Toward Efficient Kernel-Based Solvers for Nonlinear PDEs

This paper introduces a novel kernel learning framework toward efficiently solving nonlinear partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that embeds differential operators within kernels, posing challenges with a large number of collocation points, our approach eliminates these operators from the kernel. We model the solution using a standard kernel interpolation form and differentiate the interpolant to compute the derivatives. Our framework obviates the need for complex Gram matrix construction between solutions and their derivatives, allowing for a straightforward implementation and scalable computation. As an instance, we allocate the collocation points on a grid and adopt a product kernel, which yields a Kronecker product structure in the interpolation. This structure enables us to avoid computing the full Gram matrix, reducing costs and scaling efficiently to a large number of collocation points. We provide a proof of the convergence and rate analysis of our method under appropriate regularity assumptions. In numerical experiments, we demonstrate the advantages of our method in solving several benchmark PDEs.

Integrating Hierarchical Semantic into Iterative Generation Model for Entailment Tree Explanation

Manifestly and logically displaying the line of reasoning from evidence to answer is significant to explainable question answering (QA). The entailment tree exhibits the lines structurally, which is different from the self-explanation principle in large-scale language models. Existing methods rarely consider the semantic association of sentences between and within hierarchies within the tree structure, which is prone to apparent mistakes in combinations. In this work, we propose an architecture of integrating the Hierarchical Semantics of sentences under the framework of Controller-Generator (HiSCG) to explain answers. The HiSCG designs a hierarchical mapping between hypotheses and facts, discriminates the facts involved in tree constructions, and optimizes single-step entailments. To the best of our knowledge, We are the first to notice hierarchical semantics of sentences between the same layer and adjacent layers to yield improvements. The proposed method achieves comparable performance on all three settings of the EntailmentBank dataset. The generalization results on two out-of-domain datasets also demonstrate the effectiveness of our method.

Sensing-aided Near-Field Secure Communications with Mobile Eavesdroppers

The additional degree of freedom (DoF) in the distance domain of near-field communication offers new opportunities for physical layer security (PLS) design. However, existing works mainly consider static eavesdroppers, and the related study with mobile eavesdroppers is still in its infancy due to the difficulty in obtaining the channel state information (CSI) of the eavesdropper. To this end, we propose to leverage the sensing capability of integrated sensing and communication (ISAC) systems to assist PLS design. To comprehensively study the dynamic behaviors of the system, we propose a Pareto optimization framework, where a multi-objective optimization problem (MOOP) is formulated to simultaneously optimize three key performance metrics: power consumption, number of securely served users, and tracking performance, while guaranteeing the achievable rate of the users with a given leakage rate constraint. A globally optimal design based on the generalized Benders decomposition (GBD) method is proposed to achieve the Pareto optimal solutions. To reduce the computational complexity, we further design a low-complexity algorithm based on zero-forcing (ZF) beamforming and successive convex approximation (SCA). Simulation results validate the effectiveness of the proposed algorithms and reveal the intrinsic trade-offs between the three performance metrics. It is observed that near-field communication offers a favorable beam diffraction effect for PLS, where the energy of the information signal is nulled around the eavesdropper and focused on the users.

Gap Completion in Point Cloud Scene occluded by Vehicles using SGC-Net

Recent advances in mobile mapping systems have greatly enhanced the efficiency and convenience of acquiring urban 3D data. These systems utilize LiDAR sensors mounted on vehicles to capture vast cityscapes. However, a significant challenge arises due to occlusions caused by roadside parked vehicles, leading to the loss of scene information, particularly on the roads, sidewalks, curbs, and the lower sections of buildings. In this study, we present a novel approach that leverages deep neural networks to learn a model capable of filling gaps in urban scenes that are obscured by vehicle occlusion. We have developed an innovative technique where we place virtual vehicle models along road boundaries in the gap-free scene and utilize a ray-casting algorithm to create a new scene with occluded gaps. This allows us to generate diverse and realistic urban point cloud scenes with and without vehicle occlusion, surpassing the limitations of real-world training data collection and annotation. Furthermore, we introduce the Scene Gap Completion Network (SGC-Net), an end-to-end model that can generate well-defined shape boundaries and smooth surfaces within occluded gaps. The experiment results reveal that 97.66% of the filled points fall within a range of 5 centimeters relative to the high-density ground truth point cloud scene. These findings underscore the efficacy of our proposed model in gap completion and reconstructing urban scenes affected by vehicle occlusions.

Statistical ranking with dynamic covariates

We consider a covariate-assisted ranking model grounded in the Plackett--Luce framework. Unlike existing works focusing on pure covariates or individual effects with fixed covariates, our approach integrates individual effects with dynamic covariates. This added flexibility enhances realistic ranking yet poses significant challenges for analyzing the associated estimation procedures. This paper makes an initial attempt to address these challenges. We begin by discussing the sufficient and necessary condition for the model's identifiability. We then introduce an efficient alternating maximization algorithm to compute the maximum likelihood estimator (MLE). Under suitable assumptions on the topology of comparison graphs and dynamic covariates, we establish a quantitative uniform consistency result for the MLE with convergence rates characterized by the asymptotic graph connectivity. The proposed graph topology assumption holds for several popular random graph models under optimal leading-order sparsity conditions. A comprehensive numerical study is conducted to corroborate our theoretical findings and demonstrate the application of the proposed model to real-world datasets, including horse racing and tennis competitions.

Sensing-assisted Robust SWIPT for Mobile Energy Harvesting Receivers

Simultaneous wireless information and power transfer (SWIPT) has been proposed to offer communication services and transfer power to the energy harvesting receiver (EHR) concurrently. However, existing works mainly focused on static EHRs, without considering the location uncertainty caused by the movement of EHRs and location estimation errors. To tackle this issue, this paper considers the sensing-assisted SWIPT design in a networked integrated sensing and communication (ISAC) system in the presence of location uncertainty. A two-phase robust design is proposed to reduce the location uncertainty and improve the power transfer efficiency. In particular, each time frame is divided into two phases, i.e., sensing and WPT phases, via time-splitting. The sensing phase performs collaborative sensing to localize the EHR, whose results are then utilized in the WPT phase for efficient WPT. To minimize the power consumption with given communication and power transfer requirements, a two-layer optimization framework is proposed to jointly optimize the time-splitting ratio, coordinated beamforming policy, and sensing node selection. Simulation results validate the effectiveness of the proposed design and demonstrate the existence of an optimal time-splitting ratio for given location uncertainty.

Interference Mitigation for Network-Level ISAC: An Optimization Perspective

Future wireless networks are envisioned to simultaneously provide high data-rate communication and ubiquitous environment-aware services for numerous users. One promising approach to meet this demand is to employ network-level integrated sensing and communications (ISAC) by jointly designing the signal processing and resource allocation over the entire network. However, to unleash the full potential of network-level ISAC, some critical challenges must be tackled. Among them, interference management is one of the most significant ones. In this article, we build up a bridge between interference mitigation techniques and the corresponding optimization methods, which facilitates efficient interference mitigation in network-level ISAC systems. In particular, we first identify several types of interference in network-level ISAC systems, including self-interference, mutual interference, crosstalk, clutter, and multiuser interference. Then, we present several promising techniques that can be utilized to suppress specific types of interference. For each type of interference, we discuss the corresponding problem formulation and identify the associated optimization methods. Moreover, to illustrate the effectiveness of the proposed interference mitigation techniques, two concrete network-level ISAC systems, namely coordinated cellular network-based and distributed antenna-based ISAC systems, are investigated from interference management perspective. Experiment results indicate that it is beneficial to collaboratively employ different interference mitigation techniques and leverage the network structure to achieve the full potential of network-level ISAC. Finally, we highlight several promising future research directions for the design of ISAC systems.

Controllable Diverse Sampling for Diffusion Based Motion Behavior Forecasting

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

Statistical inference for pairwise comparison models

Pairwise comparison models are used for quantitatively evaluating utility and ranking in various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the number of subjects diverges, which is currently lacking in the literature except in a few special instances. This paper addresses this gap by establishing an asymptotic normality result for the maximum likelihood estimator in a broad class of pairwise comparison models. The key idea lies in identifying the Fisher information matrix as a weighted graph Laplacian matrix which can be studied via a meticulous spectral analysis. Our findings provide the first unified theory for performing statistical inference in a wide range of pairwise comparison models beyond the Bradley--Terry model, benefiting practitioners with a solid theoretical guarantee for their use. Simulations utilizing synthetic data are conducted to validate the asymptotic normality result, followed by a hypothesis test using a tennis competition dataset.

Efficient Toxic Content Detection by Bootstrapping and Distilling Large Language Models

Toxic content detection is crucial for online services to remove inappropriate content that violates community standards. To automate the detection process, prior works have proposed varieties of machine learning (ML) approaches to train Language Models (LMs) for toxic content detection. However, both their accuracy and transferability across datasets are limited. Recently, Large Language Models (LLMs) have shown promise in toxic content detection due to their superior zero-shot and few-shot in-context learning ability as well as broad transferability on ML tasks. However, efficiently designing prompts for LLMs remains challenging. Moreover, the high run-time cost of LLMs may hinder their deployments in production. To address these challenges, in this work, we propose BD-LLM, a novel and efficient approach to Bootstrapping and Distilling LLMs for toxic content detection. Specifically, we design a novel prompting method named Decision-Tree-of-Thought (DToT) to bootstrap LLMs' detection performance and extract high-quality rationales. DToT can automatically select more fine-grained context to re-prompt LLMs when their responses lack confidence. Additionally, we use the rationales extracted via DToT to fine-tune student LMs. Our experimental results on various datasets demonstrate that DToT can improve the accuracy of LLMs by up to 4.6%. Furthermore, student LMs fine-tuned with rationales extracted via DToT outperform baselines on all datasets with up to 16.9\% accuracy improvement, while being more than 60x smaller than conventional LLMs. Finally, we observe that student LMs fine-tuned with rationales exhibit better cross-dataset transferability.