The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this equation numerically is challenging due to the need to discretize complicated integral operators which increase the computational costs. These complexities are exacerbated by nonlinear source terms, nonsmooth data and irregular domains. In this study, we propose a second order Exponential Time Differencing Finite Element Method (ETD-RDP-FEM) to efficiently solve nonlinear FDE, posed in irregular domains. This approach discretizes matrix exponentials using a rational function with real and distinct poles, resulting in an L-stable scheme that damps spurious oscillations caused by non-smooth initial data. The method is shown to outperform existing second-order methods for FDEs with a higher accuracy and faster computational time.
3D panoptic segmentation is a challenging perception task, which aims to predict both semantic and instance annotations for 3D points in a scene. Although prior 3D panoptic segmentation approaches have achieved great performance on closed-set benchmarks, generalizing to novel categories remains an open problem. For unseen object categories, 2D open-vocabulary segmentation has achieved promising results that solely rely on frozen CLIP backbones and ensembling multiple classification outputs. However, we find that simply extending these 2D models to 3D does not achieve good performance due to poor per-mask classification quality on novel categories. In this paper, we propose the first method to tackle 3D open-vocabulary panoptic segmentation. Our model takes advantage of the fusion between learnable LiDAR features and dense frozen vision CLIP features, using a single classification head to make predictions for both base and novel classes. To further improve the classification performance on novel classes and leverage the CLIP model, we propose two novel loss functions: object-level distillation loss and voxel-level distillation loss. Our experiments on the nuScenes and SemanticKITTI datasets show that our method outperforms strong baselines by a large margin.
Sample efficiency is crucial in optimization, particularly in black-box scenarios characterized by expensive evaluations and zeroth-order feedback. When computing resources are plentiful, Bayesian optimization is often favored over evolution strategies. In this paper, we introduce a full invariance oriented evolution strategies algorithm, derived from its corresponding framework, that effectively rivals the leading Bayesian optimization method in tasks with dimensions at the upper limit of Bayesian capability. Specifically, we first build the framework InvIGO that fully incorporates historical information while retaining the full invariant and computational complexity. We then exemplify InvIGO on multi-dimensional Gaussian, which gives an invariant and scalable optimizer SynCMA . The theoretical behavior and advantages of our algorithm over other Gaussian-based evolution strategies are further analyzed. Finally, We benchmark SynCMA against leading algorithms in Bayesian optimization and evolution strategies on various high dimension tasks, in cluding Mujoco locomotion tasks, rover planning task and synthetic functions. In all scenarios, SynCMA demonstrates great competence, if not dominance, over other algorithms in sample efficiency, showing the underdeveloped potential of property oriented evolution strategies.
Evolutionary Multitasking (EMT) paradigm, an emerging research topic in evolutionary computation, has been successfully applied in solving high-dimensional feature selection (FS) problems recently. However, existing EMT-based FS methods suffer from several limitations, such as a single mode of multitask generation, conducting the same generic evolutionary search for all tasks, relying on implicit transfer mechanisms through sole solution encodings, and employing single-objective transformation, which result in inadequate knowledge acquisition, exploitation, and transfer. To this end, this paper develops a novel EMT framework for multiobjective high-dimensional feature selection problems, namely MO-FSEMT. In particular, multiple auxiliary tasks are constructed by distinct formulation methods to provide diverse search spaces and information representations and then simultaneously addressed with the original task through a multi-slover-based multitask optimization scheme. Each task has an independent population with task-specific representations and is solved using separate evolutionary solvers with different biases and search preferences. A task-specific knowledge transfer mechanism is designed to leverage the advantage information of each task, enabling the discovery and effective transmission of high-quality solutions during the search process. Comprehensive experimental results demonstrate that our MO-FSEMT framework can achieve overall superior performance compared to the state-of-the-art FS methods on 26 datasets. Moreover, the ablation studies verify the contributions of different components of the proposed MO-FSEMT.
In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient search process would benefit from increased opportunities to explore promising regions where global optima or good local optima are situated. In this paper, we introduce a novel robust evolutionary algorithm named the dual-stage robust evolutionary algorithm (DREA) aimed at discovering robust solutions. DREA operates in two stages: the peak-detection stage and the robust solution-searching stage. The primary objective of the peak-detection stage is to identify peaks in the fitness landscape of the original optimization problem. Conversely, the robust solution-searching stage focuses on swiftly identifying the robust optimal solution using information obtained from the peaks discovered in the initial stage. These two stages collectively enable the proposed DREA to efficiently obtain the robust optimal solution for the optimization problem. This approach achieves a balance between solution optimality and robustness by separating the search processes for optimal and robust optimal solutions. Experimental results demonstrate that DREA significantly outperforms five state-of-the-art algorithms across 18 test problems characterized by diverse complexities. Moreover, when evaluated on higher-dimensional robust optimization problems (100-$D$ and 200-$D$), DREA also demonstrates superior performance compared to all five counterpart algorithms.
We propose a novel data-driven semi-confirmatory factor analysis (SCFA) model that addresses the absence of model specification and handles the estimation and inference tasks with high-dimensional data. Confirmatory factor analysis (CFA) is a prevalent and pivotal technique for statistically validating the covariance structure of latent common factors derived from multiple observed variables. In contrast to other factor analysis methods, CFA offers a flexible covariance modeling approach for common factors, enhancing the interpretability of relationships between the common factors, as well as between common factors and observations. However, the application of classic CFA models faces dual barriers: the lack of a prerequisite specification of "non-zero loadings" or factor membership (i.e., categorizing the observations into distinct common factors), and the formidable computational burden in high-dimensional scenarios where the number of observed variables surpasses the sample size. To bridge these two gaps, we propose the SCFA model by integrating the underlying high-dimensional covariance structure of observed variables into the CFA model. Additionally, we offer computationally efficient solutions (i.e., closed-form uniformly minimum variance unbiased estimators) and ensure accurate statistical inference through closed-form exact variance estimators for all model parameters and factor scores. Through an extensive simulation analysis benchmarking against standard computational packages, SCFA exhibits superior performance in estimating model parameters and recovering factor scores, while substantially reducing the computational load, across both low- and high-dimensional scenarios. It exhibits moderate robustness to model misspecification. We illustrate the practical application of the SCFA model by conducting factor analysis on a high-dimensional gene expression dataset.
In contrast to conventional reconfigurable intelligent surface (RIS), simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) has been proposed recently to enlarge the serving area from 180o to 360o coverage. This work considers the performance of a STAR-RIS aided full-duplex (FD) non-orthogonal multiple access (NOMA) communication systems. The STAR-RIS is implemented at the cell-edge to assist the cell-edge users, while the cell-center users can communicate directly with a FD base station (BS). We first introduce new user clustering schemes for the downlink and uplink transmissions. Then, based on the proposed transmission schemes closed-form expressions of the ergodic rates in the downlink and uplink modes are derived taking into account the system impairments caused by the self interference at the FD-BS and the imperfect successive interference cancellation (SIC). Moreover, an optimization problem to maximize the total sum-rate is formulated and solved by optimizing the amplitudes and the phase-shifts of the STAR-RIS elements and allocating the transmit power efficiently. The performance of the proposed user clustering schemes and the optimal STAR-RIS design are investigated through numerical results
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.