Viewpoint planning is crucial for 3D data collection and autonomous navigation, yet existing methods often miss key optimization objectives for static LiDAR, resulting in suboptimal network designs. The Viewpoint Planning Problem (VPP), which builds upon the Art Gallery Problem (AGP), requires not only full coverage but also robust registrability and connectivity under limited sensor views. We introduce a greedy optimization algorithm that tackles these VPP and AGP challenges through a novel Visibility Field (VF) approach. The VF captures visibility characteristics unique to static LiDAR, enabling a reduction from 2D to 1D by focusing on medial axis and joints. This leads to a minimal, fully connected viewpoint network with comprehensive coverage and minimal redundancy. Experiments across diverse environments show that our method achieves high efficiency and scalability, matching or surpassing expert designs. Compared to state-of-the-art methods, our approach achieves comparable viewpoint counts (VC) while reducing Weighted Average Path Length (WAPL) by approximately 95\%, indicating a much more compact and connected network. Dataset and source code will be released upon acceptance.

We consider nonconvex optimization problem over simplex, and more generally, a product of simplices. We provide an algorithm, Langevin Multiplicative Weights Update (LMWU) for solving global optimization problems by adding a noise scaling with the non-Euclidean geometry in the simplex. Non-convex optimization has been extensively studied by machine learning community due to its application in various scenarios such as neural network approximation and finding Nash equilibrium. Despite recent progresses on provable guarantee of escaping and avoiding saddle point (convergence to local minima) and global convergence of Langevin gradient based method without constraints, the global optimization with constraints is less studied. We show that LMWU algorithm is provably convergent to interior global minima with a non-asymptotic convergence analysis. We verify the efficiency of the proposed algorithm in real data set from polynomial portfolio management, where optimization of a highly non-linear objective function plays a crucial role.

Internet of Vehicles (IoV), as the core of intelligent transportation system, enables comprehensive interconnection between vehicles and their surroundings through multiple communication modes, which is significant for autonomous driving and intelligent traffic management. However, with the emergence of new applications, traditional communication technologies face the problems of scarce spectrum resources and high latency. Semantic communication, which focuses on extracting, transmitting, and recovering some useful semantic information from messages, can reduce redundant data transmission, improve spectrum utilization, and provide innovative solutions to communication challenges in the IoV. This paper systematically reviews state of art of semantic communications in the IoV, elaborates the technical background of IoV and semantic communications, and deeply discusses key technologies of semantic communications in IoV, including semantic information extraction, semantic communication architecture, resource allocation and management, and so on. Through specific case studies, it demonstrates that semantic communications can be effectively employed in the scenarios of traffic environment perception and understanding, intelligent driving decision support, IoV service optimization, and intelligent traffic management. Additionally, it analyzes the current challenges and future research directions. This survey reveals that semantic communications has broad application prospects in IoV, but it is necessary to solve the real existing problems by combining advanced technologies to promote its wide application in IoV and contributing to the development of intelligent transportation system.

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches.

Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential equation (PDE) to regularize the expected behavior of the loss over time. This class of parabolic PDEs has a number of favorable properties that allow us to analyze the error incurred through forgetting and the error induced through generalization. Specifically, we do this through imposing boundary conditions where the boundary is given by a memory buffer. By using the memory buffer as a boundary, we can enforce long term dependencies by bounding the expected error by the boundary loss. Finally, we illustrate the empirical performance of the method on a series of continual learning tasks.

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified exact low-dimensional embeddings, the limits of the required embedding dimensions remain unclear. We presently prove that lower dimensional embeddings are possible when using Euclidean metric embeddings as opposed to vector-based Logistic PCA (LPCA) embeddings. In particular, we provide an efficient logarithmic search procedure for identifying the exact embedding dimension and demonstrate how metric embeddings enable inference of the exact embedding dimensions of large-scale networks by exploiting that the metric properties can be used to provide linearithmic scaling. Empirically, we show that our approach extracts substantially lower dimensional representations of networks than previously reported for small-sized networks. For the first time, we demonstrate that even large-scale networks can be effectively embedded in very low-dimensional spaces, and provide examples of scalable, exact reconstruction for graphs with up to a million nodes. Our approach highlights that the intrinsic dimensionality of networks is substantially lower than previously reported and provides a computationally efficient assessment of the exact embedding dimension also of large-scale networks. The surprisingly low dimensional representations achieved demonstrate that networks in general can be losslessly represented using very low dimensional feature spaces, which can be used to guide existing network analysis tasks from community detection and node classification to structure revealing exact network visualizations.

Stochastic gradient descent (SGD) optimization methods are the method of choice to train deep artificial neural networks (ANNs) in data-driven learning problems (see, for instance, [1, 7, 33, 36, 38, 41] and the references therein) as well as scientific computing problems (see, for example, [3, 13, 19, 22, 26, 40] and the references therein). However, often not the plain vanilla standard SGD optimization method is the employed optimizer but instead more sophisticated accelerated and adaptive variants of the standard SGD method such as the adaptive moment estimation SGD (Adam) optimizer (see [32]) are used in practically relevant deep ANN training problems. We also refer, for instance, to [2, 20, 23, 29, 35, 39] for monographs and surveys treating SGD optimization methods for the training of ANNs. The considered SGD optimization method is used with the aim to minimize the true risk function (the objective function) of the considered ANN learning problem so that, roughly speaking, the realization function of the deep ANN minimizing the true risk function approximates as best as possible the output data given the input data. Despite the omnipresent use of SGD optimization methods in the training of ANNs, it remains, in basically all practically relevant scenarios, a fundamental open problem to provide a rigorous theoretical description and explanation for the convergence (and non-convergence) properties of SGD optimization methods in deep learning. In particular, it remains an open question to prove or disprove convergence of the true risk of SGD optimization methods to the optimal/infimal true risk value in the training of deep ANNs (cf., for example, [11, 18, 31, 34] and the literature review in Subsection 1.4 below). In this work we contribute to this open problem of research in two aspects.

--In this paper we introduce MLINE-VINS, a novel monocular visual-inertial odometry (VIO) system that leverages line features and Manhattan Word assumption. Specifically, for line matching process, we propose a novel geometric line optical flow algorithm that efficiently tracks line features with varying lengths, whitch is do not require detections and descriptors in every frame. T o address the instability of Manhattan estimation from line features, we propose a tracking-by-detection module that consistently tracks and optimizes Manhattan framse in consecutive images. By aligning the Manhattan World with the VIO world frame, the tracking could restart using the latest pose from back-end, simplifying the coordinate transformations within the system. Furthermore, we implement a mechanism to validate Manhattan frames and a novel global structural constraints back-end optimization. Extensive experiments results on vairous datasets, including benchmark and self-collected datasets, show that the proposed approach outperforms existing methods in terms of accuracy and long-range robustness. CCURACY of pose estimation is a critical factor in various fields, such as autonomous driving, augmented reality, and robotics. Simultaneous localization and mapping (SLAM) has proven to be an effective approach to address this challenge [1], [2]. Among SLAM techniques, visual-inertial odometry (VIO) is particularly popular due to its cost-effectiveness, accuracy, and robustness. In VIO, point feature is widely used for camera pose estimation due to its simplicity and efficiency. Representative point-based VIO systems include MSCKF-VIO [3], OK-VINS [4] and VINS-MONO [5], with VINS-MONO being one of the most widely adopted algorithm. However, the performance of point-based VIO is affected by the number and spatial distribution of points and it significantly hindered in textureless environments, where the lack of texture leads to point loss. To address these limitations, line features are increasingly considered as a valuable complement to point features improving the robustness of VIO systems. Line features arecommonly found in low-texture environments, particularly in man-made environments [6].

Exploring chemical space to find novel molecules that simultaneously satisfy multiple properties is crucial in drug discovery. However, existing methods often struggle with trading off multiple properties due to the conflicting or correlated nature of chemical properties. To tackle this issue, we introduce InversionGNN framework, an effective yet sample-efficient dual-path graph neural network (GNN) for multi-objective drug discovery. In the direct prediction path of InversionGNN, we train the model for multi-property prediction to acquire knowledge of the optimal combination of functional groups. Then the learned chemical knowledge helps the inversion generation path to generate molecules with required properties. In order to decode the complex knowledge of multiple properties in the inversion path, we propose a gradient-based Pareto search method to balance conflicting properties and generate Pareto optimal molecules. Additionally, InversionGNN is able to search the full Pareto front approximately in discrete chemical space. Comprehensive experimental evaluations show that InversionGNN is both effective and sample-efficient in various discrete multi-objective settings including drug discovery.

-- Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal specifications. Due to scaling issues with respect to the complexity of the specifications and the potential occurrence of non-differentiable terms, classical optimization methods often solve STL-based problems inefficiently. Smoothing and approximation techniques can alleviate these issues but require changing the optimization problem. This paper proposes a novel sampling-based method based on model predictive path integral control to solve optimal control problems with STL cost functions. We demonstrate the effectiveness of our method on benchmark motion planning problems and compare its performance with state-of-the-art methods. The results show that our method efficiently solves optimal control problems with STL costs.