-level laptops.

Linear $L_1$-regularized models have remained one of the simplest and most effective tools in data science. Over the past decade, screening rules have risen in popularity as a way to eliminate features when producing the sparse regression weights of $L_1$ models. However, despite the increasing need of privacy-preserving models for data analysis, to the best of our knowledge, no differentially private screening rule exists. In this paper, we develop the first private screening rule for linear regression. We initially find that this screening rule is too strong: it screens too many coefficients as a result of the private screening step. However, a weakened implementation of private screening reduces overscreening and improves performance.

We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in neural network hidden representations. The represented PDEs are then solved and decoded for specific tasks. The learned PDE representations naturally express the spatiotemporal dynamics in data in neural network hidden space, enabling increased power for dynamical modeling. Solving the PDE representations in a compute and memory-efficient way, however, is a significant challenge. We develop a native, GPU-capable, parallel, sparse, and differentiable multigrid solver specialized for linear partial differential equations that acts as a module in Mechanistic PDE Networks. Leveraging the PDE solver, we propose a discovery architecture that can discover nonlinear PDEs in complex settings while also being robust to noise. We validate PDE discovery on a number of PDEs, including reaction-diffusion and Navier-Stokes equations.

Multi-preference optimization enriches language-model alignment beyond pairwise preferences by contrasting entire sets of helpful and undesired responses, thereby enabling richer training signals for large language models. During self-play alignment, these models often produce numerous candidate answers per query, rendering it computationally infeasible to include all responses in the training objective. In this work, we propose $\textit{Active Multi-Preference Optimization}$ (AMPO), a novel approach that combines on-policy generation, a multi-preference group-contrastive loss, and active subset selection. Specifically, we score and embed large candidate pools of responses and then select a small, yet informative, subset that covers reward extremes and distinct semantic clusters for preference optimization. Our contrastive training scheme is capable of identifying not only the best and worst answers but also subtle, underexplored modes that are crucial for robust alignment. Theoretically, we provide guarantees for expected reward maximization using our active selection method, and empirically, AMPO achieves state-of-the-art results on $\textit{AlpacaEval}$ using Llama 8B.

Approximate second-order optimization methods often exhibit poorer generalization compared to first-order approaches. In this work, we look into this issue through the lens of the loss landscape and find that existing second-order methods tend to converge to sharper minima compared to SGD. In response, we propose Sassha, a novel second-order method designed to enhance generalization by explicitly reducing sharpness of the solution, while stabilizing the computation of approximate Hessians along the optimization trajectory. In fact, this sharpness minimization scheme is crafted also to accommodate lazy Hessian updates, so as to secure efficiency besides flatness. To validate its effectiveness, we conduct a wide range of standard deep learning experiments where Sassha demonstrates its outstanding generalization performance that is comparable to, and mostly better than, other methods. We provide a comprehensive set of analyses including convergence, robustness, stability, efficiency, and cost.

Groundwater is eventually undermined by human exercises, such as fast industrialization, urbanization, over-extraction, and contamination from agrarian and urban sources. From among the different contaminants, the presence of heavy metals like cadmium (Cd), chromium (Cr), arsenic (As), and lead (Pb) proves to have serious dangers when present in huge concentrations in groundwater. Long-term usage of these poisonous components may lead to neurological disorders, kidney failure and different sorts of cancer. To address these issues, this study developed a machine learning-based predictive model to evaluate the Groundwater Quality Index (GWQI) and identify the main contaminants which are affecting the water quality. It has been achieved with the help of a hybrid machine learning model i.e. LCBoost Fusion . The model has undergone several processes like data preprocessing, hyperparameter tuning using Differential Evolution (DE) optimization, and evaluation through cross-validation. The LCBoost Fusion model outperforms individual models (CatBoost and LightGBM), by achieving low RMSE (0.6829), MSE (0.5102), MAE (0.3147) and a high R$^2$ score of 0.9809. Feature importance analysis highlights Potassium (K), Fluoride (F) and Total Hardness (TH) as the most influential indicators of groundwater contamination. This research successfully demonstrates the application of machine learning in assessing groundwater quality risks in Odisha. The proposed LCBoost Fusion model offers a reliable and efficient approach for real-time groundwater monitoring and risk mitigation. These findings will help the environmental organizations and the policy makers to map out targeted places for sustainable groundwater management. Future work will focus on using remote sensing data and developing an interactive decision-making system for groundwater quality assessment.

Among them, Nesterov's accelerated gradient method [7,8] has gained significant attention due to its provable acceleration on general convex functions beyond quadratics. A special focus has been on using dynamical system tools [12,10,3,14] and control-theoretical methods [5,9] for the analysis and design of such algorithms. In the standard textbook [8] by Nesterov, the convergence analysis of accelerated gradient methods is conducted using a technique known as estimating sequences. These are essentially auxiliary comparison functions used to prove the convergence rates of optimization algorithms. As pointed out in [14], estimating sequences are usually constructed inductively and can be difficult to understand and apply. This motivated the Lyapunov analysis in [14], which aims to unify the analysis of a broad class of accelerated algorithms. Despite this comprehensive work, to the best knowledge of the author, a simple and direct Lyapunov analysis of the original scheme of Nesterov's accelerated gradient method is still lacking.

The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between the reconstruction accuracy and the adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, effective for extracting low spectral density components from spectrograms of mixed signals, enhanced with sparsity constraints. We propose a new algorithm called SHINBO, which introduces a bi-level optimization framework to automatically and adaptively tune the row-dependent penalty hyperparameters, enhancing the ability of IS-NMF to isolate sparse, periodic signals against noise. Experimental results showed SHINBO ensures precise spectral decomposition and demonstrates superior performance in both synthetic and real-world applications. For the latter, SHINBO is particularly useful, as noninvasive vibration-based fault detection in rolling bearings, where the desired signal components often reside in high-frequency subbands but are obscured by stronger, spectrally broader noise. By addressing the critical issue of hyperparameter selection, SHINBO advances the state-of-the-art in signal recovery for complex, noise-dominated environments.

It is a significant requirement for a quadrotor trajectory planner to simultaneously guarantee trajectory quality and system lightweight. Many researchers focus on this problem, but there's still a gap between their performance and our common wish. In this paper, we propose an ultra lightweight quadrotor planner with time-optimal primitives. Firstly, a novel motion primitive library is proposed to generate time-optimal and dynamical feasible trajectories offline. Secondly, we propose a fast collision checking method with a deterministic time consumption, independent of the sampling resolution of the primitives. Finally, we select the minimum cost trajectory to execute among the safe primitives based on user-defined requirements. The propsed transformation relation between the local trajectories ensures the smoothness of the global trajectory. The planner reduces unnecessary online computing power consumption as much as possible, while ensuring a high-quality trajectory. Benchmark comparisons show that our method can generate the shortest flight time and distance of trajectory with the lowest computation overload. Challenging real-world experiments validate the robustness of our method.

Achieving large-scale aerial swarms is challenging due to the inherent contradictions in balancing computational efficiency and scalability. This paper introduces Primitive-Swarm, an ultra-lightweight and scalable planner designed specifically for large-scale autonomous aerial swarms. The proposed approach adopts a decentralized and asynchronous replanning strategy. Within it is a novel motion primitive library consisting of time-optimal and dynamically feasible trajectories. They are generated utlizing a novel time-optimial path parameterization algorithm based on reachability analysis (TOPP-RA). Then, a rapid collision checking mechanism is developed by associating the motion primitives with the discrete surrounding space according to conflicts. By considering both spatial and temporal conflicts, the mechanism handles robot-obstacle and robot-robot collisions simultaneously. Then, during a replanning process, each robot selects the safe and minimum cost trajectory from the library based on user-defined requirements. Both the time-optimal motion primitive library and the occupancy information are computed offline, turning a time-consuming optimization problem into a linear-complexity selection problem. This enables the planner to comprehensively explore the non-convex, discontinuous 3-D safe space filled with numerous obstacles and robots, effectively identifying the best hidden path. Benchmark comparisons demonstrate that our method achieves the shortest flight time and traveled distance with a computation time of less than 1 ms in dense environments. Super large-scale swarm simulations, involving up to 1000 robots, running in real-time, verify the scalability of our method. Real-world experiments validate the feasibility and robustness of our approach. The code will be released to foster community collaboration.